coin/0000755000176200001440000000000014130001757011200 5ustar liggesuserscoin/NAMESPACE0000644000176200001440000001204013715224731012423 0ustar liggesusersuseDynLib(coin, .registration = TRUE) importFrom("survival", is.Surv) importFrom("methods", callGeneric, callNextMethod, getSlots, new, validObject) importMethodsFrom("methods", initialize, show) importFrom("parallel", clusterApply, clusterSetRNGStream, getDefaultCluster, makePSOCKcluster, mclapply, nextRNGStream, stopCluster) importFrom("stats", complete.cases, cov2cor, dchisq, dnorm, median, model.frame, model.matrix, na.pass, pbinom, pchisq, pnorm, qbeta, qchisq, qnorm, quantile, runif, setNames, uniroot) importMethodsFrom("stats4", confint) importFrom("utils", hasName) importFrom("libcoin", LinStatExpCov) # Not used, but needed to access C API importFrom("matrixStats", colCummaxs, colCummins, colMaxs, colMins) importFrom("modeltools", ModelEnvFormula) importMethodsFrom("modeltools", has, na.omit) importFrom("mvtnorm", pmvnorm, qmvnorm) importFrom("multcomp", contrMat) export(independence_test, symmetry_test, oneway_test, wilcox_test, kruskal_test, normal_test, median_test, savage_test, taha_test, klotz_test, mood_test, ansari_test, fligner_test, conover_test, surv_test, logrank_test, sign_test, wilcoxsign_test, friedman_test, quade_test, spearman_test, fisyat_test, quadrant_test, koziol_test, maxstat_test, chisq_test, cmh_test, lbl_test, mh_test, trafo, id_trafo, rank_trafo, normal_trafo, median_trafo, savage_trafo, consal_trafo, koziol_trafo, klotz_trafo, mood_trafo, ansari_trafo, fligner_trafo, logrank_trafo, logrank_weight, maxstat_trafo, fmaxstat_trafo, ofmaxstat_trafo, f_trafo, of_trafo, zheng_trafo, mcp_trafo, asymptotic, approximate, exact) exportClasses("CovarianceMatrix", "Variance", "VarCovar", "IndependenceProblem", "IndependenceTestProblem", "IndependenceLinearStatistic", "IndependenceTestStatistic", "MaxTypeIndependenceTestStatistic", "QuadTypeIndependenceTestStatistic", "ScalarIndependenceTestStatistic", "PValue", "NullDistribution", "AsymptNullDistribution", "ApproxNullDistribution", "ExactNullDistribution", "IndependenceTest", "MaxTypeIndependenceTest", "QuadTypeIndependenceTest", "ScalarIndependenceTest", "ScalarIndependenceTestConfint", "SymmetryProblem") exportMethods("initialize", "show", "pvalue", "midpvalue", "pvalue_interval", "size", "statistic", "dperm", "pperm", "qperm", "rperm", "support", "expectation", "covariance", "variance", "AsymptNullDistribution", "ApproxNullDistribution", "ExactNullDistribution", "confint") S3method(independence_test, formula) S3method(independence_test, table) S3method(independence_test, IndependenceProblem) S3method(symmetry_test, formula) S3method(symmetry_test, table) S3method(symmetry_test, SymmetryProblem) S3method(oneway_test, formula) S3method(oneway_test, IndependenceProblem) S3method(wilcox_test, formula) S3method(wilcox_test, IndependenceProblem) S3method(kruskal_test, formula) S3method(kruskal_test, IndependenceProblem) S3method(normal_test, formula) S3method(normal_test, IndependenceProblem) S3method(median_test, formula) S3method(median_test, IndependenceProblem) S3method(savage_test, formula) S3method(savage_test, IndependenceProblem) S3method(taha_test, formula) S3method(taha_test, IndependenceProblem) S3method(klotz_test, formula) S3method(klotz_test, IndependenceProblem) S3method(mood_test, formula) S3method(mood_test, IndependenceProblem) S3method(ansari_test, formula) S3method(ansari_test, IndependenceProblem) S3method(fligner_test, formula) S3method(fligner_test, IndependenceProblem) S3method(conover_test, formula) S3method(conover_test, IndependenceProblem) S3method(logrank_test, formula) S3method(logrank_test, IndependenceProblem) S3method(sign_test, formula) S3method(sign_test, SymmetryProblem) S3method(wilcoxsign_test, formula) S3method(wilcoxsign_test, SymmetryProblem) S3method(friedman_test, formula) S3method(friedman_test, SymmetryProblem) S3method(quade_test, formula) S3method(quade_test, SymmetryProblem) S3method(spearman_test, formula) S3method(spearman_test, IndependenceProblem) S3method(fisyat_test, formula) S3method(fisyat_test, IndependenceProblem) S3method(quadrant_test, formula) S3method(quadrant_test, IndependenceProblem) S3method(koziol_test, formula) S3method(koziol_test, IndependenceProblem) S3method(maxstat_test, formula) S3method(maxstat_test, table) S3method(maxstat_test, IndependenceProblem) S3method(chisq_test, formula) S3method(chisq_test, table) S3method(chisq_test, IndependenceProblem) S3method(cmh_test, formula) S3method(cmh_test, table) S3method(cmh_test, IndependenceProblem) S3method(lbl_test, formula) S3method(lbl_test, table) S3method(lbl_test, IndependenceProblem) S3method(mh_test, formula) S3method(mh_test, table) S3method(mh_test, SymmetryProblem) S3method(format, pvalue) S3method(print, htest2) S3method(print, ci) S3method(print, pvalue) S3method(print, cutpoint) coin/data/0000755000176200001440000000000012544760377012132 5ustar liggesuserscoin/data/asat.rda0000644000176200001440000000063612116365565013552 0ustar liggesusersO@ǯ<+فȕK0U'KM):;3BkwhG%W>w~ifBN}1..1H:XXC'$vf3gSAl[3l &GO [``q=SwϟZl $ߩA'!>E~^8xB9VPO'OOyu؇~*6Ⱦẕ|Oq>>}ÄݽCAagj8} :N69v8޶Ŏ=;M4>ݨJ p9#WVŶ['zD=wnhET@/#(TB*#UH5$tPtPtPtPtPtPtPtPtPtPt0aDYߑlocoin/data/hohnloser.rda0000644000176200001440000000077412116365565014626 0ustar liggesusersBZh91AY&SY¸gJPC/g@HM4S=z0'h=@dTU?ThFFCi@#&@0`(yOPz h4S ]2bԣ a@HE:yqpM,n ʗƲ("Tzv")ZW428NBO}T#9Zs g=2xLѢybR+!T^`M&TT,U Mcd,J8')f[tujנo`JQvv׭ZV|ifa*$ B)P`WbbE8X1 1!.$f ;=Gvgo?궕iJRXp$I+giyI$g`g`g`gd )D@9f!.*!4_|#\:MV/=lC)„coin/data/CWD.rda0000644000176200001440000000162212116365565013233 0ustar liggesusers r0b```b`gd`b2Y# 'fvw@&1=+%v-el϶qұ9&pAϷP=C^ Y%J:g]=ɨ{K6gj>x=PzLO$۳i׾kgzY&?&8Ǟx7KF̿ `1@ցVPڡB;Ciw(ҁ tP9]?J[ J҇Ǡ)(} J߅85k&$H,.%@Tb {qbnAN*k5C嚣r-`֕T q4r$$%Te8`)(=&coin/data/alpha.rda0000644000176200001440000000131112116365565013676 0ustar liggesusersBZh91AY&SYw큀a0D/0 `#[d-;A!#"7zFhzCLM2 E ?*4ڀ)0 4$)FTFPɠ@j4{TK+ }&[<(%j4Vc0"Cm۔ ?~֬Kٯ@@ [u %J*l,9Ά>8WOVƒBB`m!diAfFPWP H#qOWڍJmLc#BBif`8v2!f{NDR[iOy3#E ܲV$,A6mOX kZֵ@(߬S@<1cPMmmPQmmAԥ͌c2ƽϹQધ⩘2H`6 Gs?$a&elRD'%8|3+@: ]Ţ:qZYoJmO3SM `f3i'mnwNmRsb=qL~$# hA4< e`mi@6B̀$ x *gR4]i|  [95\M> -4ߛ!\E斢H ]coin/data/glioma.rda0000644000176200001440000000105412116365565014065 0ustar liggesuserso1ƽIJ@ *ibр8jKЫnCM6[|s3ZFe?ge?QCp3aY 6N&fYD,LP.fl5p&@ עmO}t >xv+m]r[.{|qkH  =7^%Ώ) Oq2w;x؍*V_̫'zNiة>L u^؂e.ۂyWt4zw@R}<0+p2k,KMBU~J){W JeS{ȻwNrѡCoE~kȻDE~CYvR~ͭ{_욙55:icjhrm2Lbƿiqjξ <˨Uozj~;n"萐$.>=C'NUdXuYXY Xb=${H!Cd={(PCbj':ӭT۳Z4_" 祜coin/data/jobsatisfaction.rda0000644000176200001440000000044112116365565015776 0ustar liggesuserseQj0\viHqB!44J钟]ɫQZ3=mS c0xO*晖uĴ˧p c11>܃򈇎ю19hpL?%nsvdO6AYK#j>|~J2zӁF/MY}%J:)r"n_u!〹?Թ8s-?ڵh3#D AUp0y!ٶҵ-up>4D:4 yj5\q_coin/data/vision.rda0000644000176200001440000000036012544760377014130 0ustar liggesusers r0b```b`f@& 23<@!BBi']BOeP:BCUC tZ ҙPu{\ǜ xA0ba::%ŲGs^JLIrS7VW4Ue?7*^UCHԔh5t-ʔ_%RtEBTRL6x 9boOdcoin/data/ocarcinoma.rda0000644000176200001440000000057112116365565014733 0ustar liggesusers=KPO>T';*۴u\v\ Mi8q7W7"E>ܜ{ޓtO{yDde@]7\"G4K Y&=p 6܁{ |`+:]}7a EE&܂\u'$GU<övVҖhdƼC LTdMggũx}LnR|ZtaW1.Lxp=KMjy6i7W,Eh&KbitXuGbbM@%I %J2d(P$CI %Z2dhВ%CԝOZ༾)LccT~t/S}B8coin/data/malformations.rda0000644000176200001440000000111012544760377015466 0ustar liggesusersQkP$h0wll҂vM#I˫i#8ZxrsΗ/5\Oo!$I1f1Q$*_uSmnCH_!HȢfI)COdxIOVbtWG:z/_ q*oanES,,ͼʢGg< 8~hXwɻO/NѰ[拮nb+~yUwz?[KׇU*{Lg=Ly_M|d Wxcoin/data/mercuryfish.rda0000644000176200001440000000111512116365565015153 0ustar liggesusersTMo@8iHC PiH*jv~CΠr*$uh$N~8`{獰b%gf{}ށTRrnSiɉ? c> "4z?+Uc\o6ʃm0ĬfmQ8(W;aa]6r[*]c]Ʒd}wu֠+uWkWx w---~u/?nZ!+u'OCAS>s~u;S ;ؿgʜз}yQw Z/ r~π-^J?&A{ا,wEo2ߜs5s~ˬfbvޭ~<-N濔s~dKݝur,#o߽$7Qx:{w"d;Гk k2mw&--dGȮ=I&dlCMCKFMMMMMMMMMMCCCCCCCCCgO[e7Z(>'e?S[$coin/data/alzheimer.rda0000644000176200001440000000161712116365565014602 0ustar liggesusersBZh91AY&SY>@%@/JJOzi444 M*gUSʩSFAUR%&mF0#d 4ަTAD RQdHEPo7PEPddE zL@$$$JE$ %ԹC?H ގy MD@ ՀW_~ՁuuUW_ 񺻺'ޯׯkZֵ5Ӏg͛, DGQ" H h;g7uUηw߿?@ mmy6ր$Zֵmmmt*>|u$JI%]I$IWRI$$UԒI*I$uI'^zosڮr˗)WRI$$UԒI*I$u$JI%]I$IW]v۷`8MԒI*I$u$JI%]I$IWRI$ $99-{quu$$LgI&3$ĒII$q$c8I1I$8N88m㎛9k8I1I$$7c[ﾀ1cֵh[m} c1 ccZֵ-mk@ c1c1kZִ-mm $I$y=UwWVY1񤤼>Oek==)&n&ewU7Rg16Y('(~K`ҁ]BCkPcoin/data/neuropathy.rda0000644000176200001440000000123512116365565015014 0ustar liggesusers[HQ-2błH33^ HHva]" z "+EDqʌHDCIPIj˟fw~2E[s2<sDt;,EJ \ ;_ph؃=VmR+ZЙhn޶"yх9 Ec;.QoVUE/5Ab+W`LZjppߚ9ݽmz.y #۩7xҾz(L3ZJ1d9 r1g#jc88討|:y;ǗW"2 #Z(`Lh~502P+(W"!MA?qcA-T6G~&5B5hη^8vv ACrk<+8HIBl\$apap!`H0$ C!`0d2  C!Ða0d CP`(0Jݲ_R'%"coin/data/photocar.rda0000644000176200001440000000137312116365565014440 0ustar liggesusersBZh91AY&SYE) Ri@@/߀@O"v9C'E=Si!zM4OQh4z?Ҧh4OPq&CL 14@IPM4hmL5h@ӧNYD*(YG%RM=%YRt-ܖȕE)gzɆ8>΀6 =&ܽ%h͗sFi$&͢I|-/ZKcurE8[J\@R)Z% Kɍ*բ]J8'x^Ֆ[iه7,mzLN&, '[,嵓7Ҫ q+.C] ѓ94n zC:Ckl9I%` cdz߲6+]ny$I$I$K333I$I$K333I$I$On\؃!=Db AEY^VR%Ue])  $0H0d %A`H$LRc!Q |UUXϟBf@-Rd ȈUU3 Ye(ATDPU@I* !""lޫF@;1,UHYT*Ut)%KU)%ZAH,-'&ǿx0(ܚ{f.| *`azp\8Ls 8LEoafb;.p Rcoin/data/rotarod.rda0000644000176200001440000000040312116365565014264 0ustar liggesusers͊0i]iA\\Bu_phBaI^I$FZ~ zRoW Yx x3OKFCZeQvr*?M;:]SP`0L+*)ab{e(S e;WM:<F]~x^ɸa=[2;Kr@<dTbhs_?w7e: J42Zj΅AJdL2}jr-kZֵk|Z7R$t?$O4>D CG'$x>_>JֱBE߄*ϺR*@Xу `$aFpc7H(+Oi#m0H^ ~]QֆMaV8C"S! $8 c, arr.ind = TRUE) sts[unique(idx[, 1]), unique(idx[, 2]), drop = FALSE] } \keyword{datasets} coin/man/hohnloser.Rd0000644000176200001440000000245413401471036014251 0ustar liggesusers\name{hohnloser} \docType{data} \alias{hohnloser} \title{Left Ventricular Ejection Fraction} \description{ Left ventricular ejection fraction in patients with malignant ventricular tachyarrhythmias including recurrence-free month and censoring. } \usage{hohnloser} \format{ A data frame with 94 observations on 3 variables. \describe{ \item{\code{EF}}{ ejection fraction (\%). } \item{\code{time}}{ recurrence-free month. } \item{\code{event}}{ status indicator for \code{time}: \code{0} for right-censored observations and \code{1} otherwise. } } } \details{ The data was used by Lausen and Schumacher (1992) to illustrate the use of maximally selected statistics. } \source{ Hohnloser, S. H., Raeder, E. A., Podrid, P. J., Graboys, T. B. and Lown, B. (1987). Predictors of antiarrhythmic drug efficacy in patients with malignant ventricular tachyarrhythmias. \emph{American Heart Journal} \bold{114}(1 Pt 1), 1--7. \doi{10.1016/0002-8703(87)90299-7} } \references{ Lausen, B. and Schumacher, M. (1992). Maximally selected rank statistics. \emph{Biometrics} \bold{48}(1), 73--85. \doi{10.2307/2532740} } \examples{ ## Asymptotic maximally selected logrank statistics maxstat_test(Surv(time, event) ~ EF, data = hohnloser) } \keyword{datasets} coin/man/SurvivalTests.Rd0000644000176200001440000004775214113674115015124 0ustar liggesusers\name{SurvivalTests} \alias{surv_test} \alias{logrank_test} \alias{logrank_test.formula} \alias{logrank_test.IndependenceProblem} \concept{Logrank test} \concept{Gehan-Breslow test} \concept{Tarone-Ware test} \concept{Peto-Peto test} \concept{Prentice test} \concept{Prentice-Marek test} \concept{Andersen-Borgan-Gill-Keiding test} \concept{Fleming-Harrington test} \concept{Gaugler-Kim-Liao test} \concept{Self test} \encoding{UTF-8} \title{Two- and \eqn{K}-Sample Tests for Censored Data} \description{ Testing the equality of the survival distributions in two or more independent groups. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{logrank_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{logrank_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "Hothorn-Lausen", "average-scores"), type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Peto-Peto", "Prentice", "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington", "Gaugler-Kim-Liao", "Self"), rho = NULL, gamma = NULL, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} is a survival object (see \code{\link[survival]{Surv}} in package \pkg{survival}), \code{x} is a factor and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from class \code{"\linkS4class{IndependenceProblem}"}. } \item{ties.method}{ a character, the method used to handle ties: the score generating function either uses mid-ranks (\code{"mid-ranks"}, default), the Hothorn-Lausen method (\code{"Hothorn-Lausen"}) or averages the scores of randomly broken ties (\code{"average-scores"}); see \sQuote{Details}. } \item{type}{ a character, the type of test: either \code{"logrank"} (default), \code{"Gehan-Breslow"}, \code{"Tarone-Ware"}, \code{"Peto-Peto"}, \code{"Prentice"}, \code{"Prentice-Marek"}, \code{"Andersen-Borgan-Gill-Keiding"}, \code{"Fleming-Harrington"}, \code{"Gaugler-Kim-Liao"} or \code{"Self"}; see \sQuote{Details}. } \item{rho}{ a numeric, the \eqn{\rho} constant when \code{type} is \code{"Tarone-Ware"}, \code{"Fleming-Harrington"}, \code{"Gaugler-Kim-Liao"} or \code{"Self"}; see \sQuote{Details}. Defaults to \code{NULL}, implying \code{0.5} for \code{type = "Tarone-Ware"} and \code{0} otherwise. } \item{gamma}{ a numeric, the \eqn{\gamma} constant when \code{type} is \code{"Fleming-Harrington"}, \code{"Gaugler-Kim-Liao"} or \code{"Self"}; see \sQuote{Details}. Defaults to \code{NULL}, implying \code{0}. } \item{\dots}{ further arguments to be passed to \code{\link{independence_test}}. } } \details{ \code{logrank_test} provides the weighted logrank test reformulated as a linear rank test. The family of weighted logrank tests encompasses a large collection of tests commonly used in the analysis of survival data including, but not limited to, the standard (unweighted) logrank test, the Gehan-Breslow test, the Tarone-Ware class of tests, the Peto-Peto test, the Prentice test, the Prentice-Marek test, the Andersen-Borgan-Gill-Keiding test, the Fleming-Harrington class of tests, the Gaugler-Kim-Liao class of tests and the Self class of tests. A general description of these methods is given by Klein and Moeschberger (2003, Ch. 7). See \enc{Letón}{Leton} and Zuluaga (2001) for the linear rank test formulation. The null hypothesis of equality, or conditional equality given \code{block}, of the survival distribution of \code{y} in the groups defined by \code{x} is tested. In the two-sample case, the two-sided null hypothesis is \eqn{H_0\!: \theta = 1}{H_0: theta = 1}, where \eqn{\theta = \lambda_2 / \lambda_1} and \eqn{\lambda_s} is the hazard rate in the \eqn{s}th sample. In case \code{alternative = "less"}, the null hypothesis is \eqn{H_0\!: \theta \ge 1}{H_0: theta >= 1}, i.e., the survival is lower in sample 1 than in sample 2. When \code{alternative = "greater"}, the null hypothesis is \eqn{H_0\!: \theta \le 1}{H_0: theta <= 1}, i.e., the survival is higher in sample 1 than in sample 2. If \code{x} is an ordered factor, the default scores, \code{1:nlevels(x)}, can be altered using the \code{scores} argument (see \code{\link{independence_test}}); this argument can also be used to coerce nominal factors to class \code{"ordered"}. In this case, a linear-by-linear association test is computed and the direction of the alternative hypothesis can be specified using the \code{alternative} argument. This type of extension of the standard logrank test was given by Tarone (1975) and later generalized to general weights by Tarone and Ware (1977). Let \eqn{(t_i, \delta_i)}, \eqn{i = 1, 2, \ldots, n}, represent a right-censored random sample of size \eqn{n}, where \eqn{t_i} is the observed survival time and \eqn{\delta_i} is the status indicator (\eqn{\delta_i} is 0 for right-censored observations and 1 otherwise). To allow for ties in the data, let \eqn{t_{(1)} < t_{(2)} < \cdots < t_{(m)}}{t_(1) < t_(2) < \dots < t_(m)} represent the \eqn{m}, \eqn{m \le n}, ordered distinct event times. At time \eqn{t_{(k)}}{t_(k)}, \eqn{k = 1, 2, \ldots, m}, the number of events and the number of subjects at risk are given by \eqn{d_k = \sum_{i = 1}^n I\!\left(t_i = t_{(k)}\,|\, \delta_i = 1\right)}{d_k = sum(i = 1, \dots, n) I(t_i = t_(k) | delta_i = 1)} and \eqn{n_k = n - r_k}, respectively, where \eqn{r_k} depends on the ties handling method. Three different methods of handling ties are available using \code{ties.method}: mid-ranks (\code{"mid-ranks"}, default), the Hothorn-Lausen method (\code{"Hothorn-Lausen"}) and average-scores (\code{"average-scores"}). The first and last method are discussed and contrasted by Callaert (2003), whereas the second method is defined in Hothorn and Lausen (2003). The mid-ranks method leads to \deqn{ r_k = \sum_{i = 1}^n I\!\left(t_i < t_{(k)}\right) }{ r_k = sum(i = 1, \dots, n) I(t_i < t_(k)) } whereas the Hothorn-Lausen method uses \deqn{ r_k = \sum_{i = 1}^n I\!\left(t_i \le t_{(k)}\right) - 1. }{ r_k = sum(i = 1, \dots, n) I(t_i <= t_(k)) - 1. } The scores assigned to right-censored and uncensored observations at the \eqn{k}th event time are given by \deqn{ C_k = \sum_{j = 1}^k w_j \frac{d_j}{n_j} \quad \mbox{and} \quad c_k = C_k - w_k, }{ C_k = sum(j=1,\dots,k) w_j * (d_j / n_j) and c_k = C_k - w_k, } respectively, where \eqn{w} is the logrank weight. For the average-scores method, used by, e.g., the software package StatXact, the \eqn{d_k} events observed at the \eqn{k}th event time are arbitrarily ordered by assigning them distinct values \eqn{t_{(k_l)}}{t_(k_l)}, \eqn{l = 1, 2, \ldots, d_k}, infinitesimally to the left of \eqn{t_{(k)}}{t_(k)}. Then scores \eqn{C_{k_l}}{C_k_l} and \eqn{c_{k_l}}{c_k_l} are computed as indicated above, effectively assuming that no event times are tied. The scores \eqn{C_k} and \eqn{c_k} are assigned the average of the scores \eqn{C_{k_l}}{C_k_l} and \eqn{c_{k_l}}{c_k_l} respectively. It then follows that the score for the \eqn{i}th subject is \deqn{ a_i = \left\{ \begin{array}{ll} C_{k'} & \mbox{if } \delta_i = 0 \\ c_{k'} & \mbox{otherwise} \end{array} \right. }{ C_k' if delta_i = 0 a_i = c_k' otherwise } where \eqn{k' = \max \{k: t_i \ge t_{(k)}\}}{k' = max\{k : t_i >= t_(k)\}}. The \code{type} argument allows for a choice between some of the most well-known members of the family of weighted logrank tests, each corresponding to a particular weight function. The standard logrank test (\code{"logrank"}, default) was suggested by Mantel (1966), Peto and Peto (1972) and Cox (1972) and has \eqn{w_k = 1}. The Gehan-Breslow test (\code{"Gehan-Breslow"}) proposed by Gehan (1965) and later extended to \eqn{K} samples by Breslow (1970) is a generalization of the Wilcoxon rank-sum test, where \eqn{w_k = n_k}. The Tarone-Ware class of tests (\code{"Tarone-Ware"}) discussed by Tarone and Ware (1977) has \eqn{w_k = n_k^\rho}, where \eqn{\rho} is a constant; \eqn{\rho = 0.5} (default) was suggested by Tarone and Ware (1977), but note that \eqn{\rho = 0} and \eqn{\rho = 1} lead to the the standard logrank test and Gehan-Breslow test respectively. The Peto-Peto test (\code{"Peto-Peto"}) suggested by Peto and Peto (1972) is another generalization of the Wilcoxon rank-sum test, where \deqn{ w_k = \hat{S}_k = \prod_{j = 0}^{k - 1} \frac{n_j - d_j}{n_j} }{ w_k = Shat_k = prod(j = 0, \dots, k - 1) (n_j - d_j) / n_j } is the \emph{left-continuous} Kaplan-Meier estimator of the survival function, \eqn{n_0 \equiv n}{n_0 := n} and \eqn{d_0 \equiv 0}{d_0 := 0}. The Prentice test (\code{"Prentice"}) is also a generalization of the Wilcoxon rank-sum test proposed by Prentice (1978), where \deqn{ w_k = \prod_{j = 1}^k \frac{n_j}{n_j + d_j}. }{ w_k = prod(j = 1, \dots, k) n_j / (n_j + d_j). } The Prentice-Marek test (\code{"Prentice-Marek"}) is yet another generalization of the Wilcoxon rank-sum test discussed by Prentice and Marek (1979), with \deqn{ w_k = \tilde{S}_k = \prod_{j = 1}^k \frac{n_j + 1 - d_j}{n_j + 1}. }{ w_k = Stilde_k = prod(j = 1, \dots, k) (n_j + 1 - d_j) / (n_j + 1). } The Andersen-Borgan-Gill-Keiding test (\code{"Andersen-Borgan-Gill-Keiding"}) suggested by Andersen \emph{et al.} (1982) is a modified version of the Prentice-Marek test using \deqn{ w_k = \frac{n_k}{n_k + 1} \prod_{j = 0}^{k - 1} \frac{n_j + 1 - d_j}{n_j + 1}, }{ w_k = (n_k / (n_k + 1)) prod(j = 0, \dots, k - 1) (n_j + 1 - d_j) / (n_j + 1), } where, again, \eqn{n_0 \equiv n}{n_0 := n} and \eqn{d_0 \equiv 0}{d_0 := 0}. The Fleming-Harrington class of tests (\code{"Fleming-Harrington"}) proposed by Fleming and Harrington (1991) uses \eqn{w_k = \hat{S}_k^\rho (1 - \hat{S}_k)^\gamma}{w_k = Shat_k^rho * (1 - Shat_k)^gamma}, where \eqn{\rho} and \eqn{\gamma} are constants; \eqn{\rho = 0} and \eqn{\gamma = 0} lead to the standard logrank test, while \eqn{\rho = 1} and \eqn{\gamma = 0} result in the Peto-Peto test. The Gaugler-Kim-Liao class of tests (\code{"Gaugler-Kim-Liao"}) discussed by Gaugler \emph{et al.} (2007) is a modified version of the Fleming-Harrington class of tests, replacing \eqn{\hat{S}_k}{Shat_k} with \eqn{\tilde{S}_k}{Stilde_k} so that \eqn{w_k = \tilde{S}_k^\rho (1 - \tilde{S}_k)^\gamma}{w_k = Stilde_k^rho * (1 - Stilde_k)^gamma}, where \eqn{\rho} and \eqn{\gamma} are constants; \eqn{\rho = 0} and \eqn{\gamma = 0} lead to the standard logrank test, whereas \eqn{\rho = 1} and \eqn{\gamma = 0} result in the Prentice-Marek test. The Self class of tests (\code{"Self"}) suggested by Self (1991) has \eqn{w_k = v_k^\rho (1 - v_k)^\gamma}{w_k = v_k^rho * (1 - v_k)^gamma}, where \deqn{ v_k = \frac{1}{2} \frac{t_{(k-1)} + t_{(k)}}{t_{(m)}}, \quad t_{(0)} \equiv 0 }{ v_k = 1 / 2 * (t_(k - 1) + t_(k)) / t_(m), t_(0) := 0 } is the standardized mid-point between the \eqn{(k - 1)}th and the \eqn{k}th event time. (This is a slight generalization of Self's original proposal in order to allow for non-integer follow-up times.) Again, \eqn{\rho} and \eqn{\gamma} are constants and \eqn{\rho = 0} and \eqn{\gamma = 0} lead to the standard logrank test. The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ Peto and Peto (1972) proposed the test statistic implemented in \code{logrank_test} and named it the \emph{logrank test}. However, the Mantel-Cox test (Mantel, 1966; Cox, 1972), as implemented in \code{\link[survival]{survdiff}} (in package \pkg{survival}), is also known as the logrank test. These tests are similar, but differ in the choice of probability model: the (Peto-Peto) logrank test uses the permutational variance, whereas the Mantel-Cox test is based on the hypergeometric variance. Combining \code{\link{independence_test}} or \code{\link{symmetry_test}} with \code{\link{logrank_trafo}} offers more flexibility than \code{logrank_test} and allows for, among other things, maximum-type versatile test procedures (e.g., Lee, 1996; see \sQuote{Examples}) and user-supplied logrank weights (see \code{\link{GTSG}} for tests against Weibull-type or crossing-curve alternatives). Starting with version 1.1-0, \code{logrank_test} replaced \code{surv_test} which was made \strong{defunct} in version 1.2-0. Furthermore, \code{logrank_trafo} is now an increasing function for all choices of \code{ties.method}, implying that the test statistic has the same sign irrespective of the ties handling method. Consequently, the sign of the test statistic will now be the opposite of what it was in earlier versions unless \code{ties.method = "average-scores"}. (In versions of \pkg{coin} prior to 1.1-0, \code{logrank_trafo} was a decreasing function when \code{ties.method} was other than \code{"average-scores"}.) Starting with version 1.2-0, mid-ranks and the Hothorn-Lausen method can no longer be specified with \code{ties.method = "logrank"} and \code{ties-method = "HL"} respectively. } \references{ Andersen, P. K., Borgan, \enc{Ø}{O}., Gill, R. and Keiding, N. (1982). Linear nonparametric tests for comparison of counting processes, with applications to censored survival data (with discussion). \emph{International Statistical Review} \bold{50}(3), 219--258. \doi{10.2307/1402489} Breslow, N. (1970). A generalized Kruskal-Wallis test for comparing \eqn{K} samples subject to unequal patterns of censorship. \emph{Biometrika} \bold{57}(3), 579--594. \doi{10.1093/biomet/57.3.579} Callaert, H. (2003). Comparing statistical software packages: The case of the logrank test in StatXact. \emph{The American Statistician} \bold{57}(3), 214--217. \doi{10.1198/0003130031900} Cox, D. R. (1972). Regression models and life-tables (with discussion). \emph{Journal of the Royal Statistical Society} B \bold{34}(2), 187--220. \doi{10.1111/j.2517-6161.1972.tb00899.x} Fleming, T. R. and Harrington, D. P. (1991). \emph{Counting Processes and Survival Analysis}. New York: John Wiley & Sons. Gaugler, T., Kim, D. and Liao, S. (2007). Comparing two survival time distributions: An investigation of several weight functions for the weighted logrank statistic. \emph{Communications in Statistics -- Simulation and Computation} \bold{36}(2), 423--435. \doi{10.1080/03610910601161272} Gehan, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily single-censored samples. \emph{Biometrika} \bold{52}(1--2), 203--223. \doi{10.1093/biomet/52.1-2.203} Hothorn, T. and Lausen, B. (2003). On the exact distribution of maximally selected rank statistics. \emph{Computational Statistics & Data Analysis} \bold{43}(2), 121--137. \doi{10.1016/S0167-9473(02)00225-6} Klein, J. P. and Moeschberger, M. L. (2003). \emph{Survival Analysis: Techniques for Censored and Truncated Data}, Second Edition. New York: Springer. Lee, J. W. (1996). Some versatile tests based on the simultaneous use of weighted log-rank statistics. \emph{Biometrics} \bold{52}(2), 721--725. \doi{10.2307/2532911} \enc{Letón}{Leton}, E. and Zuluaga, P. (2001). Equivalence between score and weighted tests for survival curves. \emph{Communications in Statistics -- Theory and Methods} \bold{30}(4), 591--608. \doi{10.1081/STA-100002138} Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. \emph{Cancer Chemotherapy Reports} \bold{50}(3), 163--170. Peto, R. and Peto, J. (1972). Asymptotic efficient rank invariant test procedures (with discussion). \emph{Journal of the Royal Statistical Society} A \bold{135}(2), 185--207. \doi{10.2307/2344317} Prentice, R. L. (1978). Linear rank tests with right censored data. \emph{Biometrika} \bold{65}(1), 167--179. \doi{10.1093/biomet/65.1.167} Prentice, R. L. and Marek, P. (1979). A qualitative discrepancy between censored data rank tests. \emph{Biometrics} \bold{35}(4), 861--867. \doi{10.2307/2530120} Self, S. G. (1991). An adaptive weighted log-rank test with application to cancer prevention and screening trials. \emph{Biometrics} \bold{47}(3), 975--986. \doi{10.2307/2532653} Tarone, R. E. (1975). Tests for trend in life table analysis. \emph{Biometrika} \bold{62}(3), 679--682. \doi{10.1093/biomet/62.3.679} Tarone, R. E. and Ware, J. (1977). On distribution-free tests for equality of survival distributions. \emph{Biometrika} \bold{64}(1), 156--160. \doi{10.1093/biomet/64.1.156} } \examples{ ## Example data (Callaert, 2003, Tab. 1) callaert <- data.frame( time = c(1, 1, 5, 6, 6, 6, 6, 2, 2, 2, 3, 4, 4, 5, 5), group = factor(rep(0:1, c(7, 8))) ) ## Logrank scores using mid-ranks (Callaert, 2003, Tab. 2) with(callaert, logrank_trafo(Surv(time))) ## Asymptotic Mantel-Cox test (p = 0.0523) survdiff(Surv(time) ~ group, data = callaert) ## Exact logrank test using mid-ranks (p = 0.0505) logrank_test(Surv(time) ~ group, data = callaert, distribution = "exact") ## Exact logrank test using average-scores (p = 0.0468) logrank_test(Surv(time) ~ group, data = callaert, distribution = "exact", ties.method = "average-scores") ## Lung cancer data (StatXact 9 manual, p. 213, Tab. 7.19) lungcancer <- data.frame( time = c(257, 476, 355, 1779, 355, 191, 563, 242, 285, 16, 16, 16, 257, 16), event = c(0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1), group = factor(rep(1:2, c(5, 9)), labels = c("newdrug", "control")) ) ## Logrank scores using average-scores (StatXact 9 manual, p. 214) with(lungcancer, logrank_trafo(Surv(time, event), ties.method = "average-scores")) ## Exact logrank test using average-scores (StatXact 9 manual, p. 215) logrank_test(Surv(time, event) ~ group, data = lungcancer, distribution = "exact", ties.method = "average-scores") ## Exact Prentice test using average-scores (StatXact 9 manual, p. 222) logrank_test(Surv(time, event) ~ group, data = lungcancer, distribution = "exact", ties.method = "average-scores", type = "Prentice") ## Approximative (Monte Carlo) versatile test (Lee, 1996) rho.gamma <- expand.grid(rho = seq(0, 2, 1), gamma = seq(0, 2, 1)) lee_trafo <- function(y) logrank_trafo(y, ties.method = "average-scores", type = "Fleming-Harrington", rho = rho.gamma["rho"], gamma = rho.gamma["gamma"]) it <- independence_test(Surv(time, event) ~ group, data = lungcancer, distribution = approximate(nresample = 10000), ytrafo = function(data) trafo(data, surv_trafo = lee_trafo)) pvalue(it, method = "step-down") } \keyword{htest} \keyword{survival} coin/man/IndependenceLinearStatistic-class.Rd0000644000176200001440000000707513715224731020771 0ustar liggesusers\name{IndependenceLinearStatistic-class} \docType{class} \alias{IndependenceLinearStatistic-class} \alias{initialize,IndependenceLinearStatistic-method} \title{Class \code{"IndependenceLinearStatistic"}} \description{ Objects of class \code{"IndependenceLinearStatistic"} represent the linear statistic and the transformed and original data structures corresponding to an independence problem. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("IndependenceLinearStatistic", object, \dots)} where \code{object} is an object of class \code{"\linkS4class{IndependenceTestProblem}"}. } \section{Slots}{ \describe{ \item{\code{linearstatistic}:}{ Object of class \code{"matrix"}. The linear statistic for each block. } \item{\code{expectation}:}{ Object of class \code{"matrix"}. The expectation of the linear statistic for each block. } \item{\code{covariance}:}{ Object of class \code{"matrix"}. The lower triangular elements of the covariance of the linear statistic for each block. } \item{\code{xtrans}:}{ Object of class \code{"matrix"}. The transformed \code{x}. } \item{\code{ytrans}:}{ Object of class \code{"matrix"}. The transformed \code{y}. } \item{\code{xtrafo}:}{ Object of class \code{"function"}. The regression function for \code{x}. } \item{\code{ytrafo}:}{ Object of class \code{"function"}. The influence function for \code{y}. } \item{\code{x}:}{ Object of class \code{"data.frame"}. The variables \code{x}. } \item{\code{y}:}{ Object of class \code{"data.frame"}. The variables \code{y}. } \item{\code{block}:}{ Object of class \code{"factor"}. The block structure. } \item{\code{weights}:}{ Object of class \code{"numeric"}. The case weights. } } } \section{Extends}{ Class \code{"\linkS4class{IndependenceTestProblem}"}, directly. \cr Class \code{"\linkS4class{IndependenceProblem}"}, by class \code{"\linkS4class{IndependenceTestProblem}"}, distance 2. } \section{Known Subclasses}{ Class \code{"\linkS4class{IndependenceTestStatistic}"}, directly.\cr Class \code{"\linkS4class{MaxTypeIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestStatistic}"}, distance 2. \cr Class \code{"\linkS4class{QuadTypeIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestStatistic}"}, distance 2. \cr Class \code{"\linkS4class{ScalarIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestStatistic}"}, distance 2. } \section{Methods}{ \describe{ \item{covariance}{ \code{signature(object = "IndependenceLinearStatistic")}: See the documentation for \code{\link{covariance}} for details. } \item{expectation}{ \code{signature(object = "IndependenceLinearStatistic")}: See the documentation for \code{\link{expectation}} for details. } \item{initialize}{ \code{signature(.Object = "IndependenceLinearStatistic")}: See the documentation for \code{\link[methods:new]{initialize}} (in package \pkg{methods}) for details. } \item{statistic}{ \code{signature(object = "IndependenceLinearStatistic")}: See the documentation for \code{\link{statistic}} for details. } \item{variance}{ \code{signature(object = "IndependenceLinearStatistic")}: See the documentation for \code{\link{variance}} for details. } } } \keyword{classes} coin/man/MaximallySelectedStatisticsTests.Rd0000644000176200001440000002136714000321233020745 0ustar liggesusers\name{MaximallySelectedStatisticsTests} \alias{maxstat_test} \alias{maxstat_test.formula} \alias{maxstat_test.table} \alias{maxstat_test.IndependenceProblem} \concept{Generalized maximally selected statistics} \encoding{UTF-8} \title{Generalized Maximally Selected Statistics} \description{ Testing the independence of two sets of variables measured on arbitrary scales against cutpoint alternatives. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{maxstat_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{maxstat_test}{table}(object, \dots) \method{maxstat_test}{IndependenceProblem}(object, teststat = c("maximum", "quadratic"), distribution = c("asymptotic", "approximate", "none"), minprob = 0.1, maxprob = 1 - minprob, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y1 + ... + yq ~ x1 + ... + xp | block} where \code{y1}, \dots, \code{yq} and \code{x1}, \dots, \code{xp} are measured on arbitrary scales (nominal, ordinal or continuous with or without censoring) and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from classes \code{"table"} or \code{"\linkS4class{IndependenceProblem}"}. } \item{teststat}{ a character, the type of test statistic to be applied: either a maximum statistic (\code{"maximum"}, default) or a quadratic form (\code{"quadratic"}). } \item{distribution}{ a character, the conditional null distribution of the test statistic can be approximated by its asymptotic distribution (\code{"asymptotic"}, default) or via Monte Carlo resampling (\code{"approximate"}). Alternatively, the functions \code{\link{asymptotic}} or \code{\link{approximate}} can be used. Computation of the null distribution can be suppressed by specifying \code{"none"}. } \item{minprob}{ a numeric, a fraction between 0 and 0.5 specifying that cutpoints only greater than the \code{minprob} \eqn{\cdot}{*} 100\% quantile of \code{x1}, \dots, \code{xp} are considered. Defaults to \code{0.1}. } \item{maxprob}{ a numeric, a fraction between 0.5 and 1 specifying that cutpoints only smaller than the \code{maxprob} \eqn{\cdot}{*} 100\% quantile of \code{x1}, \dots, \code{xp} are considered. Defaults to \code{1 - minprob}. } \item{\dots}{ further arguments to be passed to \code{\link{independence_test}}. } } \details{ \code{maxstat_test} provides generalized maximally selected statistics. The family of maximally selected statistics encompasses a large collection of procedures used for the estimation of simple cutpoint models including, but not limited to, maximally selected \eqn{\chi^2}{chi^2} statistics, maximally selected Cochran-Armitage statistics, maximally selected rank statistics and maximally selected statistics for multiple covariates. A general description of these methods is given by Hothorn and Zeileis (2008). The null hypothesis of independence, or conditional independence given \code{block}, between \code{y1}, \dots, \code{yq} and \code{x1}, \dots, \code{xp} is tested against cutpoint alternatives. All possible partitions into two groups are evaluated for each unordered covariate \code{x1}, \dots, \code{xp}, whereas only order-preserving binary partitions are evaluated for ordered or numeric covariates. The cutpoint is then a set of levels defining one of the two groups. If both response and covariate is univariable, say \code{y1} and \code{x1}, this procedure is known as maximally selected \eqn{\chi^2}{chi^2} statistics (Miller and Siegmund, 1982) when \code{y1} is a binary factor and \code{x1} is a numeric variable, and as maximally selected rank statistics when \code{y1} is a rank transformed numeric variable and \code{x1} is a numeric variable (Lausen and Schumacher, 1992). Lausen \emph{et al.} (2004) introduced maximally selected statistics for a univariable numeric response and multiple numeric covariates \code{x1}, \dots, \code{xp}. If, say, \code{y1} and/or \code{x1} are ordered factors, the default scores, \code{1:nlevels(y1)} and \code{1:nlevels(x1)} respectively, can be altered using the \code{scores} argument (see \code{\link{independence_test}}); this argument can also be used to coerce nominal factors to class \code{"ordered"}. If both, say, \code{y1} and \code{x1} are ordered factors, a linear-by-linear association test is computed and the direction of the alternative hypothesis can be specified using the \code{alternative} argument. The particular extension to the case of a univariable ordered response and a univariable numeric covariate was given by Betensky and Rabinowitz (1999) and is known as maximally selected Cochran-Armitage statistics. The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling by setting \code{distribution} to \code{"approximate"}. See \code{\link{asymptotic}} and \code{\link{approximate}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ Starting with \pkg{coin} version 1.1-0, maximum statistics and quadratic forms can no longer be specified using \code{teststat = "maxtype"} and \code{teststat = "quadtype"} respectively (as was used in versions prior to 0.4-5). } \references{ Betensky, R. A. and Rabinowitz, D. (1999). Maximally selected \eqn{\chi^2}{chi^2} statistics for \eqn{k \times 2}{k x 2} tables. \emph{Biometrics} \bold{55}(1), 317--320. \doi{10.1111/j.0006-341X.1999.00317.x} Hothorn, T. and Lausen, B. (2003). On the exact distribution of maximally selected rank statistics. \emph{Computational Statistics & Data Analysis} \bold{43}(2), 121--137. \doi{10.1016/S0167-9473(02)00225-6} Hothorn, T. and Zeileis, A. (2008). Generalized maximally selected statistics. \emph{Biometrics} \bold{64}(4), 1263--1269. \doi{10.1111/j.1541-0420.2008.00995.x} Lausen, B., Hothorn, T., Bretz, F. and Schumacher, M. (2004). Assessment of optimal selected prognostic factors. \emph{Biometrical Journal} \bold{46}(3), 364--374. \doi{10.1002/bimj.200310030} Lausen, B. and Schumacher, M. (1992). Maximally selected rank statistics. \emph{Biometrics} \bold{48}(1), 73--85. \doi{10.2307/2532740} Miller, R. and Siegmund, D. (1982). Maximally selected chi square statistics. \emph{Biometrics} \bold{38}(4), 1011--1016. \doi{10.2307/2529881} \enc{Müller}{Mueller}, J. and Hothorn, T. (2004). Maximally selected two-sample statistics as a new tool for the identification and assessment of habitat factors with an application to breeding bird communities in oak forests. \emph{European Journal of Forest Research} \bold{123}(3), 219--228. \doi{10.1007/s10342-004-0035-5} } \examples{ \dontshow{options(useFancyQuotes = FALSE)} ## Tree pipit data (Mueller and Hothorn, 2004) ## Asymptotic maximally selected statistics maxstat_test(counts ~ coverstorey, data = treepipit) ## Asymptotic maximally selected statistics ## Note: all covariates simultaneously mt <- maxstat_test(counts ~ ., data = treepipit) mt@estimates$estimate ## Malignant arrythmias data (Hothorn and Lausen, 2003, Sec. 7.2) ## Asymptotic maximally selected statistics maxstat_test(Surv(time, event) ~ EF, data = hohnloser, ytrafo = function(data) trafo(data, surv_trafo = function(y) logrank_trafo(y, ties.method = "Hothorn-Lausen"))) ## Breast cancer data (Hothorn and Lausen, 2003, Sec. 7.3) ## Asymptotic maximally selected statistics data("sphase", package = "TH.data") maxstat_test(Surv(RFS, event) ~ SPF, data = sphase, ytrafo = function(data) trafo(data, surv_trafo = function(y) logrank_trafo(y, ties.method = "Hothorn-Lausen"))) ## Job satisfaction data (Agresti, 2002, p. 288, Tab. 7.8) ## Asymptotic maximally selected statistics maxstat_test(jobsatisfaction) ## Asymptotic maximally selected statistics ## Note: 'Job.Satisfaction' and 'Income' as ordinal maxstat_test(jobsatisfaction, scores = list("Job.Satisfaction" = 1:4, "Income" = 1:4)) } \keyword{htest} coin/man/VarCovar-class.Rd0000644000176200001440000000543513715224731015106 0ustar liggesusers\name{VarCovar-class} \docType{class} \alias{VarCovar-class} \alias{CovarianceMatrix-class} \alias{Variance-class} \alias{initialize,CovarianceMatrix-method} \alias{initialize,Variance-method} \title{Class \code{"VarCovar"} and its subclasses} \description{ Objects of class \code{"VarCovar"} and its subclasses \code{"CovarianceMatrix"} and \code{"Variance"} represent the covariance and variance, respectively, of the linear statistic. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Class \code{"VarCovar"} is a \emph{virtual} class defined as the class union of \code{"CovarianceMatrix"} and \code{"Variance"}, so objects cannot be created from it directly. Objects can be created by calls of the form \preformatted{ new("CovarianceMatrix", covariance, \dots)} and \preformatted{ new("Variance", variance, \dots)} where \code{covariance} is a covariance matrix and \code{variance} is numeric vector containing the diagonal elements of the covariance matrix. } \section{Slots}{ For objects of class \code{"CovarianceMatrix"}: \describe{ \item{\code{covariance}:}{ Object of class \code{"matrix"}. The covariance matrix. } } For objects of class \code{"Variance"}: \describe{ \item{\code{variance}:}{ Object of class \code{"numeric"}. The diagonal elements of the covariance matrix. } } } \section{Extends}{ For objects of classes \code{"CovarianceMatrix"} or \code{"Variance"}: \cr Class \code{"VarCovar"}, directly. } \section{Known Subclasses}{ For objects of class \code{"VarCovar"}: \cr Class \code{"CovarianceMatrix"}, directly. \cr Class \code{"Variance"}, directly. } \section{Methods}{ \describe{ \item{covariance}{ \code{signature(object = "CovarianceMatrix")}: See the documentation for \code{\link{covariance}} for details. } \item{initialize}{ \code{signature(.Object = "CovarianceMatrix")}: See the documentation for \code{\link[methods:new]{initialize}} (in package \pkg{methods}) for details. } \item{initialize}{ \code{signature(.Object = "Variance")}: See the documentation for \code{\link[methods:new]{initialize}} (in package \pkg{methods}) for details. } \item{variance}{ \code{signature(object = "CovarianceMatrix")}: See the documentation for \code{\link{variance}} for details. } \item{variance}{ \code{signature(object = "Variance")}: See the documentation for \code{\link{variance}} for details. } } } \note{ Starting with \pkg{coin} version 1.4-0, this class is deprecated. \strong{It will be made defunct and removed in a future release.} } \keyword{classes} coin/man/alpha.Rd0000644000176200001440000000511413527753030013337 0ustar liggesusers\name{alpha} \docType{data} \alias{alpha} \encoding{UTF-8} \title{Genetic Components of Alcoholism} \description{ Levels of expressed alpha synuclein mRNA in three groups of allele lengths of NACP-REP1. } \usage{alpha} \format{ A data frame with 97 observations on 2 variables. \describe{ \item{\code{alength}}{ allele length, a factor with levels \code{"short"}, \code{"intermediate"} and \code{"long"}. } \item{\code{elevel}}{ expression levels of alpha synuclein mRNA. } } } \details{ Various studies have linked alcohol dependence phenotypes to chromosome 4. One candidate gene is NACP (non-amyloid component of plaques), coding for alpha synuclein. \enc{Bönsch}{Boensch} \emph{et al.} (2005) found longer alleles of NACP-REP1 in alcohol-dependent patients compared with healthy controls and reported that the allele lengths show some association with levels of expressed alpha synuclein mRNA. } \source{ \enc{Bönsch}{Boensch}, D., Lederer, T., Reulbach, U., Hothorn, T., Kornhuber, J. and Bleich, S. (2005). Joint analysis of the \emph{NACP}-REP1 marker within the alpha synuclein gene concludes association with alcohol dependence. \emph{Human Molecular Genetics} \bold{14}(7), 967--971. \doi{10.1093/hmg/ddi090} } \references{ Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} Winell, H. and \enc{Lindbäck}{Lindbaeck}, J. (2018). A general score-independent test for order-restricted inference. \emph{Statistics in Medicine} \bold{37}(21), 3078--3090. \doi{10.1002/sim.7690} } \examples{ ## Boxplots boxplot(elevel ~ alength, data = alpha) ## Asymptotic Kruskal-Wallis test kruskal_test(elevel ~ alength, data = alpha) ## Asymptotic Kruskal-Wallis test using midpoint scores kruskal_test(elevel ~ alength, data = alpha, scores = list(alength = c(2, 7, 11))) ## Asymptotic score-independent test ## Winell and Lindbaeck (2018) (it <- independence_test(elevel ~ alength, data = alpha, ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), xtrafo = function(data) trafo(data, factor_trafo = function(x) zheng_trafo(as.ordered(x))))) ## Extract the "best" set of scores ss <- statistic(it, type = "standardized") idx <- which(abs(ss) == max(abs(ss)), arr.ind = TRUE) ss[idx[1], idx[2], drop = FALSE] } \keyword{datasets} coin/man/alzheimer.Rd0000644000176200001440000000334313437424312014232 0ustar liggesusers\name{alzheimer} \docType{data} \alias{alzheimer} \title{Smoking and Alzheimer's Disease} \description{ A case-control study of smoking and Alzheimer's disease. } \usage{alzheimer} \format{ A data frame with 538 observations on 3 variables. \describe{ \item{\code{smoking}}{ a factor with levels \code{"None"}, \code{"<10"}, \code{"10-20"} and \code{">20"} (cigarettes per day). } \item{\code{disease}}{ a factor with levels \code{"Alzheimer"}, \code{"Other dementias"} and \code{"Other diagnoses"}. } \item{\code{gender}}{ a factor with levels \code{"Female"} and \code{"Male"}. } } } \details{ Subjects with Alzheimer's disease are compared to two different control groups with respect to smoking history. The data are given in Salib and Hillier (1997, Tab. 4). } \source{ Salib, E. and Hillier, V. (1997). A case-control study of smoking and Alzheimer's disease. \emph{International Journal of Geriatric Psychiatry} \bold{12}(3), 295--300. \doi{10.1002/(SICI)1099-1166(199703)12:3<295::AID-GPS476>3.0.CO;2-3} } \references{ Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} } \examples{ ## Spineplots op <- par(no.readonly = TRUE) # save current settings layout(matrix(1:2, ncol = 2)) spineplot(disease ~ smoking, data = alzheimer, subset = gender == "Male", main = "Male") spineplot(disease ~ smoking, data = alzheimer, subset = gender == "Female", main = "Female") par(op) # reset ## Asymptotic Cochran-Mantel-Haenszel test cmh_test(disease ~ smoking | gender, data = alzheimer) } \keyword{datasets} coin/man/LocationTests.Rd0000644000176200001440000003107513401471036015044 0ustar liggesusers\name{LocationTests} \alias{oneway_test} \alias{oneway_test.formula} \alias{oneway_test.IndependenceProblem} \alias{wilcox_test} \alias{wilcox_test.formula} \alias{wilcox_test.IndependenceProblem} \alias{kruskal_test} \alias{kruskal_test.formula} \alias{kruskal_test.IndependenceProblem} \alias{normal_test} \alias{normal_test.formula} \alias{normal_test.IndependenceProblem} \alias{median_test} \alias{median_test.formula} \alias{median_test.IndependenceProblem} \alias{savage_test} \alias{savage_test.formula} \alias{savage_test.IndependenceProblem} \concept{Fisher-Pitman permutation test} \concept{Wilcoxon-Mann-Whitney test} \concept{Kruskal-Wallis test} \concept{van der Waerden test} \concept{Brown-Mood median test} \concept{Savage test} \encoding{UTF-8} \title{Two- and \eqn{K}-Sample Location Tests} \description{ Testing the equality of the distributions of a numeric response variable in two or more independent groups against shift alternatives. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{oneway_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{oneway_test}{IndependenceProblem}(object, \dots) \method{wilcox_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{wilcox_test}{IndependenceProblem}(object, conf.int = FALSE, conf.level = 0.95, \dots) \method{kruskal_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{kruskal_test}{IndependenceProblem}(object, \dots) \method{normal_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{normal_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "average-scores"), conf.int = FALSE, conf.level = 0.95, \dots) \method{median_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{median_test}{IndependenceProblem}(object, mid.score = c("0", "0.5", "1"), conf.int = FALSE, conf.level = 0.95, \dots) \method{savage_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{savage_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "average-scores"), conf.int = FALSE, conf.level = 0.95, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} is a numeric variable, \code{x} is a factor and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from class \code{"\linkS4class{IndependenceProblem}"}. } \item{conf.int}{ a logical indicating whether a confidence interval for the difference in location should be computed. Defaults to \code{FALSE}. } \item{conf.level}{ a numeric, confidence level of the interval. Defaults to \code{0.95}. } \item{ties.method}{ a character, the method used to handle ties: the score generating function either uses mid-ranks (\code{"mid-ranks"}, default) or averages the scores of randomly broken ties (\code{"average-scores"}). } \item{mid.score}{ a character, the score assigned to observations exactly equal to the median: either 0 (\code{"0"}, default), 0.5 (\code{"0.5"}) or 1 (\code{"1"}); see \sQuote{Details}. } \item{\dots}{ further arguments to be passed to \code{\link{independence_test}}. } } \details{ \code{oneway_test}, \code{wilcox_test}, \code{kruskal_test}, \code{normal_test}, \code{median_test} and \code{savage_test} provide the Fisher-Pitman permutation test, the Wilcoxon-Mann-Whitney test, the Kruskal-Wallis test, the van der Waerden test, the Brown-Mood median test and the Savage test. A general description of these methods is given by Hollander and Wolfe (1999). For the adjustment of scores for tied values see \enc{Hájek}{Hajek}, \enc{Šidák}{Sidak} and Sen (1999, pp. 133--135). The null hypothesis of equality, or conditional equality given \code{block}, of the distribution of \code{y} in the groups defined by \code{x} is tested against shift alternatives. In the two-sample case, the two-sided null hypothesis is \eqn{H_0\!: \mu = 0}{H_0: mu = 0}, where \eqn{\mu = Y_1 - Y_2} and \eqn{Y_s} is the median of the responses in the \eqn{s}th sample. In case \code{alternative = "less"}, the null hypothesis is \eqn{H_0\!: \mu \ge 0}{H_0: mu >= 0}. When \code{alternative = "greater"}, the null hypothesis is \eqn{H_0\!: \mu \le 0}{H_0: mu <= 0}. Confidence intervals for the difference in location are available (except for \code{oneway_test}) and computed according to Bauer (1972). If \code{x} is an ordered factor, the default scores, \code{1:nlevels(x)}, can be altered using the \code{scores} argument (see \code{\link{independence_test}}); this argument can also be used to coerce nominal factors to class \code{"ordered"}. In this case, a linear-by-linear association test is computed and the direction of the alternative hypothesis can be specified using the \code{alternative} argument. The Brown-Mood median test offers a choice of mid-score, i.e., the score assigned to observations exactly equal to the median. In the two-sample case, \code{mid-score = "0"} implies that the linear test statistic is simply the number of subjects in the second sample with observations greater than the median of the pooled sample. Similarly, the linear test statistic for the last alternative, \code{mid-score = "1"}, is the number of subjects in the second sample with observations greater than or equal to the median of the pooled sample. If \code{mid-score = "0.5"} is selected, the linear test statistic is the mean of the test statistics corresponding to the first and last alternatives and has a symmetric distribution, or at least approximately so, under the null hypothesis (see \enc{Hájek}{Hajek}, \enc{Šidák}{Sidak} and Sen, 1999, pp. 97--98). The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. Confidence intervals can be extracted by \link[stats]{confint}. } \note{ Starting with version 1.1-0, \code{oneway_test} no longer allows the test statistic to be specified; a quadratic form is now used in the \eqn{K}-sample case. Please use \code{\link{independence_test}} if more control is desired. } \references{ Bauer, D. F. (1972). Constructing confidence sets using rank statistics. \emph{Journal of the American Statistical Association} \bold{67}(339), 687--690. \doi{10.1080/01621459.1972.10481279} \enc{Hájek}{Hajek}, J., \enc{Šidák}{Sidak}, Z. and Sen, P. K. (1999). \emph{Theory of Rank Tests}, Second Edition. San Diego: Academic Press. Hollander, M. and Wolfe, D. A. (1999). \emph{Nonparametric Statistical Methods}, Second Edition. New York: John Wiley & Sons. } \examples{\dontshow{options(useFancyQuotes = FALSE)} ## Tritiated Water Diffusion Across Human Chorioamnion ## Hollander and Wolfe (1999, p. 110, Tab. 4.1) diffusion <- data.frame( pd = c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46, 1.15, 0.88, 0.90, 0.74, 1.21), age = factor(rep(c("At term", "12-26 Weeks"), c(10, 5))) ) ## Exact Wilcoxon-Mann-Whitney test ## Hollander and Wolfe (1999, p. 111) ## (At term - 12-26 Weeks) (wt <- wilcox_test(pd ~ age, data = diffusion, distribution = "exact", conf.int = TRUE)) ## Extract observed Wilcoxon statistic ## Note: this is the sum of the ranks for age = "12-26 Weeks" statistic(wt, type = "linear") ## Expectation, variance, two-sided pvalue and confidence interval expectation(wt) covariance(wt) pvalue(wt) confint(wt) ## For two samples, the Kruskal-Wallis test is equivalent to the W-M-W test kruskal_test(pd ~ age, data = diffusion, distribution = "exact") ## Asymptotic Fisher-Pitman test oneway_test(pd ~ age, data = diffusion) ## Approximative (Monte Carlo) Fisher-Pitman test pvalue(oneway_test(pd ~ age, data = diffusion, distribution = approximate(nresample = 10000))) ## Exact Fisher-Pitman test pvalue(ot <- oneway_test(pd ~ age, data = diffusion, distribution = "exact")) ## Plot density and distribution of the standardized test statistic op <- par(no.readonly = TRUE) # save current settings layout(matrix(1:2, nrow = 2)) s <- support(ot) d <- dperm(ot, s) p <- pperm(ot, s) plot(s, d, type = "S", xlab = "Test Statistic", ylab = "Density") plot(s, p, type = "S", xlab = "Test Statistic", ylab = "Cum. Probability") par(op) # reset ## Example data ex <- data.frame( y = c(3, 4, 8, 9, 1, 2, 5, 6, 7), x = factor(rep(c("no", "yes"), c(4, 5))) ) ## Boxplots boxplot(y ~ x, data = ex) ## Exact Brown-Mood median test with different mid-scores (mt1 <- median_test(y ~ x, data = ex, distribution = "exact")) (mt2 <- median_test(y ~ x, data = ex, distribution = "exact", mid.score = "0.5")) (mt3 <- median_test(y ~ x, data = ex, distribution = "exact", mid.score = "1")) # sign change! ## Plot density and distribution of the standardized test statistics op <- par(no.readonly = TRUE) # save current settings layout(matrix(1:3, nrow = 3)) s1 <- support(mt1); d1 <- dperm(mt1, s1) plot(s1, d1, type = "h", main = "Mid-score: 0", xlab = "Test Statistic", ylab = "Density") s2 <- support(mt2); d2 <- dperm(mt2, s2) plot(s2, d2, type = "h", main = "Mid-score: 0.5", xlab = "Test Statistic", ylab = "Density") s3 <- support(mt3); d3 <- dperm(mt3, s3) plot(s3, d3, type = "h", main = "Mid-score: 1", xlab = "Test Statistic", ylab = "Density") par(op) # reset ## Length of YOY Gizzard Shad ## Hollander and Wolfe (1999, p. 200, Tab. 6.3) yoy <- data.frame( length = c(46, 28, 46, 37, 32, 41, 42, 45, 38, 44, 42, 60, 32, 42, 45, 58, 27, 51, 42, 52, 38, 33, 26, 25, 28, 28, 26, 27, 27, 27, 31, 30, 27, 29, 30, 25, 25, 24, 27, 30), site = gl(4, 10, labels = as.roman(1:4)) ) ## Approximative (Monte Carlo) Kruskal-Wallis test kruskal_test(length ~ site, data = yoy, distribution = approximate(nresample = 10000)) ## Approximative (Monte Carlo) Nemenyi-Damico-Wolfe-Dunn test (joint ranking) ## Hollander and Wolfe (1999, p. 244) ## (where Steel-Dwass results are given) it <- independence_test(length ~ site, data = yoy, distribution = approximate(nresample = 50000), ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), xtrafo = mcp_trafo(site = "Tukey")) ## Global p-value pvalue(it) ## Sites (I = II) != (III = IV) at alpha = 0.01 (p. 244) pvalue(it, method = "single-step") # subset pivotality is violated } \keyword{htest} %% NOTE: %% The Jonckhere-Terpstra linear statistic is formulated as the sum of the %% Mann-Whitney U's for each pairwise comparison, i.e., the outcome is ranked %% separately for each comparison. The example below uses the joint ranking and %% then performs the pairwise comparisons and is *not* equivalent to the J-T %% test. %% %% ## Asymptotic Jonckheere-Terpstra test for ordered groups %% pieces <- data.frame( %% control = c(40, 35, 38, 43, 44, 41), %% rough = c(38, 40, 47, 44, 40, 42), %% accurate = c(48, 40, 45, 43, 46, 44) %% ) %% pieces <- stack(pieces) %% pieces$ind <- ordered(pieces$ind, %% levels = c("control", "rough", "accurate")) %% %% ## Look at K: the second line just sums up. %% ff <- function(x) { %% K <- multcomp::contrMat(table(x), "Tukey")[, x] %% as.vector(rep(1, nrow(K)) \%*\% K) %% } %% %% independence_test(values ~ ind, data = pieces, %% alternative = "greater", %% ytrafo = function(data) %% trafo(data, numeric_trafo = rank_trafo), %% xtrafo = function(data) %% trafo(data, ordered_trafo = ff)) coin/man/PermutationDistribution-methods.Rd0000644000176200001440000000731313401471036020617 0ustar liggesusers\name{PermutationDistribution-methods} \docType{methods} \alias{dperm} \alias{dperm-methods} \alias{dperm,NullDistribution-method} \alias{dperm,IndependenceTest-method} \alias{pperm} \alias{pperm-methods} \alias{pperm,NullDistribution-method} \alias{pperm,IndependenceTest-method} \alias{qperm} \alias{qperm-methods} \alias{qperm,NullDistribution-method} \alias{qperm,IndependenceTest-method} \alias{rperm} \alias{rperm-methods} \alias{rperm,NullDistribution-method} \alias{rperm,IndependenceTest-method} \alias{support} \alias{support-methods} \alias{support,NullDistribution-method} \alias{support,IndependenceTest-method} \title{Computation of the Permutation Distribution} \description{ Methods for computation of the density function, distribution function, quantile function, random numbers and support of the permutation distribution. } \usage{ \S4method{dperm}{NullDistribution}(object, x, \dots) \S4method{dperm}{IndependenceTest}(object, x, \dots) \S4method{pperm}{NullDistribution}(object, q, \dots) \S4method{pperm}{IndependenceTest}(object, q, \dots) \S4method{qperm}{NullDistribution}(object, p, \dots) \S4method{qperm}{IndependenceTest}(object, p, \dots) \S4method{rperm}{NullDistribution}(object, n, \dots) \S4method{rperm}{IndependenceTest}(object, n, \dots) \S4method{support}{NullDistribution}(object, \dots) \S4method{support}{IndependenceTest}(object, \dots) } \arguments{ \item{object}{ an object from which the density function, distribution function, quantile function, random numbers or support of the permutation distribution can be computed. } \item{x, q}{ a numeric vector, the quantiles for which the density function or distribution function is computed. } \item{p}{ a numeric vector, the probabilities for which the quantile function is computed. } \item{n}{ a numeric vector, the number of observations. If \code{length(n) > 1}, the length is taken to be the number required. } \item{\dots}{ further arguments to be passed to methods. } } \details{ The methods \code{dperm}, \code{pperm}, \code{qperm}, \code{rperm} and \code{support} compute the density function, distribution function, quantile function, random deviates and support, respectively, of the permutation distribution. } \value{ The density function, distribution function, quantile function, random deviates or support of the permutation distribution computed from \code{object}. A numeric vector. } \note{ The density of asymptotic permutation distributions for maximum-type tests or exact permutation distributions obtained by the split-up algoritm is reported as \code{NA}. The quantile function of asymptotic permutation distributions for maximum-type tests cannot be computed for \code{p} less than 0.5, due to limitations in the \pkg{mvtnorm} package. The support of exact permutation distributions obtained by the split-up algorithm is reported as \code{NA}. In versions of \pkg{coin} prior to 1.1-0, the support of asymptotic permutation distributions was given as an interval containing 99.999 \% of the probability mass. It is now reported as \code{NA}. } \examples{ ## Two-sample problem dta <- data.frame( y = rnorm(20), x = gl(2, 10) ) ## Exact Ansari-Bradley test at <- ansari_test(y ~ x, data = dta, distribution = "exact") ## Support of the exact distribution of the Ansari-Bradley statistic supp <- support(at) ## Density of the exact distribution of the Ansari-Bradley statistic dens <- dperm(at, x = supp) ## Plotting the density plot(supp, dens, type = "s") ## 95\% quantile qperm(at, p = 0.95) ## One-sided p-value pperm(at, q = statistic(at)) ## Random number generation rperm(at, n = 5) } \keyword{methods} \keyword{htest} \keyword{distribution} coin/man/NullDistribution-class.Rd0000644000176200001440000001177514113674115016677 0ustar liggesusers\name{NullDistribution-class} \docType{class} \alias{NullDistribution-class} \alias{ApproxNullDistribution-class} \alias{AsymptNullDistribution-class} \alias{ExactNullDistribution-class} \title{Class \code{"NullDistribution"} and Its Subclasses} \description{ Objects of class \code{"NullDistribution"} and its subclasses \code{"ApproxNullDistribution"}, \code{"AsymptNullDistribution"} and \code{"ExactNullDistribution"} represent the reference distribution. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("NullDistribution", \dots), new("ApproxNullDistribution", \dots), new("AsymptNullDistribution", \dots)} and \preformatted{ new("ExactNullDistribution", \dots).} } \section{Slots}{ For objects of classes \code{"NullDistribution"}, \code{"ApproxNullDistribution"}, \code{"AsymptNullDistribution"} or \code{"ExactNullDistribution"}: \describe{ \item{\code{name}:}{ Object of class \code{"character"}. The name of the reference distribution. } \item{\code{p}:}{ Object of class \code{"function"}. The distribution function of the reference distribution. } \item{\code{pvalue}:}{ Object of class \code{"function"}. The \eqn{p}-value function of the reference distribution. } \item{\code{parameters}:}{ Object of class \code{"list"}. Additional parameters. } \item{\code{support}:}{ Object of class \code{"function"}. The support of the reference distribution. } \item{\code{d}:}{ Object of class \code{"function"}. The density function of the reference distribution. } \item{\code{q}:}{ Object of class \code{"function"}. The quantile function of the reference distribution. } \item{\code{midpvalue}:}{ Object of class \code{"function"}. The mid-\eqn{p}-value function of the reference distribution. } \item{\code{pvalueinterval}:}{ Object of class \code{"function"}. The \eqn{p}-value interval function of the reference distribution. } \item{\code{size}:}{ Object of class \code{"function"}. The size function of the reference distribution. } } Additionally, for objects of classes \code{"ApproxNullDistribution"} or \code{"AsymptNullDistribution"}: \describe{ \item{\code{seed}:}{ Object of class \code{"integer"}. The random number generator state (i.e., the value of \code{.Random.seed}). } } Additionally, for objects of class \code{"ApproxNullDistribution"}: \describe{ \item{\code{nresample}:}{ Object of class \code{"numeric"}. The number of Monte Carlo replicates. } } } \section{Extends}{ For objects of class \code{"NullDistribution"}: \cr Class \code{"\linkS4class{PValue}"}, directly. For objects of classes \code{"ApproxNullDistribution"}, \code{"AsymptNullDistribution"} or \code{"ExactNullDistribution"}: \cr Class \code{"NullDistribution"}, directly. \cr Class \code{"\linkS4class{PValue}"}, by class \code{"NullDistribution"}, distance 2. } \section{Known Subclasses}{ For objects of class \code{"NullDistribution"}: \cr Class \code{"ApproxNullDistribution"}, directly. \cr Class \code{"AsymptNullDistribution"}, directly. \cr Class \code{"ExactNullDistribution"}, directly. } \section{Methods}{ \describe{ \item{dperm}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{dperm}} for details. } \item{midpvalue}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{midpvalue}} for details. } \item{midpvalue}{ \code{signature(object = "ApproxNullDistribution")}: See the documentation for \code{\link{midpvalue}} for details. } \item{pperm}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{pperm}} for details. } \item{pvalue}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{pvalue}} for details. } \item{pvalue}{ \code{signature(object = "ApproxNullDistribution")}: See the documentation for \code{\link{pvalue}} for details. } \item{pvalue_interval}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{pvalue_interval}} for details. } \item{qperm}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{qperm}} for details. } \item{rperm}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{rperm}} for details. } \item{size}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{size}} for details. } \item{support}{ \code{signature(object = "NullDistribution")}: See the documentation for \code{\link{support}} for details. } } } \keyword{classes} coin/man/mercuryfish.Rd0000644000176200001440000000621513401471036014607 0ustar liggesusers\name{mercuryfish} \docType{data} \alias{mercuryfish} \title{Chromosomal Effects of Mercury-Contaminated Fish Consumption} \description{ The mercury level in blood, the proportion of cells with abnormalities, and the proportion of cells with chromosome aberrations in consumers of mercury-contaminated fish and a control group. } \usage{mercuryfish} \format{ A data frame with 39 observations on 4 variables. \describe{ \item{\code{group}}{ a factor with levels \code{"control"} and \code{"exposed"}. } \item{\code{mercury}}{ mercury level in blood. } \item{\code{abnormal}}{ the proportion of cells with structural abnormalities. } \item{\code{ccells}}{ the proportion of \eqn{C_u} cells, i.e., cells with asymmetrical or incomplete-symmetrical chromosome aberrations. } } } \details{ Control subjects (\code{"control"}) and subjects who ate contaminated fish for more than three years (\code{"exposed"}) are under study. Rosenbaum (1994) proposed a coherence criterion defining a partial ordering, i.e., an observation is smaller than another when all responses are smaller, and a score reflecting the \dQuote{ranking} is attached to each observation. The corresponding partially ordered set (POSET) test can be used to test if the distribution of the scores differ between the groups. Alternatively, a multivariate test can be applied. } \source{ Skerfving, S., Hansson, K., Mangs, C., Lindsten, J. and Ryman, N. (1974). Methylmercury-induced chromosome damage in men. \emph{Environmental Research} \bold{7}(1), 83--98. \doi{10.1016/0013-9351(74)90078-4} } \references{ Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} Rosenbaum, P. R. (1994). Coherence in observational studies. \emph{Biometrics} \bold{50}(2), 368--374. \doi{10.2307/2533380} } \examples{ ## Coherence criterion coherence <- function(data) { x <- as.matrix(data) matrix(apply(x, 1, function(y) sum(colSums(t(x) < y) == ncol(x)) - sum(colSums(t(x) > y) == ncol(x))), ncol = 1) } ## Asymptotic POSET test poset <- independence_test(mercury + abnormal + ccells ~ group, data = mercuryfish, ytrafo = coherence) ## Linear statistic (T in the notation of Rosenbaum, 1994) statistic(poset, type = "linear") ## Expectation expectation(poset) ## Variance ## Note: typo in Rosenbaum (1994, p. 371, Sec. 2, last paragraph) variance(poset) ## Standardized statistic statistic(poset) ## P-value pvalue(poset) ## Exact POSET test independence_test(mercury + abnormal + ccells ~ group, data = mercuryfish, ytrafo = coherence, distribution = "exact") ## Asymptotic multivariate test mvtest <- independence_test(mercury + abnormal + ccells ~ group, data = mercuryfish) ## Global p-value pvalue(mvtest) ## Single-step adjusted p-values pvalue(mvtest, method = "single-step") ## Step-down adjusted p-values pvalue(mvtest, method = "step-down") } \keyword{datasets} coin/man/SymmetryTest.Rd0000644000176200001440000002435313401471036014743 0ustar liggesusers\name{SymmetryTest} \alias{symmetry_test} \alias{symmetry_test.formula} \alias{symmetry_test.table} \alias{symmetry_test.SymmetryProblem} \title{General Symmetry Test} \description{ Testing the symmetry of set of repeated measurements variables measured on arbitrary scales in a complete block design. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{symmetry_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{symmetry_test}{table}(object, \dots) \method{symmetry_test}{SymmetryProblem}(object, teststat = c("maximum", "quadratic", "scalar"), distribution = c("asymptotic", "approximate", "exact", "none"), alternative = c("two.sided", "less", "greater"), xtrafo = trafo, ytrafo = trafo, scores = NULL, check = NULL, paired = FALSE, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y1 + ... + yq ~ x | block} where \code{y1}, \dots, \code{yq} are measured on arbitrary scales (nominal, ordinal or continuous with or without censoring), \code{x} is a factor and \code{block} is an optional factor (which is generated automatically if omitted). } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from classes \code{"table"} (with identical \code{dimnames} components) or \code{"\linkS4class{SymmetryProblem}"}. } \item{teststat}{ a character, the type of test statistic to be applied: either a maximum statistic (\code{"maximum"}, default), a quadratic form (\code{"quadratic"}) or a standardized scalar test statistic (\code{"scalar"}). } \item{distribution}{ a character, the conditional null distribution of the test statistic can be approximated by its asymptotic distribution (\code{"asymptotic"}, default) or via Monte Carlo resampling (\code{"approximate"}). Alternatively, the functions \code{\link{asymptotic}} or \code{\link{approximate}} can be used. For univariate two-sample problems, \code{"exact"} or use of the function \code{\link{exact}} computes the exact distribution. Computation of the null distribution can be suppressed by specifying \code{"none"}. It is also possible to specify a function with one argument (an object inheriting from \code{"\linkS4class{IndependenceTestStatistic}"}) that returns an object of class \code{"\linkS4class{NullDistribution}"}. } \item{alternative}{ a character, the alternative hypothesis: either \code{"two.sided"} (default), \code{"greater"} or \code{"less"}. } \item{xtrafo}{ a function of transformations to be applied to the factor \code{x} supplied in \code{formula}; see \sQuote{Details}. Defaults to \code{\link{trafo}}. } \item{ytrafo}{ a function of transformations to be applied to the variables \code{y1}, \dots, \code{yq} supplied in \code{formula}; see \sQuote{Details}. Defaults to \code{\link{trafo}}. } \item{scores}{ a named list of scores to be attached to ordered factors; see \sQuote{Details}. Defaults to \code{NULL}, implying equally spaced scores. } \item{check}{ a function to be applied to objects of class \code{"\linkS4class{IndependenceTest}"} in order to check for specific properties of the data. Defaults to \code{NULL}. } \item{paired}{ a logical, indicating that paired data have been transformed in such a way that the (unstandardized) linear statistic is the sum of the absolute values of the positive differences between the paired observations. Defaults to \code{FALSE}. } \item{\dots}{ further arguments to be passed to or from other methods (currently ignored). } } \details{ \code{symmetry_test} provides a general symmetry test for a set of variables measured on arbitrary scales. This function is based on the general framework for conditional inference procedures proposed by Strasser and Weber (1999). The salient parts of the Strasser-Weber framework are elucidated by Hothorn \emph{et al.} (2006) and a thorough description of the software implementation is given by Hothorn \emph{et al.} (2008). The null hypothesis of symmetry is tested. The response variables and the measurement conditions are given by \code{y1}, \dots, \code{yq} and \code{x}, respectively, and \code{block} is a factor where each level corresponds to exactly one subject with repeated measurements. A vector of case weights, e.g., observation counts, can be supplied through the \code{weights} argument and the type of test statistic is specified by the \code{teststat} argument. Influence and regression functions, i.e., transformations of \code{y1}, \dots, \code{yq} and \code{x}, are specified by the \code{ytrafo} and \code{xtrafo} arguments respectively; see \code{\link{trafo}} for the collection of transformation functions currently available. This allows for implementation of both novel and familiar test statistics, e.g., the McNemar test, the Cochran \eqn{Q} test, the Wilcoxon signed-rank test and the Friedman test. Furthermore, multivariate extensions such as the multivariate Friedman test (Gerig, 1969; Puri and Sen, 1971) can be implemented without much effort (see \sQuote{Examples}). If, say, \code{y1} and/or \code{x} are ordered factors, the default scores, \code{1:nlevels(y1)} and \code{1:nlevels(x)} respectively, can be altered using the \code{scores} argument; this argument can also be used to coerce nominal factors to class \code{"ordered"}. For example, when \code{y1} is an ordered factor with four levels and \code{x} is a nominal factor with three levels, \code{scores = list(y1 = c(1, 3:5), x = c(1:2, 4))} supplies the scores to be used. For ordered alternatives the scores must be monotonic, but non-montonic scores are also allowed for testing against, e.g., umbrella alternatives. The length of the score vector must be equal to the number of factor levels. The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ Starting with \pkg{coin} version 1.1-0, maximum statistics and quadratic forms can no longer be specified using \code{teststat = "maxtype"} and \code{teststat = "quadtype"} respectively (as was used in versions prior to 0.4-5). } \references{ Gerig, T. (1969). A multivariate extension of Friedman's \eqn{\chi^2_r}{chi^2_r}-test. \emph{Journal of the American Statistical Association} \bold{64}(328), 1595--1608. \doi{10.1080/01621459.1969.10501079} Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2008). Implementing a class of permutation tests: The coin package. \emph{Journal of Statistical Software} \bold{28}(8), 1--23. \doi{10.18637/jss.v028.i08} Puri, M. L. and Sen, P. K. (1971). \emph{Nonparametric Methods in Multivariate Analysis}. New York: John Wiley & Sons. Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. \emph{Mathematical Methods of Statistics} \bold{8}(2), 220--250. } \examples{ ## One-sided exact Fisher-Pitman test for paired observations y1 <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) y2 <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) dta <- data.frame( y = c(y1, y2), x = gl(2, length(y1)), block = factor(rep(seq_along(y1), 2)) ) symmetry_test(y ~ x | block, data = dta, distribution = "exact", alternative = "greater") ## Alternatively: transform data and set 'paired = TRUE' delta <- y1 - y2 y <- as.vector(rbind(abs(delta) * (delta >= 0), abs(delta) * (delta < 0))) x <- factor(rep(0:1, length(delta)), labels = c("pos", "neg")) block <- gl(length(delta), 2) symmetry_test(y ~ x | block, distribution = "exact", alternative = "greater", paired = TRUE) ### Example data ### Gerig (1969, p. 1597) gerig <- data.frame( y1 = c( 0.547, 1.811, 2.561, 1.706, 2.509, 1.414, -0.288, 2.524, 3.310, 1.417, 0.703, 0.961, 0.878, 0.094, 1.682, -0.680, 2.077, 3.181, 0.056, 0.542, 2.983, 0.711, 0.269, 1.662, -1.335, 1.545, 2.920, 1.635, 0.200, 2.065), y2 = c(-0.575, 1.840, 2.399, 1.252, 1.574, 3.059, -0.310, 1.553, 0.560, 0.932, 1.390, 3.083, 0.819, 0.045, 3.348, 0.497, 1.747, 1.355, -0.285, 0.760, 2.332, 0.089, 1.076, 0.960, -0.349, 1.471, 4.121, 0.845, 1.480, 3.391), x = factor(rep(1:3, 10)), b = factor(rep(1:10, each = 3)) ) ### Asymptotic multivariate Friedman test ### Gerig (1969, p. 1599) symmetry_test(y1 + y2 ~ x | b, data = gerig, teststat = "quadratic", ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo, block = gerig$b)) # L_n = 17.238 ### Asymptotic multivariate Page test (st <- symmetry_test(y1 + y2 ~ x | b, data = gerig, ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo, block = gerig$b), scores = list(x = 1:3))) pvalue(st, method = "step-down") } \keyword{htest} coin/man/statistic-methods.Rd0000644000176200001440000000575613715224731015736 0ustar liggesusers\name{statistic-methods} \docType{methods} \alias{statistic} \alias{statistic-methods} \alias{statistic,IndependenceLinearStatistic-method} \alias{statistic,IndependenceTestStatistic-method} \alias{statistic,IndependenceTest-method} \title{Extraction of the Test Statistic and the Linear Statistic} \description{ Methods for extraction of the test statistic and the linear statistic. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \S4method{statistic}{IndependenceLinearStatistic}(object, type = c("test", "linear", "centered", "standardized"), partial = FALSE, \dots) \S4method{statistic}{IndependenceTestStatistic}(object, type = c("test", "linear", "centered", "standardized"), partial = FALSE, \dots) \S4method{statistic}{IndependenceTest}(object, type = c("test", "linear", "centered", "standardized"), partial = FALSE, \dots) } \arguments{ \item{object}{ an object from which the test statistic or the linear statistic can be extracted. } \item{type}{ a character string indicating the type of statistic: either \code{"test"} (default) for the test statistic, \code{"linear"} for the unstandardized linear statistic, \code{"centered"} for the centered linear statistic or \code{"standardized"} for the standardized linear statistic. } \item{partial}{ a logical indicating that the partial linear statistic for each block should be extracted. Defaults to \code{FALSE}. } \item{\dots}{ further arguments (currently ignored). } } \details{ The method \code{statistic} extracts the univariate test statistic or the, possibly multivariate, linear statistic in its unstandardized, centered or standardized form. The test statistic (\code{type = "test"}) is returned by default. The unstandardized, centered or standardized linear statistic is obtained by setting \code{type} to \code{"linear"}, \code{"centered"} or \code{"standardized"}, respectively. For tests of conditional independence within blocks, the partial linear statistic for each block is obtained by setting \code{partial = TRUE}. } \value{ The test statistic or the unstandardized, centered or standardized linear statistic extracted from \code{object}. A numeric vector, matrix or array. } \examples{ ## Example data dta <- data.frame( y = gl(4, 5), x = gl(5, 4) ) ## Asymptotic Cochran-Mantel-Haenszel Test ct <- cmh_test(y ~ x, data = dta) ## Test statistic statistic(ct) ## The unstandardized linear statistic... statistic(ct, type = "linear") ## ...is identical to the contingency table xtabs(~ x + y, data = dta) ## The centered linear statistic... statistic(ct, type = "centered") ## ...is identical to statistic(ct, type = "linear") - expectation(ct) ## The standardized linear statistic, illustrating departures from the null ## hypothesis of independence... statistic(ct, type = "standardized") ## ...is identical to (statistic(ct, type = "linear") - expectation(ct)) / sqrt(variance(ct)) } \keyword{methods} coin/man/jobsatisfaction.Rd0000644000176200001440000000421413401471036015426 0ustar liggesusers\name{jobsatisfaction} \docType{data} \alias{jobsatisfaction} \encoding{UTF-8} \title{Income and Job Satisfaction} \description{ Income and job satisfaction by gender. } \usage{jobsatisfaction} \format{ A contingency table with 104 observations on 3 variables. \describe{ \item{\code{Income}}{ a factor with levels \code{"<5000"}, \code{"5000-15000"}, \code{"15000-25000"} and \code{">25000"}. } \item{\code{Job.Satisfaction}}{ a factor with levels \code{"Very Dissatisfied"}, \code{"A Little Satisfied"}, \code{"Moderately Satisfied"} and \code{"Very Satisfied"}. } \item{\code{Gender}}{ a factor with levels \code{"Female"} and \code{"Male"}. } } } \details{ This data set was given in Agresti (2002, p. 288, Tab. 7.8). Winell and \enc{Lindbäck}{Lindbaeck} (2018) used the data to demonstrate a score-independent test for ordered categorical data. } \source{ Agresti, A. (2002). \emph{Categorical Data Analysis}, Second Edition. Hoboken, New Jersey: John Wiley & Sons. } \references{ Winell, H. and \enc{Lindbäck}{Lindbaeck}, J. (2018). A general score-independent test for order-restricted inference. \emph{Statistics in Medicine} \bold{37}(21), 3078--3090. \doi{10.1002/sim.7690} } \examples{ ## Approximative (Monte Carlo) linear-by-linear association test lbl_test(jobsatisfaction, distribution = approximate(nresample = 10000)) \dontrun{ ## Approximative (Monte Carlo) score-independent test ## Winell and Lindbaeck (2018) (it <- independence_test(jobsatisfaction, distribution = approximate(nresample = 10000), xtrafo = function(data) trafo(data, factor_trafo = function(x) zheng_trafo(as.ordered(x))), ytrafo = function(data) trafo(data, factor_trafo = function(y) zheng_trafo(as.ordered(y))))) ## Extract the "best" set of scores ss <- statistic(it, type = "standardized") idx <- which(abs(ss) == max(abs(ss)), arr.ind = TRUE) ss[idx[1], idx[2], drop = FALSE]} } \keyword{datasets} coin/man/vision.Rd0000644000176200001440000000423613401471036013557 0ustar liggesusers\name{vision} \docType{data} \alias{vision} \encoding{UTF-8} \title{Unaided Distance Vision} \description{ Assessment of unaided distance vision of women in Britain. } \usage{vision} \format{ A contingency table with 7477 observations on 2 variables. \describe{ \item{\code{Right.Eye}}{ a factor with levels \code{"Highest Grade"}, \code{"Second Grade"}, \code{"Third Grade"} and \code{"Lowest Grade"}. } \item{\code{Left.Eye}}{ a factor with levels \code{"Highest Grade"}, \code{"Second Grade"}, \code{"Third Grade"} and \code{"Lowest Grade"}. } } } \details{ Paired ordered categorical data from case-records of eye-testing of 7477 women aged 30--39 years employed by Royal Ordnance Factories in Britain during 1943--46, as given by Stuart (1953). This data set was used by Stuart (1955) to illustrate a test of marginal homogeneity. Winell and \enc{Lindbäck}{Lindbaeck} (2018) also used the data, demonstrating a score-independent test for ordered categorical data. } \source{ Stuart, A. (1953). The estimation and comparison of strengths of association in contingency tables. \emph{Biometrika} \bold{40}(1/2), 105--110. \doi{10.2307/2333101} } \references{ Stuart, A. (1955). A test for homogeneity of the marginal distributions in a two-way classification. \emph{Biometrika} \bold{42}(3/4), 412--416. \doi{10.1093/biomet/42.3-4.412} Winell, H. and \enc{Lindbäck}{Lindbaeck}, J. (2018). A general score-independent test for order-restricted inference. \emph{Statistics in Medicine} \bold{37}(21), 3078--3090. \doi{10.1002/sim.7690} } \examples{ ## Asymptotic Stuart test (Q = 11.96) diag(vision) <- 0 # speed-up mh_test(vision) ## Asymptotic score-independent test ## Winell and Lindbaeck (2018) (st <- symmetry_test(vision, ytrafo = function(data) trafo(data, factor_trafo = function(y) zheng_trafo(as.ordered(y))))) ss <- statistic(st, type = "standardized") idx <- which(abs(ss) == max(abs(ss)), arr.ind = TRUE) ss[idx[1], idx[2], drop = FALSE] } \keyword{datasets} coin/man/malformations.Rd0000644000176200001440000000766313401471036015132 0ustar liggesusers\name{malformations} \docType{data} \alias{malformations} \encoding{UTF-8} \title{Maternal Drinking and Congenital Sex Organ Malformation} \description{ A subset of data from a study on the relationship between maternal alcohol consumption and congenital malformations. } \usage{malformations} \format{ A data frame with 32574 observations on 2 variables. \describe{ \item{\code{consumption}}{ alcohol consumption, an ordered factor with levels \code{"0"}, \code{"<1"}, \code{"1-2"}, \code{"3-5"} and \code{">=6"}. } \item{\code{malformation}}{ congenital sex organ malformation, a factor with levels \code{"Present"} and \code{"Absent"}. } } } \details{ Data from a prospective study undertaken to determine whether moderate or light drinking during the first trimester of pregnancy increases the risk for congenital malformations (Mills and Graubard, 1987). The subset given here concerns only sex organ malformation (Mills and Graubard, 1987, Tab. 4). This data set was used by Graubard and Korn (1987) to illustrate that different choices of scores for ordinal variables can lead to conflicting conclusions. Zheng (2008) also used the data, demonstrating two different score-independent tests for ordered categorical data; see also Winell and \enc{Lindbäck}{Lindbaeck} (2018). } \source{ Mills, J. L. and Graubard, B. I. (1987). Is moderate drinking during pregnancy associated with an increased risk for malformations? \emph{Pediatrics} \bold{80}(3), 309--314. } \references{ Graubard, B. I. and Korn, E. L. (1987). Choice of column scores for testing independence in ordered \eqn{2 \times K}{2 x K} contingency tables. \emph{Biometrics} \bold{43}(2), 471--476. \doi{10.2307/2531828} Winell, H. and \enc{Lindbäck}{Lindbaeck}, J. (2018). A general score-independent test for order-restricted inference. \emph{Statistics in Medicine} \bold{37}(21), 3078--3090. \doi{10.1002/sim.7690} Zheng, G. (2008). Analysis of ordered categorical data: Two score-independent approaches. \emph{Biometrics} \bold{64}(4), 1276–-1279. \doi{10.1111/j.1541-0420.2008.00992.x} } \examples{ ## Graubard and Korn (1987, Tab. 3) ## One-sided approximative (Monte Carlo) Cochran-Armitage test ## Note: midpoint scores (p < 0.05) midpoints <- c(0, 0.5, 1.5, 4.0, 7.0) chisq_test(malformation ~ consumption, data = malformations, distribution = approximate(nresample = 1000), alternative = "greater", scores = list(consumption = midpoints)) ## One-sided approximative (Monte Carlo) Cochran-Armitage test ## Note: midrank scores (p > 0.05) midranks <- c(8557.5, 24375.5, 32013.0, 32473.0, 32555.5) chisq_test(malformation ~ consumption, data = malformations, distribution = approximate(nresample = 1000), alternative = "greater", scores = list(consumption = midranks)) ## One-sided approximative (Monte Carlo) Cochran-Armitage test ## Note: equally spaced scores (p > 0.05) chisq_test(malformation ~ consumption, data = malformations, distribution = approximate(nresample = 1000), alternative = "greater") \dontrun{ ## One-sided approximative (Monte Carlo) score-independent test ## Winell and Lindbaeck (2018) (it <- independence_test(malformation ~ consumption, data = malformations, distribution = approximate(nresample = 1000, parallel = "snow", ncpus = 8), alternative = "greater", xtrafo = function(data) trafo(data, ordered_trafo = zheng_trafo))) ## Extract the "best" set of scores ss <- statistic(it, type = "standardized") idx <- which(ss == max(ss), arr.ind = TRUE) ss[idx[1], idx[2], drop = FALSE]} } \keyword{datasets} coin/man/neuropathy.Rd0000644000176200001440000000374313401471036014450 0ustar liggesusers\name{neuropathy} \docType{data} \alias{neuropathy} \title{Acute Painful Diabetic Neuropathy} \description{ The logarithm of the ratio of pain scores measured at baseline and after four weeks in a control group and a treatment group. } \usage{neuropathy} \format{ A data frame with 58 observations on 2 variables. \describe{ \item{\code{pain}}{ pain scores: ln(baseline / final). } \item{\code{group}}{ a factor with levels \code{"control"} and \code{"treat"}. } } } \details{ Data from Conover and Salsburg (1988, Tab. 1). } \source{ Conover, W. J. and Salsburg, D. S. (1988). Locally most powerful tests for detecting treatment effects when only a subset of patients can be expected to \dQuote{respond} to treatment. \emph{Biometrics} \bold{44}(1), 189--196. \doi{10.2307/2531906} } \examples{ ## Conover and Salsburg (1988, Tab. 2) ## One-sided approximative Fisher-Pitman test oneway_test(pain ~ group, data = neuropathy, alternative = "less", distribution = approximate(nresample = 10000)) ## One-sided approximative Wilcoxon-Mann-Whitney test wilcox_test(pain ~ group, data = neuropathy, alternative = "less", distribution = approximate(nresample = 10000)) ## One-sided approximative Conover-Salsburg test oneway_test(pain ~ group, data = neuropathy, alternative = "less", distribution = approximate(nresample = 10000), ytrafo = function(data) trafo(data, numeric_trafo = consal_trafo)) ## One-sided approximative maximum test for a range of 'a' values it <- independence_test(pain ~ group, data = neuropathy, alternative = "less", distribution = approximate(nresample = 10000), ytrafo = function(data) trafo(data, numeric_trafo = function(y) consal_trafo(y, a = 2:7))) pvalue(it, method = "single-step") } \keyword{datasets} coin/man/ScaleTests.Rd0000644000176200001440000002171513401471036014323 0ustar liggesusers\name{ScaleTests} \alias{taha_test} \alias{taha_test.formula} \alias{taha_test.IndependenceProblem} \alias{klotz_test} \alias{klotz_test.formula} \alias{klotz_test.IndependenceProblem} \alias{mood_test} \alias{mood_test.formula} \alias{mood_test.IndependenceProblem} \alias{ansari_test} \alias{ansari_test.formula} \alias{ansari_test.IndependenceProblem} \alias{fligner_test} \alias{fligner_test.formula} \alias{fligner_test.IndependenceProblem} \alias{conover_test} \alias{conover_test.formula} \alias{conover_test.IndependenceProblem} \concept{Taha test} \concept{Klotz test} \concept{Mood test} \concept{Ansari-Bradley test} \concept{Fligner-Killeen test} \concept{Conover-Iman test} \encoding{UTF-8} \title{Two- and \eqn{K}-Sample Scale Tests} \description{ Testing the equality of the distributions of a numeric response variable in two or more independent groups against scale alternatives. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{taha_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{taha_test}{IndependenceProblem}(object, conf.int = FALSE, conf.level = 0.95, \dots) \method{klotz_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{klotz_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "average-scores"), conf.int = FALSE, conf.level = 0.95, \dots) \method{mood_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{mood_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "average-scores"), conf.int = FALSE, conf.level = 0.95, \dots) \method{ansari_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{ansari_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "average-scores"), conf.int = FALSE, conf.level = 0.95, \dots) \method{fligner_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{fligner_test}{IndependenceProblem}(object, ties.method = c("mid-ranks", "average-scores"), conf.int = FALSE, conf.level = 0.95, \dots) \method{conover_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{conover_test}{IndependenceProblem}(object, conf.int = FALSE, conf.level = 0.95, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} is a numeric variable, \code{x} is a factor and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from class \code{"\linkS4class{IndependenceProblem}"}. } \item{conf.int}{ a logical indicating whether a confidence interval for the ratio of scales should be computed. Defaults to \code{FALSE}. } \item{conf.level}{ a numeric, confidence level of the interval. Defaults to \code{0.95}. } \item{ties.method}{ a character, the method used to handle ties: the score generating function either uses mid-ranks (\code{"mid-ranks"}, default) or averages the scores of randomly broken ties (\code{"average-scores"}). } \item{\dots}{ further arguments to be passed to \code{\link{independence_test}}. } } \details{ \code{taha_test}, \code{klotz_test}, \code{mood_test}, \code{ansari_test}, \code{fligner_test} and \code{conover_test} provide the Taha test, the Klotz test, the Mood test, the Ansari-Bradley test, the Fligner-Killeen test and the Conover-Iman test. A general description of these methods is given by Hollander and Wolfe (1999). For the adjustment of scores for tied values see \enc{Hájek}{Hajek}, \enc{Šidák}{Sidak} and Sen (1999, pp. 133--135). The null hypothesis of equality, or conditional equality given \code{block}, of the distribution of \code{y} in the groups defined by \code{x} is tested against scale alternatives. In the two-sample case, the two-sided null hypothesis is \eqn{H_0\!: V(Y_1) / V(Y_2) = 1}{H_0: V(Y_1) / V(Y_2) = 1}, where \eqn{V(Y_s)} is the variance of the responses in the \eqn{s}th sample. In case \code{alternative = "less"}, the null hypothesis is \eqn{H_0\!: V(Y_1) / V(Y_2) \ge 1}{H_0: V(Y_1) / V(Y_2) >= 1}. When \code{alternative = "greater"}, the null hypothesis is \eqn{H_0\!: V(Y_1) / V(Y_2) \le 1}{H_0: V(Y_1) / V(Y_2) <= 1}. Confidence intervals for the ratio of scales are available and computed according to Bauer (1972). The Fligner-Killeen test uses median centering in each of the samples, as suggested by Conover, Johnson and Johnson (1981), whereas the Conover-Iman test, following Conover and Iman (1978), uses mean centering in each of the samples. The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. Confidence intervals can be extracted by \link[stats]{confint}. } \note{ In the two-sample case, a \emph{large} value of the Ansari-Bradley statistic indicates that sample 1 is \emph{less} variable than sample 2, whereas a \emph{large} value of the statistics due to Taha, Klotz, Mood, Fligner-Killeen, and Conover-Iman indicate that sample 1 is \emph{more} variable than sample 2. } \references{ Bauer, D. F. (1972). Constructing confidence sets using rank statistics. \emph{Journal of the American Statistical Association} \bold{67}(339), 687--690. \doi{10.1080/01621459.1972.10481279} Conover, W. J. and Iman, R. L. (1978). Some exact tables for the squared ranks test. \emph{Communications in Statistics -- Simulation and Computation} \bold{7}(5), 491--513. \doi{10.1080/03610917808812093} Conover, W. J., Johnson, M. E. and Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. \emph{Technometrics} \bold{23}(4), 351--361. \doi{10.1080/00401706.1981.10487680} \enc{Hájek}{Hajek}, J., \enc{Šidák}{Sidak}, Z. and Sen, P. K. (1999). \emph{Theory of Rank Tests}, Second Edition. San Diego: Academic Press. Hollander, M. and Wolfe, D. A. (1999). \emph{Nonparametric Statistical Methods}, Second Edition. York: John Wiley & Sons. } \examples{ ## Serum Iron Determination Using Hyland Control Sera ## Hollander and Wolfe (1999, p. 147, Tab 5.1) sid <- data.frame( serum = c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99, 101, 96, 97, 102, 107, 113, 116, 113, 110, 98, 107, 108, 106, 98, 105, 103, 110, 105, 104, 100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99), method = gl(2, 20, labels = c("Ramsay", "Jung-Parekh")) ) ## Asymptotic Ansari-Bradley test ansari_test(serum ~ method, data = sid) ## Exact Ansari-Bradley test pvalue(ansari_test(serum ~ method, data = sid, distribution = "exact")) ## Platelet Counts of Newborn Infants ## Hollander and Wolfe (1999, p. 171, Tab. 5.4) platelet <- data.frame( counts = c(120, 124, 215, 90, 67, 95, 190, 180, 135, 399, 12, 20, 112, 32, 60, 40), treatment = factor(rep(c("Prednisone", "Control"), c(10, 6))) ) ## Approximative (Monte Carlo) Lepage test ## Hollander and Wolfe (1999, p. 172) lepage_trafo <- function(y) cbind("Location" = rank_trafo(y), "Scale" = ansari_trafo(y)) independence_test(counts ~ treatment, data = platelet, distribution = approximate(nresample = 10000), ytrafo = function(data) trafo(data, numeric_trafo = lepage_trafo), teststat = "quadratic") ## Why was the null hypothesis rejected? ## Note: maximum statistic instead of quadratic form ltm <- independence_test(counts ~ treatment, data = platelet, distribution = approximate(nresample = 10000), ytrafo = function(data) trafo(data, numeric_trafo = lepage_trafo)) ## Step-down adjustment suggests a difference in location pvalue(ltm, method = "step-down") ## The same results are obtained from the simple Sidak-Holm procedure since the ## correlation between Wilcoxon and Ansari-Bradley test statistics is zero cov2cor(covariance(ltm)) pvalue(ltm, method = "step-down", distribution = "marginal", type = "Sidak") } \keyword{htest} coin/man/IndependenceTest.Rd0000644000176200001440000002507313401471036015473 0ustar liggesusers\name{IndependenceTest} \alias{independence_test} \alias{independence_test.formula} \alias{independence_test.table} \alias{independence_test.IndependenceProblem} \title{General Independence Test} \description{ Testing the independence of two sets of variables measured on arbitrary scales. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{independence_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{independence_test}{table}(object, \dots) \method{independence_test}{IndependenceProblem}(object, teststat = c("maximum", "quadratic", "scalar"), distribution = c("asymptotic", "approximate", "exact", "none"), alternative = c("two.sided", "less", "greater"), xtrafo = trafo, ytrafo = trafo, scores = NULL, check = NULL, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y1 + ... + yq ~ x1 + ... + xp | block} where \code{y1}, \dots, \code{yq} and \code{x1}, \dots, \code{xp} are measured on arbitrary scales (nominal, ordinal or continuous with or without censoring) and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from classes \code{"table"} or \code{"\linkS4class{IndependenceProblem}"}. } \item{teststat}{ a character, the type of test statistic to be applied: either a maximum statistic (\code{"maximum"}, default), a quadratic form (\code{"quadratic"}) or a standardized scalar test statistic (\code{"scalar"}). } \item{distribution}{ a character, the conditional null distribution of the test statistic can be approximated by its asymptotic distribution (\code{"asymptotic"}, default) or via Monte Carlo resampling (\code{"approximate"}). Alternatively, the functions \code{\link{asymptotic}} or \code{\link{approximate}} can be used. For univariate two-sample problems, \code{"exact"} or use of the function \code{\link{exact}} computes the exact distribution. Computation of the null distribution can be suppressed by specifying \code{"none"}. It is also possible to specify a function with one argument (an object inheriting from \code{"\linkS4class{IndependenceTestStatistic}"}) that returns an object of class \code{"\linkS4class{NullDistribution}"}. } \item{alternative}{ a character, the alternative hypothesis: either \code{"two.sided"} (default), \code{"greater"} or \code{"less"}. } \item{xtrafo}{ a function of transformations to be applied to the variables \code{x1}, \dots, \code{xp} supplied in \code{formula}; see \sQuote{Details}. Defaults to \code{\link{trafo}}. } \item{ytrafo}{ a function of transformations to be applied to the variables \code{y1}, \dots, \code{yq} supplied in \code{formula}; see \sQuote{Details}. Defaults to \code{\link{trafo}}. } \item{scores}{ a named list of scores to be attached to ordered factors; see \sQuote{Details}. Defaults to \code{NULL}, implying equally spaced scores. } \item{check}{ a function to be applied to objects of class \code{"\linkS4class{IndependenceTest}"} in order to check for specific properties of the data. Defaults to \code{NULL}. } \item{\dots}{ further arguments to be passed to or from other methods (currently ignored). } } \details{ \code{independence_test} provides a general independence test for two sets of variables measured on arbitrary scales. This function is based on the general framework for conditional inference procedures proposed by Strasser and Weber (1999). The salient parts of the Strasser-Weber framework are elucidated by Hothorn \emph{et al.} (2006) and a thorough description of the software implementation is given by Hothorn \emph{et al.} (2008). The null hypothesis of independence, or conditional independence given \code{block}, between \code{y1}, \dots, \code{yq} and \code{x1}, \dots, \code{xp} is tested. A vector of case weights, e.g., observation counts, can be supplied through the \code{weights} argument and the type of test statistic is specified by the \code{teststat} argument. Influence and regression functions, i.e., transformations of \code{y1}, \dots, \code{yq} and \code{x1}, \dots, \code{xp}, are specified by the \code{ytrafo} and \code{xtrafo} arguments respectively; see \code{\link{trafo}} for the collection of transformation functions currently available. This allows for implementation of both novel and familiar test statistics, e.g., the Pearson \eqn{\chi^2} test, the generalized Cochran-Mantel-Haenszel test, the Spearman correlation test, the Fisher-Pitman permutation test, the Wilcoxon-Mann-Whitney test, the Kruskal-Wallis test and the family of weighted logrank tests for censored data. Furthermore, multivariate extensions such as the multivariate Kruskal-Wallis test (Puri and Sen, 1966, 1971) can be implemented without much effort (see \sQuote{Examples}). If, say, \code{y1} and/or \code{x1} are ordered factors, the default scores, \code{1:nlevels(y1)} and \code{1:nlevels(x1)} respectively, can be altered using the \code{scores} argument; this argument can also be used to coerce nominal factors to class \code{"ordered"}. For example, when \code{y1} is an ordered factor with four levels and \code{x1} is a nominal factor with three levels, \code{scores = list(y1 = c(1, 3:5), x1 = c(1:2, 4))} supplies the scores to be used. For ordered alternatives the scores must be monotonic, but non-montonic scores are also allowed for testing against, e.g., umbrella alternatives. The length of the score vector must be equal to the number of factor levels. The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ Starting with \pkg{coin} version 1.1-0, maximum statistics and quadratic forms can no longer be specified using \code{teststat = "maxtype"} and \code{teststat = "quadtype"} respectively (as was used in versions prior to 0.4-5). } \references{ Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2008). Implementing a class of permutation tests: The coin package. \emph{Journal of Statistical Software} \bold{28}(8), 1--23. \doi{10.18637/jss.v028.i08} Johnson, W. D., Mercante, D. E. and May, W. L. (1993). A computer package for the multivariate nonparametric rank test in completely randomized experimental designs. \emph{Computer Methods and Programs in Biomedicine} \bold{40}(3), 217--225. \doi{10.1016/0169-2607(93)90059-T} Puri, M. L. and Sen, P. K. (1966). On a class of multivariate multisample rank order tests. \emph{Sankhya} A \bold{28}(4), 353--376. Puri, M. L. and Sen, P. K. (1971). \emph{Nonparametric Methods in Multivariate Analysis}. New York: John Wiley & Sons. Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. \emph{Mathematical Methods of Statistics} \bold{8}(2), 220--250. } \examples{ ## One-sided exact van der Waerden (normal scores) test... independence_test(asat ~ group, data = asat, ## exact null distribution distribution = "exact", ## one-sided test alternative = "greater", ## apply normal scores to asat$asat ytrafo = function(data) trafo(data, numeric_trafo = normal_trafo), ## indicator matrix of 1st level of asat$group xtrafo = function(data) trafo(data, factor_trafo = function(x) matrix(x == levels(x)[1], ncol = 1))) ## ...or more conveniently normal_test(asat ~ group, data = asat, ## exact null distribution distribution = "exact", ## one-sided test alternative = "greater") ## Receptor binding assay of benzodiazepines ## Johnson, Mercante and May (1993, Tab. 1) benzos <- data.frame( cerebellum = c( 3.41, 3.50, 2.85, 4.43, 4.04, 7.40, 5.63, 12.86, 6.03, 6.08, 5.75, 8.09, 7.56), brainstem = c( 3.46, 2.73, 2.22, 3.16, 2.59, 4.18, 3.10, 4.49, 6.78, 7.54, 5.29, 4.57, 5.39), cortex = c(10.52, 7.52, 4.57, 5.48, 7.16, 12.00, 9.36, 9.35, 11.54, 11.05, 9.92, 13.59, 13.21), hypothalamus = c(19.51, 10.00, 8.27, 10.26, 11.43, 19.13, 14.03, 15.59, 24.87, 14.16, 22.68, 19.93, 29.32), striatum = c( 6.98, 5.07, 3.57, 5.34, 4.57, 8.82, 5.76, 11.72, 6.98, 7.54, 7.66, 9.69, 8.09), hippocampus = c(20.31, 13.20, 8.58, 11.42, 13.79, 23.71, 18.35, 38.52, 21.56, 18.66, 19.24, 27.39, 26.55), treatment = factor(rep(c("Lorazepam", "Alprazolam", "Saline"), c(4, 4, 5))) ) ## Approximative (Monte Carlo) multivariate Kruskal-Wallis test ## Johnson, Mercante and May (1993, Tab. 2) independence_test(cerebellum + brainstem + cortex + hypothalamus + striatum + hippocampus ~ treatment, data = benzos, teststat = "quadratic", distribution = approximate(nresample = 10000), ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo)) # Q = 16.129 } \keyword{htest} coin/man/IndependenceTestProblem-class.Rd0000644000176200001440000000520312557641056020124 0ustar liggesusers\name{IndependenceTestProblem-class} \docType{class} \alias{IndependenceTestProblem-class} \alias{initialize,IndependenceTestProblem-method} \title{Class \code{"IndependenceTestProblem"}} \description{ Objects of class \code{"IndependenceTestProblem"} represent the transformed and original data structures corresponding to an independence problem. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("IndependenceTestProblem", object, xtrafo = trafo, ytrafo = trafo, \dots)} where \code{object} is an object of class \code{"\linkS4class{IndependenceProblem}"}, \code{xtrafo} is the regression function \eqn{g(\mathbf{X})}{g(X)} and \code{ytrafo} is the influence function \eqn{h(\mathbf{Y})}{h(Y)}. } \section{Slots}{ \describe{ \item{\code{xtrans}:}{ Object of class \code{"matrix"}. The transformed \code{x}. } \item{\code{ytrans}:}{ Object of class \code{"matrix"}. The transformed \code{y}. } \item{\code{xtrafo}:}{ Object of class \code{"function"}. The regression function for \code{x}. } \item{\code{ytrafo}:}{ Object of class \code{"function"}. The influence function for \code{y}. } \item{\code{x}:}{ Object of class \code{"data.frame"}. The variables \code{x}. } \item{\code{y}:}{ Object of class \code{"data.frame"}. The variables \code{y}. } \item{\code{block}:}{ Object of class \code{"factor"}. The block structure. } \item{\code{weights}:}{ Object of class \code{"numeric"}. The case weights. } } } \section{Extends}{ Class \code{"\linkS4class{IndependenceProblem}"}, directly. } \section{Known Subclasses}{ Class \code{"\linkS4class{IndependenceLinearStatistic}"}, directly. \cr Class \code{"\linkS4class{IndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceLinearStatistic}"}, distance 2. \cr Class \code{"\linkS4class{MaxTypeIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestStatistic}"}, distance 3. \cr Class \code{"\linkS4class{QuadTypeIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestStatistic}"}, distance 3. \cr Class \code{"\linkS4class{ScalarIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestStatistic}"}, distance 3. } \section{Methods}{ \describe{ \item{initialize}{ \code{signature(.Object = "IndependenceTestProblem")}: See the documentation for \code{\link[methods:new]{initialize}} (in package \pkg{methods}) for details. } } } \keyword{classes} coin/man/rotarod.Rd0000644000176200001440000000356313401471036013724 0ustar liggesusers\name{rotarod} \docType{data} \alias{rotarod} \title{Rotating Rats} \description{ The endurance time of 24 rats in two groups on a rotating cylinder. } \usage{rotarod} \format{ A data frame with 24 observations on 2 variables. \describe{ \item{\code{time}}{ endurance time (seconds). } \item{\code{group}}{ a factor with levels \code{"control"} and \code{"treatment"}. } } } \details{ The rats were randomly assigned to receive a fixed oral dose of a centrally acting muscle relaxant (\code{"treatment"}) or a saline solvent (\code{"control"}). The animals were placed on a rotating cylinder and the endurance time of each rat, i.e., the length of time each rat remained on the cylinder, was measured up to a maximum of 300 seconds. This dataset is the basis of a comparison of 11 different software implementations of the Wilcoxon-Mann-Whitney test presented in Bergmann, Ludbrook and Spooren (2000). } \note{ The empirical variance in the control group is 0 and the group medians are identical. The exact conditional \eqn{p}-values are 0.0373 (two-sided) and 0.0186 (one-sided). The asymptotic two-sided \eqn{p}-value (corrected for ties) is 0.0147. } \source{ Bergmann, R., Ludbrook, J. and Spooren, W. P. J. M. (2000). Different outcomes of the Wilcoxon-Mann-Whitney test from different statistics packages. \emph{The American Statistician} \bold{54}(1), 72--77. \doi{10.1080/00031305.2000.10474513} } \examples{ ## One-sided exact Wilcoxon-Mann-Whitney test (p = 0.0186) wilcox_test(time ~ group, data = rotarod, distribution = "exact", alternative = "greater") ## Two-sided exact Wilcoxon-Mann-Whitney test (p = 0.0373) wilcox_test(time ~ group, data = rotarod, distribution = "exact") ## Two-sided asymptotic Wilcoxon-Mann-Whitney test (p = 0.0147) wilcox_test(time ~ group, data = rotarod) } \keyword{datasets} coin/man/SymmetryProblem-class.Rd0000644000176200001440000000306113401471036016520 0ustar liggesusers\name{SymmetryProblem-class} \docType{class} \alias{SymmetryProblem-class} \alias{initialize,SymmetryProblem-method} \title{Class \code{"SymmetryProblem"}} \description{ Objects of class \code{"SymmetryProblem"} represent the data structure corresponding to a symmetry problem. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("SymmetryProblem", x, y, block = NULL, weights = NULL, \dots)} where \code{x} and \code{y} are data frames containing the variables \eqn{\mathbf{X}}{X} and \eqn{\mathbf{Y}}{Y} respectively, \code{block} is an optional factor representing the block structure \eqn{b} and \code{weights} is an optional integer vector corresponding to the case weights \eqn{w}. } \section{Slots}{ \describe{ \item{\code{x}:}{ Object of class \code{"data.frame"}. The variables \code{x}. } \item{\code{y}:}{ Object of class \code{"data.frame"}. The variables \code{y}. } \item{\code{block}:}{ Object of class \code{"factor"}. The block structure. } \item{\code{weights}:}{ Object of class \code{"numeric"}. The case weights. } } } \section{Extends}{ Class \code{"\linkS4class{IndependenceProblem}"}, directly. } \section{Methods}{ \describe{ \item{initialize}{ \code{signature(.Object = "SymmetryProblem")}: See the documentation for \code{\link[methods:new]{initialize}} (in package \pkg{methods}) for details. } } } \keyword{classes} coin/man/PValue-class.Rd0000644000176200001440000000237013401471036014544 0ustar liggesusers\name{PValue-class} \docType{class} \alias{PValue-class} \title{Class \code{"PValue"}} \description{ Objects of class \code{"PValue"} represent the \eqn{p}-value, mid-\eqn{p}-value and \eqn{p}-value interval of the reference distribution. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("PValue", \dots).} } \section{Slots}{ \describe{ \item{\code{name}:}{ Object of class \code{"character"}. The name of the reference distribution. } \item{\code{p}:}{ Object of class \code{"function"}. The distribution function of the reference distribution. } \item{\code{pvalue}:}{ Object of class \code{"function"}. The \eqn{p}-value function of the reference distribution. } } } \section{Methods}{ \describe{ \item{pvalue}{ \code{signature(object = "PValue")}: See the documentation for \code{\link{pvalue}} for details. } } } \note{ Starting with \pkg{coin} version 1.3-0, this class is deprecated and will be replaced by class \code{"NullDistribution"}. \strong{It will be made defunct and removed in a future release.} } \keyword{classes} coin/man/glioma.Rd0000644000176200001440000000552113401471036013516 0ustar liggesusers\name{glioma} \docType{data} \alias{glioma} \title{Malignant Glioma Pilot Study} \description{ A non-randomized pilot study on malignant glioma patients with pretargeted adjuvant radioimmunotherapy using yttrium-90-biotin. } \usage{glioma} \format{ A data frame with 37 observations on 7 variables. \describe{ \item{\code{no.}}{ patient number. } \item{\code{age}}{ patient age (years). } \item{\code{sex}}{ a factor with levels \code{"F"} (Female) and \code{"M"} (Male). } \item{\code{histology}}{ a factor with levels \code{"GBM"} (grade IV) and \code{"Grade3"} (grade III). } \item{\code{group}}{ a factor with levels \code{"Control"} and \code{"RIT"}. } \item{\code{event}}{ status indicator for \code{time}: \code{FALSE} for right-censored observations and \code{TRUE} otherwise. } \item{\code{time}}{ survival time (months). } } } \details{ The primary endpoint of this small pilot study is survival. Since the survival times are tied, the classical asymptotic logrank test may be inadequate in this setup. Therefore, a permutation test using Monte Carlo resampling was computed in the original paper. The data are taken from Tables 1 and 2 of Grana \emph{et al.} (2002). } \source{ Grana, C., Chinol, M., Robertson, C., Mazzetta, C., Bartolomei, M., De Cicco, C., Fiorenza, M., Gatti, M., Caliceti, P. and Paganelli, G. (2002). Pretargeted adjuvant radioimmunotherapy with Yttrium-90-biotin in malignant glioma patients: A pilot study. \emph{British Journal of Cancer} \bold{86}(2), 207--212. \doi{10.1038/sj.bjc.6600047} } \examples{ ## Grade III glioma g3 <- subset(glioma, histology == "Grade3") ## Plot Kaplan-Meier estimates op <- par(no.readonly = TRUE) # save current settings layout(matrix(1:2, ncol = 2)) plot(survfit(Surv(time, event) ~ group, data = g3), main = "Grade III Glioma", lty = 2:1, ylab = "Probability", xlab = "Survival Time in Month", xlim = c(-2, 72)) legend("bottomleft", lty = 2:1, c("Control", "Treated"), bty = "n") ## Exact logrank test logrank_test(Surv(time, event) ~ group, data = g3, distribution = "exact") ## Grade IV glioma gbm <- subset(glioma, histology == "GBM") ## Plot Kaplan-Meier estimates plot(survfit(Surv(time, event) ~ group, data = gbm), main = "Grade IV Glioma", lty = 2:1, ylab = "Probability", xlab = "Survival Time in Month", xlim = c(-2, 72)) legend("topright", lty = 2:1, c("Control", "Treated"), bty = "n") par(op) # reset ## Exact logrank test logrank_test(Surv(time, event) ~ group, data = gbm, distribution = "exact") ## Stratified approximative (Monte Carlo) logrank test logrank_test(Surv(time, event) ~ group | histology, data = glioma, distribution = approximate(nresample = 10000)) } \keyword{datasets} coin/man/MarginalHomogeneityTests.Rd0000644000176200001440000002241613715224731017243 0ustar liggesusers\name{MarginalHomogeneityTests} \alias{mh_test} \alias{mh_test.formula} \alias{mh_test.table} \alias{mh_test.SymmetryProblem} \concept{McNemar test} \concept{Cochran Q test} \concept{Stuart(-Maxwell) test} \concept{Madansky test of interchangeability} \title{Marginal Homogeneity Tests} \description{ Testing the marginal homogeneity of a repeated measurements factor in a complete block design. } \usage{ \method{mh_test}{formula}(formula, data, subset = NULL, \dots) \method{mh_test}{table}(object, \dots) \method{mh_test}{SymmetryProblem}(object, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} and \code{x} are factors and \code{block} is an optional factor (which is generated automatically if omitted). } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{object}{ an object inheriting from classes \code{"table"} (with identical \code{dimnames} components) or \code{"\linkS4class{SymmetryProblem}"}. } \item{\dots}{ further arguments to be passed to \code{\link{symmetry_test}}. } } \details{ \code{mh_test} provides the McNemar test, the Cochran \eqn{Q} test, the Stuart(-Maxwell) test and the Madansky test of interchangeability. A general description of these methods is given by Agresti (2002). The null hypothesis of marginal homogeneity is tested. The response variable and the measurement conditions are given by \code{y} and \code{x}, respectively, and \code{block} is a factor where each level corresponds to exactly one subject with repeated measurements. This procedure is known as the McNemar test (McNemar, 1947) when both \code{y} and \code{x} are binary factors, as the Cochran \eqn{Q} test (Cochran, 1950) when \code{y} is a binary factor and \code{x} is a factor with an arbitrary number of levels, as the Stuart(-Maxwell) test (Stuart, 1955; Maxwell, 1970) when \code{y} is a factor with an arbitrary number of levels and \code{x} is a binary factor, and as the Madansky test of interchangeability (Madansky, 1963), which implies marginal homogeneity, when both \code{y} and \code{x} are factors with an arbitrary number of levels. %% See also Bhapkar (1966) for a more powerful Wald-type test. (As noted by %% Ireland, Ku and Kullback (1969), Bhapkar's statistic is given by %% \eqn{Q / (1 - Q / n)}, where \eqn{Q} is Stuart's statistic and \eqn{n} is %% the sample size). If \code{y} and/or \code{x} are ordered factors, the default scores, \code{1:nlevels(y)} and \code{1:nlevels(x)} respectively, can be altered using the \code{scores} argument (see \code{\link{symmetry_test}}); this argument can also be used to coerce nominal factors to class \code{"ordered"}. If both \code{y} and \code{x} are ordered factors, a linear-by-linear association test is computed and the direction of the alternative hypothesis can be specified using the \code{alternative} argument. This extension was given by Birch (1965) who also discussed the situation when either the response or the measurement condition is an ordered factor; see also White, Landis and Cooper (1982). The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ This function is currently computationally inefficient for data with a large number of pairs or sets. } \references{ Agresti, A. (2002). \emph{Categorical Data Analysis}, Second Edition. Hoboken, New Jersey: John Wiley & Sons. %% Bhapkar, V. P. (1966). A note on the equivalence of two test criteria for %% hypotheses in categorical data. \emph{Journal of the American Statistical %% Association} \bold{61}(313), 228--235. \doi{10.1080/01621459.1966.10502021} Birch, M. W. (1965). The detection of partial association, II: The general case. \emph{Journal of the Royal Statistical Society} B \bold{27}(1), 111--124. \doi{10.1111/j.2517-6161.1965.tb00593.x} Cochran, W. G. (1950). The comparison of percentages in matched samples. \emph{Biometrika} \bold{37}(3/4), 256--266. \doi{10.1093/biomet/37.3-4.256} %% Ireland, C. T., Ku, H. H. and Kullback, S. (1969). Symmetry and marginal %% homogeneity of an \eqn{r \times r} contingency table. \emph{Journal of the %% American Statistical Association} \bold{64}(328), 1323--1341. %% \doi{10.1080/01621459.1969.10501059} Madansky, A. (1963). Tests of homogeneity for correlated samples. \emph{Journal of the American Statistical Association} \bold{58}(301), 97--119. \doi{10.1080/01621459.1963.10500835} Maxwell, A. E. (1970). Comparing the classification of subjects by two independent judges. \emph{British Journal of Psychiatry} \bold{116}(535), 651--655. \doi{10.1192/bjp.116.535.651} McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. \emph{Psychometrika} \bold{12}(2), 153--157. \doi{10.1007/BF02295996} Stuart, A. (1955). A test for homogeneity of the marginal distributions in a two-way classification. \emph{Biometrika} \bold{42}(3/4), 412--416. \doi{10.1093/biomet/42.3-4.412} White, A. A., Landis, J. R. and Cooper, M. M. (1982). A note on the equivalence of several marginal homogeneity test criteria for categorical data. \emph{International Statistical Review} \bold{50}(1), 27--34. \doi{10.2307/1402457} } \examples{ ## Performance of prime minister ## Agresti (2002, p. 409) performance <- matrix( c(794, 150, 86, 570), nrow = 2, byrow = TRUE, dimnames = list( "First" = c("Approve", "Disprove"), "Second" = c("Approve", "Disprove") ) ) performance <- as.table(performance) diag(performance) <- 0 # speed-up: only off-diagonal elements contribute ## Asymptotic McNemar Test mh_test(performance) ## Exact McNemar Test mh_test(performance, distribution = "exact") ## Effectiveness of different media for the growth of diphtheria ## Cochran (1950, Tab. 2) cases <- c(4, 2, 3, 1, 59) n <- sum(cases) cochran <- data.frame( diphtheria = factor( unlist(rep(list(c(1, 1, 1, 1), c(1, 1, 0, 1), c(0, 1, 1, 1), c(0, 1, 0, 1), c(0, 0, 0, 0)), cases)) ), media = factor(rep(LETTERS[1:4], n)), case = factor(rep(seq_len(n), each = 4)) ) ## Asymptotic Cochran Q test (Cochran, 1950, p. 260) mh_test(diphtheria ~ media | case, data = cochran) # Q = 8.05 ## Approximative Cochran Q test mt <- mh_test(diphtheria ~ media | case, data = cochran, distribution = approximate(nresample = 10000)) pvalue(mt) # standard p-value midpvalue(mt) # mid-p-value pvalue_interval(mt) # p-value interval size(mt, alpha = 0.05) # test size at alpha = 0.05 using the p-value ## Opinions on Pre- and Extramarital Sex ## Agresti (2002, p. 421) opinions <- c("Always wrong", "Almost always wrong", "Wrong only sometimes", "Not wrong at all") PreExSex <- matrix( c(144, 33, 84, 126, 2, 4, 14, 29, 0, 2, 6, 25, 0, 0, 1, 5), nrow = 4, dimnames = list( "Premarital Sex" = opinions, "Extramarital Sex" = opinions ) ) PreExSex <- as.table(PreExSex) ## Asymptotic Stuart test mh_test(PreExSex) ## Asymptotic Stuart-Birch test ## Note: response as ordinal mh_test(PreExSex, scores = list(response = 1:length(opinions))) ## Vote intention ## Madansky (1963, pp. 107-108) vote <- array( c(120, 1, 8, 2, 2, 1, 2, 1, 7, 6, 2, 1, 1, 103, 5, 1, 4, 8, 20, 3, 31, 1, 6, 30, 2, 1, 81), dim = c(3, 3, 3), dimnames = list( "July" = c("Republican", "Democratic", "Uncertain"), "August" = c("Republican", "Democratic", "Uncertain"), "June" = c("Republican", "Democratic", "Uncertain") ) ) vote <- as.table(vote) ## Asymptotic Madansky test (Q = 70.77) mh_test(vote) ## Cross-over study ## http://www.nesug.org/proceedings/nesug00/st/st9005.pdf dysmenorrhea <- array( c(6, 2, 1, 3, 1, 0, 1, 2, 1, 4, 3, 0, 13, 3, 0, 8, 1, 1, 5, 2, 2, 10, 1, 0, 14, 2, 0), dim = c(3, 3, 3), dimnames = list( "Placebo" = c("None", "Moderate", "Complete"), "Low dose" = c("None", "Moderate", "Complete"), "High dose" = c("None", "Moderate", "Complete") ) ) dysmenorrhea <- as.table(dysmenorrhea) ## Asymptotic Madansky-Birch test (Q = 53.76) ## Note: response as ordinal mh_test(dysmenorrhea, scores = list(response = 1:3)) ## Asymptotic Madansky-Birch test (Q = 47.29) ## Note: response and measurement conditions as ordinal mh_test(dysmenorrhea, scores = list(response = 1:3, conditions = 1:3)) } \keyword{htest} coin/man/photocar.Rd0000644000176200001440000000623013401471036014063 0ustar liggesusers\name{photocar} \docType{data} \alias{photocar} \title{Multiple Dosing Photococarcinogenicity Experiment} \description{ Survival time, time to first tumor, and total number of tumors in three groups of animals in a photococarcinogenicity study. } \usage{photocar} \format{ A data frame with 108 observations on 6 variables. \describe{ \item{\code{group}}{ a factor with levels \code{"A"}, \code{"B"}, and \code{"C"}. } \item{\code{ntumor}}{ total number of tumors. } \item{\code{time}}{ survival time. } \item{\code{event}}{ status indicator for \code{time}: \code{FALSE} for right-censored observations and \code{TRUE} otherwise. } \item{\code{dmin}}{ time to first tumor. } \item{\code{tumor}}{ status indicator for \code{dmin}: \code{FALSE} when no tumor was observed and \code{TRUE} otherwise. } } } \details{ The animals were exposed to different levels of ultraviolet radiation (UVR) exposure (group A: topical vehicle and 600 Robertson--Berger units of UVR, group B: no topical vehicle and 600 Robertson--Berger units of UVR and group C: no topical vehicle and 1200 Robertson--Berger units of UVR). The data are taken from Tables 1 to 3 in Molefe \emph{et al.} (2005). The main interest is testing the global null hypothesis of no treatment effect with respect to survival time, time to first tumor and number of tumors. (Molefe \emph{et al.}, 2005, also analysed the detection time of tumors, but that data is not given here.) In case the global null hypothesis can be rejected, the deviations from the partial null hypotheses are of special interest. } \source{ Molefe, D. F., Chen, J. J., Howard, P. C., Miller, B. J., Sambuco, C. P., Forbes, P. D. and Kodell, R. L. (2005). Tests for effects on tumor frequency and latency in multiple dosing photococarcinogenicity experiments. \emph{Journal of Statistical Planning and Inference} \bold{129}(1--2), 39--58. \doi{10.1016/j.jspi.2004.06.038} } \references{ Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} } \examples{ ## Plotting data op <- par(no.readonly = TRUE) # save current settings layout(matrix(1:3, ncol = 3)) with(photocar, { plot(survfit(Surv(time, event) ~ group), lty = 1:3, xmax = 50, main = "Survival Time") legend("bottomleft", lty = 1:3, levels(group), bty = "n") plot(survfit(Surv(dmin, tumor) ~ group), lty = 1:3, xmax = 50, main = "Time to First Tumor") legend("bottomleft", lty = 1:3, levels(group), bty = "n") boxplot(ntumor ~ group, main = "Number of Tumors") }) par(op) # reset ## Approximative multivariate (all three responses) test it <- independence_test(Surv(time, event) + Surv(dmin, tumor) + ntumor ~ group, data = photocar, distribution = approximate(nresample = 10000)) ## Global p-value pvalue(it) ## Why was the global null hypothesis rejected? statistic(it, type = "standardized") pvalue(it, method = "single-step") } \keyword{datasets} coin/man/NullDistribution-methods.Rd0000644000176200001440000000640013323122257017217 0ustar liggesusers\name{NullDistribution-methods} \docType{methods} \alias{AsymptNullDistribution} \alias{AsymptNullDistribution-methods} \alias{AsymptNullDistribution,MaxTypeIndependenceTestStatistic-method} \alias{AsymptNullDistribution,QuadTypeIndependenceTestStatistic-method} \alias{AsymptNullDistribution,ScalarIndependenceTestStatistic-method} \alias{ApproxNullDistribution} \alias{ApproxNullDistribution-methods} \alias{ApproxNullDistribution,MaxTypeIndependenceTestStatistic-method} \alias{ApproxNullDistribution,QuadTypeIndependenceTestStatistic-method} \alias{ApproxNullDistribution,ScalarIndependenceTestStatistic-method} \alias{ExactNullDistribution} \alias{ExactNullDistribution-methods} \alias{ExactNullDistribution,QuadTypeIndependenceTestStatistic-method} \alias{ExactNullDistribution,ScalarIndependenceTestStatistic-method} \title{Computation of the Reference Distribution} \description{ Methods for computation of the asymptotic, approximative (Monte Carlo) and exact reference distribution. } \usage{ \S4method{AsymptNullDistribution}{MaxTypeIndependenceTestStatistic}(object, \dots) \S4method{AsymptNullDistribution}{QuadTypeIndependenceTestStatistic}(object, \dots) \S4method{AsymptNullDistribution}{ScalarIndependenceTestStatistic}(object, \dots) \S4method{ApproxNullDistribution}{MaxTypeIndependenceTestStatistic}(object, nresample = 10000L, B, \dots) \S4method{ApproxNullDistribution}{QuadTypeIndependenceTestStatistic}(object, nresample = 10000L, B, \dots) \S4method{ApproxNullDistribution}{ScalarIndependenceTestStatistic}(object, nresample = 10000L, B, \dots) \S4method{ExactNullDistribution}{QuadTypeIndependenceTestStatistic}(object, algorithm = c("auto", "shift", "split-up"), \dots) \S4method{ExactNullDistribution}{ScalarIndependenceTestStatistic}(object, algorithm = c("auto", "shift", "split-up"), \dots) } \arguments{ \item{object}{ an object from which the asymptotic, approximative (Monte Carlo) or exact reference distribution can be computed. } \item{nresample}{ a positive integer, the number of Monte Carlo replicates used for the computation of the approximative reference distribution. Defaults to \code{10000L}. } \item{B}{ deprecated, use \code{nresample} instead. } \item{algorithm}{ a character, the algorithm used for the computation of the exact reference distribution: either \code{"auto"} (default), \code{"shift"} or \code{"split-up"}. } \item{\dots}{ further arguments to be passed to or from methods. } } \details{ The methods \code{AsymptNullDistribution}, \code{ApproxNullDistribution} and \code{ExactNullDistribution} compute the asymptotic, approximative (Monte Carlo) and exact reference distribution respectively. } \note{ In versions of \pkg{coin} prior to 1.3-0, the number of Monte Carlo replicates in \code{ApproxNullDistribution()} was specified using the now deprecated \code{B} argument. \strong{This will be made defunct and removed in a future release.} It has been replaced by the \code{nresample} argument (for conformity with the \pkg{libcoin}, \pkg{party} and \pkg{partykit} packages). } \value{ An object of class \code{"\linkS4class{AsymptNullDistribution}"}, \code{"\linkS4class{ApproxNullDistribution}"} or \code{"\linkS4class{ExactNullDistribution}"}. } \keyword{methods} coin/man/pvalue-methods.Rd0000644000176200001440000002664113437424271015221 0ustar liggesusers\name{pvalue-methods} \docType{methods} \alias{pvalue} \alias{pvalue-methods} \alias{pvalue,PValue-method} \alias{pvalue,NullDistribution-method} \alias{pvalue,ApproxNullDistribution-method} \alias{pvalue,IndependenceTest-method} \alias{pvalue,MaxTypeIndependenceTest-method} \alias{midpvalue} \alias{midpvalue-methods} \alias{midpvalue,NullDistribution-method} \alias{midpvalue,ApproxNullDistribution-method} \alias{midpvalue,IndependenceTest-method} \alias{pvalue_interval} \alias{pvalue_interval-methods} \alias{pvalue_interval,NullDistribution-method} \alias{pvalue_interval,IndependenceTest-method} \alias{size} \alias{size-methods} \alias{size,NullDistribution-method} \alias{size,IndependenceTest-method} \encoding{UTF-8} \title{Computation of the \eqn{p}-Value, Mid-\eqn{p}-Value, \eqn{p}-Value Interval and Test Size} \description{ Methods for computation of the \eqn{p}-value, mid-\eqn{p}-value, \eqn{p}-value interval and test size. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \S4method{pvalue}{PValue}(object, q, \dots) \S4method{pvalue}{NullDistribution}(object, q, \dots) \S4method{pvalue}{ApproxNullDistribution}(object, q, \dots) \S4method{pvalue}{IndependenceTest}(object, \dots) \S4method{pvalue}{MaxTypeIndependenceTest}(object, method = c("global", "single-step", "step-down", "unadjusted"), distribution = c("joint", "marginal"), type = c("Bonferroni", "Sidak"), \dots) \S4method{midpvalue}{NullDistribution}(object, q, \dots) \S4method{midpvalue}{ApproxNullDistribution}(object, q, \dots) \S4method{midpvalue}{IndependenceTest}(object, \dots) \S4method{pvalue_interval}{NullDistribution}(object, q, \dots) \S4method{pvalue_interval}{IndependenceTest}(object, \dots) \S4method{size}{NullDistribution}(object, alpha, type = c("p-value", "mid-p-value"), \dots) \S4method{size}{IndependenceTest}(object, alpha, type = c("p-value", "mid-p-value"), \dots) } \arguments{ \item{object}{ an object from which the \eqn{p}-value, mid-\eqn{p}-value, \eqn{p}-value interval or test size can be computed. } \item{q}{ a numeric, the quantile for which the \eqn{p}-value, mid-\eqn{p}-value or \eqn{p}-value interval is computed. } \item{method}{ a character, the method used for the \eqn{p}-value computation: either \code{"global"} (default), \code{"single-step"}, \code{"step-down"} or \code{"unadjusted"}. } \item{distribution}{ a character, the distribution used for the computation of adjusted \eqn{p}-values: either \code{"joint"} (default) or \code{"marginal"}. } \item{type}{ \code{pvalue()}: a character, the type of \eqn{p}-value adjustment when the marginal distributions are used: either \code{"Bonferroni"} (default) or \code{"Sidak"}. % NOTE: this line is necessary for correct rendering \code{size()}: a character, the type of rejection region used when computing the test size: either \code{"p-value"} (default) or \code{"mid-p-value"}. } \item{alpha}{ a numeric, the nominal significance level \eqn{\alpha} at which the test size is computed. } \item{\dots}{ further arguments (currently ignored). } } \details{ The methods \code{pvalue}, \code{midpvalue}, \code{pvalue_interval} and \code{size} compute the \eqn{p}-value, mid-\eqn{p}-value, \eqn{p}-value interval and test size respectively. For \code{pvalue}, the global \eqn{p}-value (\code{method = "global"}) is returned by default and is given with an associated 99\% confidence interval when resampling is used to determine the null distribution (which for maximum statistics may be true even in the asymptotic case). The familywise error rate (FWER) is always controlled under the global null hypothesis, i.e., in the \emph{weak} sense, implying that the smallest adjusted \eqn{p}-value is valid without further assumptions. Control of the FWER under any partial configuration of the null hypotheses, i.e., in the \emph{strong} sense, as is typically desired for multiple tests and comparisons, requires that the \emph{subset pivotality} condition holds (Westfall and Young, 1993, pp. 42--43; Bretz, Hothorn and Westfall, 2011, pp. 136--137). In addition, for methods based on the joint distribution of the test statistics, failure of the \emph{joint exchangeability} assumption (Westfall and Troendle, 2008; Bretz, Hothorn and Westfall, 2011, pp. 129--130) may cause excess Type I errors. Assuming \emph{subset pivotality}, single-step or \emph{free} step-down adjusted \eqn{p}-values using max-\eqn{T} procedures are obtained by setting \code{method} to \code{"single-step"} or \code{"step-down"} respectively. In both cases, the \code{distribution} argument specifies whether the adjustment is based on the joint distribution (\code{"joint"}) or the marginal distributions (\code{"marginal"}) of the test statistics. For procedures based on the marginal distributions, Bonferroni- or \enc{Šidák}{Sidak}-type adjustment can be specified through the \code{type} argument by setting it to \code{"Bonferroni"} or \code{"Sidak"} respectively. The \eqn{p}-value adjustment procedures based on the joint distribution of the test statistics fully utilizes distributional characteristics, such as discreteness and dependence structure, whereas procedures using the marginal distributions only incorporate discreteness. Hence, the joint distribution-based procedures are typically more powerful. Details regarding the single-step and \emph{free} step-down procedures based on the joint distribution can be found in Westfall and Young (1993); in particular, this implementation uses Equation 2.8 with Algorithm 2.5 and 2.8 respectively. Westfall and Wolfinger (1997) provide details of the marginal distributions-based single-step and \emph{free} step-down procedures. The generalization of Westfall and Wolfinger (1997) to arbitrary test statistics, as implemented here, is given by Westfall and Troendle (2008). Unadjusted \eqn{p}-values are obtained using \code{method = "unadjusted"}. For \code{midpvalue}, the global mid-\eqn{p}-value is given with an associated 99\% mid-\eqn{p} confidence interval when resampling is used to determine the null distribution. The two-sided mid-\eqn{p}-value is computed according to the minimum likelihood method (Hirji \emph{et al.}, 1991). The \eqn{p}-value interval \eqn{(p_0, p_1]} obtained by \code{pvalue_interval} was proposed by Berger (2000, 2001), where the upper endpoint \eqn{p_1} is the conventional \eqn{p}-value and the mid-point, i.e., \eqn{p_{0.5}}{p_0.5}, is the mid-\eqn{p}-value. The lower endpoint \eqn{p_0} is the smallest \eqn{p}-value attainable if no conservatism attributable to the discreteness of the null distribution is present. The length of the \eqn{p}-value interval is the null probability of the observed outcome and provides a data-dependent measure of conservatism that is completely independent of the nominal significance level. For \code{size}, the test size, i.e., the actual significance level, at the nominal significance level \eqn{\alpha} is computed using either the rejection region corresponding to the \eqn{p}-value (\code{type = "p-value"}, default) or the mid-\eqn{p}-value (\code{type = "mid-p-value"}). The test size is, in contrast to the \eqn{p}-value interval, a data-independent measure of conservatism that depends on the nominal significance level. A test size smaller or larger than the nominal significance level indicates that the test procedure is conservative or anti-conservative, respectively, at that particular nominal significance level. However, as pointed out by Berger (2001), even when the actual and nominal significance levels are identical, conservatism may still affect the \eqn{p}-value. } \value{ The \eqn{p}-value, mid-\eqn{p}-value, \eqn{p}-value interval or test size computed from \code{object}. A numeric vector or matrix. } \note{ The mid-\eqn{p}-value, \eqn{p}-value interval and test size of asymptotic permutation distributions or exact permutation distributions obtained by the split-up algoritm is reported as \code{NA}. In versions of \pkg{coin} prior to 1.1-0, a min-\eqn{P} procedure computing \enc{Šidák}{Sidak} single-step adjusted \eqn{p}-values accounting for discreteness was available when specifying \code{method = "discrete"}. \strong{This is now deprecated and will be removed in a future release} due to the introduction of a more general max-\eqn{T} version of the same algorithm. } \references{ Berger, V. W. (2000). Pros and cons of permutation tests in clinical trials. \emph{Statistics in Medicine} \bold{19}(10), 1319--1328. \doi{10.1002/(SICI)1097-0258(20000530)19:10<1319::AID-SIM490>3.0.CO;2-0} Berger, V. W. (2001). The \eqn{p}-value interval as an inferential tool. \emph{The Statistician} \bold{50}(1), 79--85. \doi{10.1111/1467-9884.00262} Bretz, F., Hothorn, T. and Westfall, P. (2011). \emph{Multiple Comparisons Using R}. Boca Raton: CRC Press. Hirji, K. F., Tan, S.-J. and Elashoff, R. M. (1991). A quasi-exact test for comparing two binomial proportions. \emph{Statistics in Medicine} \bold{10}(7), 1137--1153. \doi{10.1002/sim.4780100713} Westfall, P. H. and Troendle, J. F. (2008). Multiple testing with minimal assumptions. \emph{Biometrical Journal} \bold{50}(5), 745--755. \doi{10.1002/bimj.200710456} Westfall, P. H. and Wolfinger, R. D. (1997). Multiple tests with discrete distributions. \emph{The American Statistician} \bold{51}(1), 3--8. \doi{10.1080/00031305.1997.10473577} Westfall, P. H. and Young, S. S. (1993). \emph{Resampling-Based Multiple Testing: Examples and Methods for \eqn{p}-Value Adjustment}. New York: John Wiley & Sons. } \examples{ ## Two-sample problem dta <- data.frame( y = rnorm(20), x = gl(2, 10) ) ## Exact Ansari-Bradley test (at <- ansari_test(y ~ x, data = dta, distribution = "exact")) pvalue(at) midpvalue(at) pvalue_interval(at) size(at, alpha = 0.05) size(at, alpha = 0.05, type = "mid-p-value") ## Bivariate two-sample problem dta2 <- data.frame( y1 = rnorm(20) + rep(0:1, each = 10), y2 = rnorm(20), x = gl(2, 10) ) ## Approximative (Monte Carlo) bivariate Fisher-Pitman test (it <- independence_test(y1 + y2 ~ x, data = dta2, distribution = approximate(nresample = 10000))) ## Global p-value pvalue(it) ## Joint distribution single-step p-values pvalue(it, method = "single-step") ## Joint distribution step-down p-values pvalue(it, method = "step-down") ## Sidak step-down p-values pvalue(it, method = "step-down", distribution = "marginal", type = "Sidak") ## Unadjusted p-values pvalue(it, method = "unadjusted") ## Length of YOY Gizzard Shad (Hollander and Wolfe, 1999, p. 200, Tab. 6.3) yoy <- data.frame( length = c(46, 28, 46, 37, 32, 41, 42, 45, 38, 44, 42, 60, 32, 42, 45, 58, 27, 51, 42, 52, 38, 33, 26, 25, 28, 28, 26, 27, 27, 27, 31, 30, 27, 29, 30, 25, 25, 24, 27, 30), site = gl(4, 10, labels = as.roman(1:4)) ) ## Approximative (Monte Carlo) Fisher-Pitman test with contrasts ## Note: all pairwise comparisons (it <- independence_test(length ~ site, data = yoy, distribution = approximate(nresample = 10000), xtrafo = mcp_trafo(site = "Tukey"))) ## Joint distribution step-down p-values pvalue(it, method = "step-down") # subset pivotality is violated } \keyword{methods} \keyword{htest} coin/man/coin-package.Rd0000644000176200001440000000703313401471036014567 0ustar liggesusers\name{coin-package} \docType{package} \alias{coin-package} \alias{coin} \title{General Information on the \pkg{coin} Package} \description{ The \pkg{coin} package provides an implementation of a general framework for conditional inference procedures commonly known as \emph{permutation tests}. The framework was developed by Strasser and Weber (1999) and is based on a multivariate linear statistic and its conditional expectation, covariance and limiting distribution. These results are utilized to construct tests of independence between two sets of variables. The package does not only provide a flexible implementation of the abstract framework, but also provides a large set of convenience functions implementing well-known as well as lesser-known classical and non-classical test procedures within the framework. Many of the tests presented in prominent text books, such as Hollander and Wolfe (1999) or Agresti (2002), are immediately available or can be implemented without much effort. Examples include linear rank statistics for the two- and \eqn{K}-sample location and scale problem against ordered and unordered alternatives including post-hoc tests for arbitrary contrasts, tests of independence for contingency tables, two- and \eqn{K}-sample tests for censored data, tests of independence between two continuous variables as well as tests of marginal homogeneity and symmetry. Approximations of the exact null distribution via the limiting distribution or conditional Monte Carlo resampling are available for every test procedure, while the exact null distribution is currently available for univariate two-sample problems only. The salient parts of the Strasser-Weber framework are elucidated by Hothorn \emph{et al.} (2006) and a thorough description of the software implementation is given by Hothorn \emph{et al.} (2008). } \author{ This package is authored by \cr Torsten Hothorn , \cr Kurt Hornik , \cr Mark A. van de Wiel , \cr Henric Winell and \cr Achim Zeileis . } \references{ Agresti, A. (2002). \emph{Categorical Data Analysis}, Second Edition. Hoboken, New Jersey: John Wiley & Sons. Hollander, M. and Wolfe, D. A. (1999). \emph{Nonparametric Statistical Methods}, Second Edition. New York: John Wiley & Sons. Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2006). A Lego system for conditional inference. \emph{The American Statistician} \bold{60}(3), 257--263. \doi{10.1198/000313006X118430} Hothorn, T., Hornik, K., van de Wiel, M. A. and Zeileis, A. (2008). Implementing a class of permutation tests: The coin package. \emph{Journal of Statistical Software} \bold{28}(8), 1--23. \doi{10.18637/jss.v028.i08} Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. \emph{Mathematical Methods of Statistics} \bold{8}(2), 220--250. } \examples{ \dontrun{ ## Generate doxygen documentation if you are interested in the internals: ## Download source package into a temporary directory tmpdir <- tempdir() tgz <- download.packages("coin", destdir = tmpdir, type = "source")[2] ## Extract contents untar(tgz, exdir = tmpdir) ## Run doxygen (assuming it is installed) wd <- setwd(file.path(tmpdir, "coin")) system("doxygen inst/doxygen.cfg") setwd(wd) ## Have fun! browseURL(file.path(tmpdir, "coin", "inst", "documentation", "html", "index.html"))} } \keyword{package} coin/man/ocarcinoma.Rd0000644000176200001440000000320113401471036014352 0ustar liggesusers\name{ocarcinoma} \docType{data} \alias{ocarcinoma} \encoding{UTF-8} \title{Ovarian Carcinoma} \description{ Survival times of 35 women suffering from ovarian carcinoma at stadium II and IIA. } \usage{ocarcinoma} \format{ A data frame with 35 observations on 3 variables. \describe{ \item{\code{time}}{ time (days). } \item{\code{stadium}}{ a factor with levels \code{"II"} and \code{"IIA"}. } \item{\code{event}}{ status indicator for \code{time}: \code{FALSE} for right-censored observations and \code{TRUE} otherwise. } } } \details{ Data from Fleming \emph{et al.} (1980) and Fleming, Green and Harrington (1984). Reanalysed in Schumacher and Schulgen (2002). } \source{ Fleming, T. R., Green, S. J. and Harrington, D. P. (1984). Considerations for monitoring and evaluating treatment effects in clinical trials. \emph{Controlled Clinical Trials} \bold{5}(1), 55--66. \doi{10.1016/0197-2456(84)90150-8} Fleming, T. R., O'Fallon, J. R., O'Brien, P. C. and Harrington, D. P. (1980). Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right-censored data. \emph{Biometrics} \bold{36}(4), 607--625. \doi{10.2307/2556114} } \references{ Schumacher, M. and Schulgen, G. (2002). \emph{Methodik Klinischer Studien: Methodische Grundlagen der Planung, \enc{Durchführung}{Durchfuehrung} und Auswertung}. Heidelberg: Springer. } \examples{ ## Exact logrank test lt <- logrank_test(Surv(time, event) ~ stadium, data = ocarcinoma, distribution = "exact") ## Test statistic statistic(lt) ## P-value pvalue(lt) } \keyword{datasets} coin/man/ContingencyTests.Rd0000644000176200001440000002545413715224731015566 0ustar liggesusers\name{ContingencyTests} \alias{chisq_test} \alias{chisq_test.formula} \alias{chisq_test.table} \alias{chisq_test.IndependenceProblem} \alias{cmh_test} \alias{cmh_test.formula} \alias{cmh_test.table} \alias{cmh_test.IndependenceProblem} \alias{lbl_test} \alias{lbl_test.formula} \alias{lbl_test.table} \alias{lbl_test.IndependenceProblem} \concept{Pearson chi-squared test} \concept{Generalized Cochran-Mantel-Haenszel test} \concept{Linear-by-linear association test} \concept{Cochran-Armitage test} \title{Tests of Independence in Two- or Three-Way Contingency Tables} \description{ Testing the independence of two nominal or ordered factors. } \usage{ \method{chisq_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{chisq_test}{table}(object, \dots) \method{chisq_test}{IndependenceProblem}(object, \dots) \method{cmh_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{cmh_test}{table}(object, \dots) \method{cmh_test}{IndependenceProblem}(object, \dots) \method{lbl_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{lbl_test}{table}(object, \dots) \method{lbl_test}{IndependenceProblem}(object, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} and \code{x} are factors and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from classes \code{"table"} or \code{"\linkS4class{IndependenceProblem}"}. } \item{\dots}{ further arguments to be passed to \code{\link{independence_test}}. } } \details{ \code{chisq_test}, \code{cmh_test} and \code{lbl_test} provide the Pearson chi-squared test, the generalized Cochran-Mantel-Haenszel test and the linear-by-linear association test. A general description of these methods is given by Agresti (2002). The null hypothesis of independence, or conditional independence given \code{block}, between \code{y} and \code{x} is tested. If \code{y} and/or \code{x} are ordered factors, the default scores, \code{1:nlevels(y)} and \code{1:nlevels(x)} respectively, can be altered using the \code{scores} argument (see \code{\link{independence_test}}); this argument can also be used to coerce nominal factors to class \code{"ordered"}. (\code{lbl_test} coerces to class \code{"ordered"} under any circumstances.) If both \code{y} and \code{x} are ordered factors, a linear-by-linear association test is computed and the direction of the alternative hypothesis can be specified using the \code{alternative} argument. For the Pearson chi-squared test, this extension was given by Yates (1948) who also discussed the situation when either the response or the covariate is an ordered factor; see also Cochran (1954) and Armitage (1955) for the particular case when \code{y} is a binary factor and \code{x} is ordered. The Mantel-Haenszel statistic (Mantel and Haenszel, 1959) was similarly extended by Mantel (1963) and Landis, Heyman and Koch (1978). The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ The exact versions of the Pearson chi-squared test and the generalized Cochran-Mantel-Haenszel test do not necessarily result in the same \eqn{p}-value as Fisher's exact test (Davis, 1986). } \references{ Agresti, A. (2002). \emph{Categorical Data Analysis}, Second Edition. Hoboken, New Jersey: John Wiley & Sons. Armitage, P. (1955). Tests for linear trends in proportions and frequencies. \emph{Biometrics} \bold{11}(3), 375--386. \doi{10.2307/3001775} Cochran, W.G. (1954). Some methods for strengthening the common \eqn{\chi^2} tests. \emph{Biometrics} \bold{10}(4), 417--451. \doi{10.2307/3001616} Davis, L. J. (1986). Exact tests for \eqn{2 \times 2}{2 x 2} contingency tables. \emph{The American Statistician} \bold{40}(2), 139--141. \doi{10.1080/00031305.1986.10475377} Landis, J. R., Heyman, E. R. and Koch, G. G. (1978). Average partial association in three-way contingency tables: a review and discussion of alternative tests. \emph{International Statistical Review} \bold{46}(3), 237--254. \doi{10.2307/1402373} Mantel, N. and Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies of disease. \emph{Journal of the National Cancer Institute} \bold{22}(4), 719--748. \doi{10.1093/jnci/22.4.719} Mantel, N. (1963). Chi-square tests with one degree of freedom: extensions of the Mantel-Haenszel procedure. \emph{Journal of the American Statistical Association} \bold{58}(303), 690--700. \doi{10.1080/01621459.1963.10500879} Yates, F. (1948). The analysis of contingency tables with groupings based on quantitative characters. \emph{Biometrika} \bold{35}(1/2), 176--181. \doi{10.1093/biomet/35.1-2.176} } \examples{ ## Example data ## Davis (1986, p. 140) davis <- matrix( c(3, 6, 2, 19), nrow = 2, byrow = TRUE ) davis <- as.table(davis) ## Asymptotic Pearson chi-squared test chisq_test(davis) chisq.test(davis, correct = FALSE) # same as above ## Approximative (Monte Carlo) Pearson chi-squared test ct <- chisq_test(davis, distribution = approximate(nresample = 10000)) pvalue(ct) # standard p-value midpvalue(ct) # mid-p-value pvalue_interval(ct) # p-value interval size(ct, alpha = 0.05) # test size at alpha = 0.05 using the p-value ## Exact Pearson chi-squared test (Davis, 1986) ## Note: disagrees with Fisher's exact test ct <- chisq_test(davis, distribution = "exact") pvalue(ct) # standard p-value midpvalue(ct) # mid-p-value pvalue_interval(ct) # p-value interval size(ct, alpha = 0.05) # test size at alpha = 0.05 using the p-value fisher.test(davis) ## Laryngeal cancer data ## Agresti (2002, p. 107, Tab. 3.13) cancer <- matrix( c(21, 2, 15, 3), nrow = 2, byrow = TRUE, dimnames = list( "Treatment" = c("Surgery", "Radiation"), "Cancer" = c("Controlled", "Not Controlled") ) ) cancer <- as.table(cancer) ## Exact Pearson chi-squared test (Agresti, 2002, p. 108, Tab. 3.14) ## Note: agrees with Fishers's exact test (ct <- chisq_test(cancer, distribution = "exact")) midpvalue(ct) # mid-p-value pvalue_interval(ct) # p-value interval size(ct, alpha = 0.05) # test size at alpha = 0.05 using the p-value fisher.test(cancer) ## Homework conditions and teacher's rating ## Yates (1948, Tab. 1) yates <- matrix( c(141, 67, 114, 79, 39, 131, 66, 143, 72, 35, 36, 14, 38, 28, 16), byrow = TRUE, ncol = 5, dimnames = list( "Rating" = c("A", "B", "C"), "Condition" = c("A", "B", "C", "D", "E") ) ) yates <- as.table(yates) ## Asymptotic Pearson chi-squared test (Yates, 1948, p. 176) chisq_test(yates) ## Asymptotic Pearson-Yates chi-squared test (Yates, 1948, pp. 180-181) ## Note: 'Rating' and 'Condition' as ordinal (ct <- chisq_test(yates, alternative = "less", scores = list("Rating" = c(-1, 0, 1), "Condition" = c(2, 1, 0, -1, -2)))) statistic(ct)^2 # chi^2 = 2.332 ## Asymptotic Pearson-Yates chi-squared test (Yates, 1948, p. 181) ## Note: 'Rating' as ordinal chisq_test(yates, scores = list("Rating" = c(-1, 0, 1))) # Q = 3.825 ## Change in clinical condition and degree of infiltration ## Cochran (1954, Tab. 6) cochran <- matrix( c(11, 7, 27, 15, 42, 16, 53, 13, 11, 1), byrow = TRUE, ncol = 2, dimnames = list( "Change" = c("Marked", "Moderate", "Slight", "Stationary", "Worse"), "Infiltration" = c("0-7", "8-15") ) ) cochran <- as.table(cochran) ## Asymptotic Pearson chi-squared test (Cochran, 1954, p. 435) chisq_test(cochran) # X^2 = 6.88 ## Asymptotic Cochran-Armitage test (Cochran, 1954, p. 436) ## Note: 'Change' as ordinal (ct <- chisq_test(cochran, scores = list("Change" = c(3, 2, 1, 0, -1)))) statistic(ct)^2 # X^2 = 6.66 ## Change in size of ulcer crater for two treatment groups ## Armitage (1955, Tab. 2) armitage <- matrix( c( 6, 4, 10, 12, 11, 8, 8, 5), byrow = TRUE, ncol = 4, dimnames = list( "Treatment" = c("A", "B"), "Crater" = c("Larger", "< 2/3 healed", ">= 2/3 healed", "Healed") ) ) armitage <- as.table(armitage) ## Approximative (Monte Carlo) Pearson chi-squared test (Armitage, 1955, p. 379) chisq_test(armitage, distribution = approximate(nresample = 10000)) # chi^2 = 5.91 ## Approximative (Monte Carlo) Cochran-Armitage test (Armitage, 1955, p. 379) (ct <- chisq_test(armitage, distribution = approximate(nresample = 10000), scores = list("Crater" = c(-1.5, -0.5, 0.5, 1.5)))) statistic(ct)^2 # chi_0^2 = 5.26 ## Relationship between job satisfaction and income stratified by gender ## Agresti (2002, p. 288, Tab. 7.8) ## Asymptotic generalized Cochran-Mantel-Haenszel test (Agresti, p. 297) (ct <- cmh_test(jobsatisfaction)) # CMH = 10.2001 ## The standardized linear statistic statistic(ct, type = "standardized") ## The standardized linear statistic for each block statistic(ct, type = "standardized", partial = TRUE) ## Asymptotic generalized Cochran-Mantel-Haenszel test (Agresti, p. 297) ## Note: 'Job.Satisfaction' as ordinal cmh_test(jobsatisfaction, scores = list("Job.Satisfaction" = c(1, 3, 4, 5))) # L^2 = 9.0342 ## Asymptotic linear-by-linear association test (Agresti, p. 297) ## Note: 'Job.Satisfaction' and 'Income' as ordinal (lt <- lbl_test(jobsatisfaction, scores = list("Job.Satisfaction" = c(1, 3, 4, 5), "Income" = c(3, 10, 20, 35)))) statistic(lt)^2 # M^2 = 6.1563 ## The standardized linear statistic statistic(lt, type = "standardized") ## The standardized linear statistic for each block statistic(lt, type = "standardized", partial = TRUE) } \keyword{htest} coin/man/CorrelationTests.Rd0000644000176200001440000001231113401471036015545 0ustar liggesusers\name{CorrelationTests} \alias{spearman_test} \alias{spearman_test.formula} \alias{spearman_test.IndependenceProblem} \alias{fisyat_test} \alias{fisyat_test.formula} \alias{fisyat_test.IndependenceProblem} \alias{quadrant_test} \alias{quadrant_test.formula} \alias{quadrant_test.IndependenceProblem} \alias{koziol_test} \alias{koziol_test.formula} \alias{koziol_test.IndependenceProblem} \concept{Spearman correlation test} \concept{Fisher-Yates correlation test} \concept{Quadrant test} \concept{Koziol-Nemec test} \encoding{UTF-8} \title{Correlation Tests} \description{ Testing the independence of two numeric variables. } % NOTE: the markup in the following section is necessary for correct rendering \usage{ \method{spearman_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{spearman_test}{IndependenceProblem}(object, distribution = c("asymptotic", "approximate", "none"), \dots) \method{fisyat_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{fisyat_test}{IndependenceProblem}(object, distribution = c("asymptotic", "approximate", "none"), ties.method = c("mid-ranks", "average-scores"), \dots) \method{quadrant_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{quadrant_test}{IndependenceProblem}(object, distribution = c("asymptotic", "approximate", "none"), mid.score = c("0", "0.5", "1"), \dots) \method{koziol_test}{formula}(formula, data, subset = NULL, weights = NULL, \dots) \method{koziol_test}{IndependenceProblem}(object, distribution = c("asymptotic", "approximate", "none"), ties.method = c("mid-ranks", "average-scores"), \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} and \code{x} are numeric variables and \code{block} is an optional factor for stratification. } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{weights}{ an optional formula of the form \code{~ w} defining integer valued case weights for each observation. Defaults to \code{NULL}, implying equal weight for all observations. } \item{object}{ an object inheriting from class \code{"\linkS4class{IndependenceProblem}"}. } \item{distribution}{ a character, the conditional null distribution of the test statistic can be approximated by its asymptotic distribution (\code{"asymptotic"}, default) or via Monte Carlo resampling (\code{"approximate"}). Alternatively, the functions \code{\link{asymptotic}} or \code{\link{approximate}} can be used. Computation of the null distribution can be suppressed by specifying \code{"none"}. } \item{ties.method}{ a character, the method used to handle ties: the score generating function either uses mid-ranks (\code{"mid-ranks"}, default) or averages the scores of randomly broken ties (\code{"average-scores"}). } \item{mid.score}{ a character, the score assigned to observations exactly equal to the median: either 0 (\code{"0"}, default), 0.5 (\code{"0.5"}) or 1 (\code{"1"}); see \code{\link{median_test}}. } \item{\dots}{ further arguments to be passed to \code{\link{independence_test}}. } } \details{ \code{spearman_test}, \code{fisyat_test}, \code{quadrant_test} and \code{koziol_test} provide the Spearman correlation test, the Fisher-Yates correlation test using van der Waerden scores, the quadrant test and the Koziol-Nemec test. A general description of these methods is given by \enc{Hájek}{Hajek}, \enc{Šidák}{Sidak} and Sen (1999, Sec. 4.6). The Koziol-Nemec test was suggested by Koziol and Nemec (1979). For the adjustment of scores for tied values see \enc{Hájek}{Hajek}, \enc{Šidák}{Sidak} and Sen (1999, pp. 133--135). The null hypothesis of independence, or conditional independence given \code{block}, between \code{y} and \code{x} is tested. The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling by setting \code{distribution} to \code{"approximate"}. See \code{\link{asymptotic}} and \code{\link{approximate}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \references{ \enc{Hájek}{Hajek}, J., \enc{Šidák}{Sidak}, Z. and Sen, P. K. (1999). \emph{Theory of Rank Tests}, Second Edition. San Diego: Academic Press. Koziol, J. A. and Nemec, A. F. (1979). On a \enc{Cramér}{Cramer}-von Mises type statistic for testing bivariate independence. \emph{The Canadian Journal of Statistics} \bold{7}(1), 43--52. \doi{10.2307/3315014} } \examples{ ## Asymptotic Spearman test spearman_test(CONT ~ INTG, data = USJudgeRatings) ## Asymptotic Fisher-Yates test fisyat_test(CONT ~ INTG, data = USJudgeRatings) ## Asymptotic quadrant test quadrant_test(CONT ~ INTG, data = USJudgeRatings) ## Asymptotic Koziol-Nemec test koziol_test(CONT ~ INTG, data = USJudgeRatings) } \keyword{htest} coin/man/IndependenceProblem-class.Rd0000644000176200001440000000451512712365071017262 0ustar liggesusers\name{IndependenceProblem-class} \docType{class} \alias{IndependenceProblem-class} \alias{initialize,IndependenceProblem-method} \title{Class \code{"IndependenceProblem"}} \description{ Objects of class \code{"IndependenceProblem"} represent the data structure corresponding to an independence problem. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("IndependenceProblem", x, y, block = NULL, weights = NULL, \dots)} where \code{x} and \code{y} are data frames containing the variables \eqn{\mathbf{X}}{X} and \eqn{\mathbf{Y}}{Y} respectively, \code{block} is an optional factor representing the block structure \eqn{b} and \code{weights} is an optional integer vector corresponding to the case weights \eqn{w}. } \section{Slots}{ \describe{ \item{\code{x}:}{ Object of class \code{"data.frame"}. The variables \code{x}. } \item{\code{y}:}{ Object of class \code{"data.frame"}. The variables \code{y}. } \item{\code{block}:}{ Object of class \code{"factor"}. The block structure. } \item{\code{weights}:}{ Object of class \code{"numeric"}. The case weights. } } } \section{Known Subclasses}{ Class \code{"\linkS4class{IndependenceTestProblem}"}, directly. \cr Class \code{"\linkS4class{SymmetryProblem}"}, directly. \cr Class \code{"\linkS4class{IndependenceLinearStatistic}"}, by class \code{"\linkS4class{IndependenceTestProblem}"}, distance 2. \cr Class \code{"\linkS4class{IndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestProblem}"}, distance 3. \cr Class \code{"\linkS4class{MaxTypeIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestProblem}"}, distance 4. \cr Class \code{"\linkS4class{QuadTypeIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestProblem}"}, distance 4. \cr Class \code{"\linkS4class{ScalarIndependenceTestStatistic}"}, by class \code{"\linkS4class{IndependenceTestProblem}"}, distance 4. } \section{Methods}{ \describe{ \item{initialize}{ \code{signature(.Object = "IndependenceProblem")}: See the documentation for \code{\link[methods:new]{initialize}} (in package \pkg{methods}) for details. } } } \keyword{classes} coin/man/SymmetryTests.Rd0000644000176200001440000002440613401471036015125 0ustar liggesusers\name{SymmetryTests} \alias{sign_test} \alias{sign_test.formula} \alias{sign_test.SymmetryProblem} \alias{wilcoxsign_test} \alias{wilcoxsign_test.formula} \alias{wilcoxsign_test.SymmetryProblem} \alias{friedman_test} \alias{friedman_test.formula} \alias{friedman_test.SymmetryProblem} \alias{quade_test} \alias{quade_test.formula} \alias{quade_test.SymmetryProblem} \concept{Sign test} \concept{Wilcoxon signed-rank test} \concept{Friedman test} \concept{Page test} \concept{Quade test} \title{Symmetry Tests} \description{ Testing the symmetry of a numeric repeated measurements variable in a complete block design. } \usage{ \method{sign_test}{formula}(formula, data, subset = NULL, \dots) \method{sign_test}{SymmetryProblem}(object, \dots) \method{wilcoxsign_test}{formula}(formula, data, subset = NULL, \dots) \method{wilcoxsign_test}{SymmetryProblem}(object, zero.method = c("Pratt", "Wilcoxon"), \dots) \method{friedman_test}{formula}(formula, data, subset = NULL, \dots) \method{friedman_test}{SymmetryProblem}(object, \dots) \method{quade_test}{formula}(formula, data, subset = NULL, \dots) \method{quade_test}{SymmetryProblem}(object, \dots) } \arguments{ \item{formula}{ a formula of the form \code{y ~ x | block} where \code{y} is a numeric variable, \code{x} is a factor with two (\code{sign_test} and \code{wilcoxsign_test}) or more levels and \code{block} is an optional factor (which is generated automatically if omitted). } \item{data}{ an optional data frame containing the variables in the model formula. } \item{subset}{ an optional vector specifying a subset of observations to be used. Defaults to \code{NULL}. } \item{object}{ an object inheriting from class \code{"\linkS4class{SymmetryProblem}"}. } \item{zero.method}{ a character, the method used to handle zeros: either \code{"Pratt"} (default) or \code{"Wilcoxon"}; see \sQuote{Details}. } \item{\dots}{ further arguments to be passed to \code{\link{symmetry_test}}. } } \details{ \code{sign_test}, \code{wilcoxsign_test}, \code{friedman_test} and \code{quade_test} provide the sign test, the Wilcoxon signed-rank test, the Friedman test, the Page test and the Quade test. A general description of these methods is given by Hollander and Wolfe (1999). The null hypothesis of symmetry is tested. The response variable and the measurement conditions are given by \code{y} and \code{x}, respectively, and \code{block} is a factor where each level corresponds to exactly one subject with repeated measurements. For \code{sign_test} and \code{wilcoxsign_test}, formulae of the form \code{y ~ x | block} and \code{y ~ x} are allowed. The latter form is interpreted as \code{y} is the first and \code{x} the second measurement on the same subject. If \code{x} is an ordered factor, the default scores, \code{1:nlevels(x)}, can be altered using the \code{scores} argument (see \code{\link{symmetry_test}}); this argument can also be used to coerce nominal factors to class \code{"ordered"}. In this case, a linear-by-linear association test is computed and the direction of the alternative hypothesis can be specified using the \code{alternative} argument. For the Friedman test, this extension was given by Page (1963) and is known as the Page test. For \code{wilcoxsign_test}, the default method of handling zeros (\code{zero.method = "Pratt"}), due to Pratt (1959), first rank-transforms the absolute differences (including zeros) and then discards the ranks corresponding to the zero-differences. The proposal by Wilcoxon (1949, p. 6) first discards the zero-differences and then rank-transforms the remaining absolute differences (\code{zero.method = "Wilcoxon"}). The conditional null distribution of the test statistic is used to obtain \eqn{p}-values and an asymptotic approximation of the exact distribution is used by default (\code{distribution = "asymptotic"}). Alternatively, the distribution can be approximated via Monte Carlo resampling or computed exactly for univariate two-sample problems by setting \code{distribution} to \code{"approximate"} or \code{"exact"} respectively. See \code{\link{asymptotic}}, \code{\link{approximate}} and \code{\link{exact}} for details. } \value{ An object inheriting from class \code{"\linkS4class{IndependenceTest}"}. } \note{ Starting with \pkg{coin} version 1.0-16, the \code{zero.method} argument replaced the (now removed) \code{ties.method} argument. The current default is \code{zero.method = "Pratt"} whereas earlier versions had \code{ties.method = "HollanderWolfe"}, which is equivalent to \code{zero.method = "Wilcoxon"}. } \references{ Hollander, M. and Wolfe, D. A. (1999). \emph{Nonparametric Statistical Methods}, Second Edition. New York: John Wiley & Sons. Page, E. B. (1963). Ordered hypotheses for multiple treatments: a significance test for linear ranks. \emph{Journal of the American Statistical Association} \bold{58}(301), 216--230. \doi{10.1080/01621459.1963.10500843} Pratt, J. W. (1959). Remarks on zeros and ties in the Wilcoxon signed rank procedures. \emph{Journal of the American Statistical Association} \bold{54}(287), 655--667. \doi{10.1080/01621459.1959.10501526} Quade, D. (1979). Using weighted rankings in the analysis of complete blocks with additive block effects. \emph{Journal of the American Statistical Association} \bold{74}(367), 680--683. \doi{10.1080/01621459.1979.10481670} Wilcoxon, F. (1949). \emph{Some Rapid Approximate Statistical Procedures}. New York: American Cyanamid Company. } \examples{ ## Example data from ?wilcox.test y1 <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) y2 <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) ## One-sided exact sign test (st <- sign_test(y1 ~ y2, distribution = "exact", alternative = "greater")) midpvalue(st) # mid-p-value ## One-sided exact Wilcoxon signed-rank test (wt <- wilcoxsign_test(y1 ~ y2, distribution = "exact", alternative = "greater")) statistic(wt, type = "linear") midpvalue(wt) # mid-p-value ## Comparison with R's wilcox.test() function wilcox.test(y1, y2, paired = TRUE, alternative = "greater") ## Data with explicit group and block information dta <- data.frame(y = c(y1, y2), x = gl(2, length(y1)), block = factor(rep(seq_along(y1), 2))) ## For two samples, the sign test is equivalent to the Friedman test... sign_test(y ~ x | block, data = dta, distribution = "exact") friedman_test(y ~ x | block, data = dta, distribution = "exact") ## ...and the signed-rank test is equivalent to the Quade test wilcoxsign_test(y ~ x | block, data = dta, distribution = "exact") quade_test(y ~ x | block, data = dta, distribution = "exact") ## Comparison of three methods ("round out", "narrow angle", and "wide angle") ## for rounding first base. ## Hollander and Wolfe (1999, p. 274, Tab. 7.1) rounding <- data.frame( times = c(5.40, 5.50, 5.55, 5.85, 5.70, 5.75, 5.20, 5.60, 5.50, 5.55, 5.50, 5.40, 5.90, 5.85, 5.70, 5.45, 5.55, 5.60, 5.40, 5.40, 5.35, 5.45, 5.50, 5.35, 5.25, 5.15, 5.00, 5.85, 5.80, 5.70, 5.25, 5.20, 5.10, 5.65, 5.55, 5.45, 5.60, 5.35, 5.45, 5.05, 5.00, 4.95, 5.50, 5.50, 5.40, 5.45, 5.55, 5.50, 5.55, 5.55, 5.35, 5.45, 5.50, 5.55, 5.50, 5.45, 5.25, 5.65, 5.60, 5.40, 5.70, 5.65, 5.55, 6.30, 6.30, 6.25), methods = factor(rep(1:3, 22), labels = c("Round Out", "Narrow Angle", "Wide Angle")), block = gl(22, 3) ) ## Asymptotic Friedman test friedman_test(times ~ methods | block, data = rounding) ## Parallel coordinates plot with(rounding, { matplot(t(matrix(times, ncol = 3, byrow = TRUE)), type = "l", lty = 1, col = 1, ylab = "Time", xlim = c(0.5, 3.5), axes = FALSE) axis(1, at = 1:3, labels = levels(methods)) axis(2) }) ## Where do the differences come from? ## Wilcoxon-Nemenyi-McDonald-Thompson test (Hollander and Wolfe, 1999, p. 295) ## Note: all pairwise comparisons (st <- symmetry_test(times ~ methods | block, data = rounding, ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo, block = rounding$block), xtrafo = mcp_trafo(methods = "Tukey"))) ## Simultaneous test of all pairwise comparisons ## Wide Angle vs. Round Out differ (Hollander and Wolfe, 1999, p. 296) pvalue(st, method = "single-step") # subset pivotality is violated ## Strength Index of Cotton ## Hollander and Wolfe (1999, p. 286, Tab. 7.5) cotton <- data.frame( strength = c(7.46, 7.17, 7.76, 8.14, 7.63, 7.68, 7.57, 7.73, 8.15, 8.00, 7.21, 7.80, 7.74, 7.87, 7.93), potash = ordered(rep(c(144, 108, 72, 54, 36), 3), levels = c(144, 108, 72, 54, 36)), block = gl(3, 5) ) ## One-sided asymptotic Page test friedman_test(strength ~ potash | block, data = cotton, alternative = "greater") ## One-sided approximative (Monte Carlo) Page test friedman_test(strength ~ potash | block, data = cotton, alternative = "greater", distribution = approximate(nresample = 10000)) ## Data from Quade (1979, p. 683) dta <- data.frame( y = c(52, 45, 38, 63, 79, 50, 45, 57, 39, 53, 51, 43, 47, 50, 56, 62, 72, 49, 49, 52, 40), x = factor(rep(LETTERS[1:3], 7)), b = factor(rep(1:7, each = 3)) ) ## Approximative (Monte Carlo) Friedman test ## Quade (1979, p. 683) friedman_test(y ~ x | b, data = dta, distribution = approximate(nresample = 10000)) # chi^2 = 6.000 ## Approximative (Monte Carlo) Quade test ## Quade (1979, p. 683) (qt <- quade_test(y ~ x | b, data = dta, distribution = approximate(nresample = 10000))) # W = 8.157 ## Comparison with R's quade.test() function quade.test(y ~ x | b, data = dta) ## quade.test() uses an F-statistic b <- nlevels(qt@statistic@block) A <- sum(qt@statistic@y^2) B <- sum(statistic(qt, type = "linear")^2) / b (b - 1) * B / (A - B) # F = 8.3765 } \keyword{htest} coin/man/IndependenceTest-class.Rd0000644000176200001440000001570514113674115016603 0ustar liggesusers\name{IndependenceTest-class} \docType{class} \alias{IndependenceTest-class} \alias{MaxTypeIndependenceTest-class} \alias{QuadTypeIndependenceTest-class} \alias{ScalarIndependenceTest-class} \alias{ScalarIndependenceTestConfint-class} \alias{confint,IndependenceTest-method} \alias{confint,ScalarIndependenceTestConfint-method} \alias{show,IndependenceTest-method} \alias{show,MaxTypeIndependenceTest-method} \alias{show,QuadTypeIndependenceTest-method} \alias{show,ScalarIndependenceTest-method} \alias{show,ScalarIndependenceTestConfint-method} \title{Class \code{"IndependenceTest"} and Its Subclasses} \description{ Objects of class \code{"IndependenceTest"} and its subclasses \code{"MaxTypeIndependenceTest"}, \code{"QuadTypeIndependenceTest"}, \code{"ScalarIndependenceTest"} and \code{"ScalarIndependenceTestConfint"} represent an independence test including its original and transformed data structure, linear statistic, test statistic and reference distribution. } % NOTE: the markup in the following section is necessary for correct rendering \section{Objects from the Class}{ Objects can be created by calls of the form \preformatted{ new("IndependenceTest", \dots), new("MaxTypeIndependenceTest", \dots), new("QuadTypeIndependenceTest", \dots), new("ScalarIndependenceTest", \dots)} and \preformatted{ new("ScalarIndependenceTestConfint", \dots).} } \section{Slots}{ For objects of classes \code{"IndependenceTest"}, \code{"MaxTypeIndependenceTest"}, \code{"QuadTypeIndependenceTest"}, \code{"ScalarIndependenceTest"} or \code{"ScalarIndependenceTestConfint"}: \describe{ \item{\code{distribution}:}{ Object of class \code{"\linkS4class{PValue}"}. The reference distribution. } \item{\code{statistic}:}{ Object of class \code{"\linkS4class{IndependenceTestStatistic}"}. The test statistic, the linear statistic, and the transformed and original data structures. } \item{\code{estimates}:}{ Object of class \code{"list"}. The estimated parameters. } \item{\code{method}:}{ Object of class \code{"character"}. The test method. } \item{\code{call}:}{ Object of class \code{"call"}. The matched call. } } Additionally, for objects of classes \code{"ScalarIndependenceTest"} or \code{"ScalarIndependenceTestConfint"}: \describe{ \item{\code{parameter}:}{ Object of class \code{"character"}. The tested parameter. } \item{\code{nullvalue}:}{ Object of class \code{"numeric"}. The hypothesized value of the null hypothesis. } } Additionally, for objects of class \code{"ScalarIndependenceTestConfint"}: \describe{ \item{\code{confint}:}{ Object of class \code{"function"}. The confidence interval function. } \item{\code{conf.level}:}{ Object of class \code{"numeric"}. The confidence level. } } } \section{Extends}{ For objects of classes \code{"MaxTypeIndependenceTest"}, \code{"QuadTypeIndependenceTest"} or \code{"ScalarIndependenceTest"}: \cr Class \code{"IndependenceTest"}, directly. For objects of class \code{"ScalarIndependenceTestConfint"}: \cr Class \code{"ScalarIndependenceTest"}, directly. \cr Class \code{"IndependenceTest"}, by class \code{"ScalarIndependenceTest"}, distance 2. } \section{Known Subclasses}{ For objects of class \code{"IndependenceTest"}: \cr Class \code{"MaxTypeIndependenceTest"}, directly. \cr Class \code{"QuadTypeIndependenceTest"}, directly. \cr Class \code{"ScalarIndependenceTest"}, directly. \cr Class \code{"ScalarIndependenceTestConfint"}, by class \code{"ScalarIndependenceTest"}, distance 2. For objects of class \code{"ScalarIndependenceTest"}: \cr Class \code{"ScalarIndependenceTestConfint"}, directly. } \section{Methods}{ \describe{ \item{confint}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link[stats4]{confint-methods}} (in package \pkg{stats4}) for details. } \item{confint}{ \code{signature(object = "ScalarIndependenceTestConfint")}: See the documentation for \code{\link[stats4]{confint-methods}} (in package \pkg{stats4}) for details. } \item{covariance}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{covariance}} for details. } \item{dperm}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{dperm}} for details. } \item{expectation}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{expectation}} for details. } \item{midpvalue}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{midpvalue}} for details. } \item{pperm}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{pperm}} for details. } \item{pvalue}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{pvalue}} for details. } \item{pvalue_interval}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{pvalue_interval}} for details. } \item{qperm}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{qperm}} for details. } \item{rperm}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{rperm}} for details. } \item{show}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link[methods]{show}} (in package \pkg{methods}) for details. } \item{show}{ \code{signature(object = "MaxTypeIndependenceTest")}: See the documentation for \code{\link[methods]{show}} (in package \pkg{methods}) for details. } \item{show}{ \code{signature(object = "QuadTypeIndependenceTest")}: See the documentation for \code{\link[methods]{show}} (in package \pkg{methods}) for details. } \item{show}{ \code{signature(object = "ScalarIndependenceTest")}: See the documentation for \code{\link[methods]{show}} (in package \pkg{methods}) for details. } \item{show}{ \code{signature(object = "ScalarIndependenceTestConfint")}: See the documentation for \code{\link[methods]{show}} (in package \pkg{methods}) for details. } \item{size}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{size}} for details. } \item{statistic}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{statistic}} for details. } \item{support}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{support}} for details. } \item{variance}{ \code{signature(object = "IndependenceTest")}: See the documentation for \code{\link{variance}} for details. } } } \keyword{classes} coin/man/GTSG.Rd0000644000176200001440000000613713401471036013016 0ustar liggesusers\name{GTSG} \docType{data} \alias{GTSG} \encoding{UTF-8} \title{Gastrointestinal Tumor Study Group} \description{ A randomized clinical trial in gastric cancer. } \usage{GTSG} \format{ A data frame with 90 observations on 3 variables. \describe{ \item{\code{time}}{ survival time (days). } \item{\code{event}}{ status indicator for \code{time}: \code{0} for right-censored observations and \code{1} otherwise. } \item{\code{group}}{ a factor with levels \code{"Chemotherapy+Radiation"} and \code{"Chemotherapy"}. } } } \details{ A clinical trial comparing chemotherapy alone versus a combination of chemotherapy and radiation therapy in the treatment of locally advanced, nonresectable gastric carcinoma. } \note{ There is substantial separation between the estimated survival distributions at 8 to 10 months, but by month 26 the distributions intersect. } \source{ Stablein, D. M., Carter, W. H., Jr. and Novak, J. W. (1981). Analysis of survival data with nonproportional hazard functions. \emph{Controlled Clinical Trials} \bold{2}(2), 149--159. \doi{10.1016/0197-2456(81)90005-2} } \references{ Moreau, T., Maccario, J., Lellouch, J. and Huber, C. (1992). Weighted log rank statistics for comparing two distributions. \emph{Biometrika} \bold{79}(1), 195--198. \doi{10.1093/biomet/79.1.195} Shen, W. and Le, C. T. (2000). Linear rank tests for censored survival data. \emph{Communications in Statistics -- Simulation and Computation} \bold{29}(1), 21--36. \doi{10.1080/03610910008813599} Tubert-Bitter, P., Kramar, A., \enc{Chalé}{Chale}, J. J. and Moureau, T. (1994). Linear rank tests for comparing survival in two groups with crossing hazards. \emph{Computational Statistics & Data Analysis} \bold{18}(5), 547--559. \doi{10.1016/0167-9473(94)90084-1} } \examples{ ## Plot Kaplan-Meier estimates plot(survfit(Surv(time / (365.25 / 12), event) ~ group, data = GTSG), lty = 1:2, ylab = "\% Survival", xlab = "Survival Time in Months") legend("topright", lty = 1:2, c("Chemotherapy+Radiation", "Chemotherapy"), bty = "n") ## Asymptotic logrank test logrank_test(Surv(time, event) ~ group, data = GTSG) ## Asymptotic Prentice test logrank_test(Surv(time, event) ~ group, data = GTSG, type = "Prentice") ## Asymptotic test against Weibull-type alternatives (Moreau et al., 1992) moreau_weight <- function(time, n.risk, n.event) 1 + log(-log(cumprod(n.risk / (n.risk + n.event)))) independence_test(Surv(time, event) ~ group, data = GTSG, ytrafo = function(data) trafo(data, surv_trafo = function(y) logrank_trafo(y, weight = moreau_weight))) ## Asymptotic test against crossing-curve alternatives (Shen and Le, 2000) shen_trafo <- function(x) ansari_trafo(logrank_trafo(x, type = "Prentice")) independence_test(Surv(time, event) ~ group, data = GTSG, ytrafo = function(data) trafo(data, surv_trafo = shen_trafo)) } \keyword{datasets} coin/man/asat.Rd0000644000176200001440000000356713437424262013216 0ustar liggesusers\name{asat} \docType{data} \alias{asat} \encoding{UTF-8} \title{Toxicological Study on Female Wistar Rats} \description{ Measurements of the liver enzyme aspartate aminotransferase (ASAT) for a new compound and a control group of 34 female Wistar rats. } \usage{asat} \format{ A data frame with 34 observations on 2 variables. \describe{ \item{\code{asat}}{ ASAT values. } \item{\code{group}}{ a factor with levels \code{"Compound"} and \code{"Control"}. } } } \details{ The aim of this toxicological study is the proof of safety for the new compound. The data were originally given in Hothorn (1992) and later reproduced by Hauschke, Kieser and Hothorn (1999). } \source{ Hauschke, D., Kieser, M. and Hothorn, L. A. (1999). Proof of safety in toxicology based on the ratio of two means for normally distributed data. \emph{Biometrical Journal} \bold{41}(3), 295--304. \doi{10.1002/(SICI)1521-4036(199906)41:3<295::AID-BIMJ295>3.0.CO;2-2} Hothorn, L. A. (1992). Biometrische analyse toxikologischer untersuchungen. In J. Adam (Ed.), \emph{Statistisches Know-How in der Medizinischen Forschung}, pp. 475--590. Berlin: Ullstein Mosby. } \references{ \enc{Pflüger}{Pflueger}, R. and Hothorn, T. (2002). Assessing equivalence tests with respect to their expected \eqn{p}-value. \emph{Biometrical Journal} \bold{44}(8), 1015--1027. \doi{10.1002/bimj.200290001} } \examples{ ## Proof-of-safety based on ratio of medians (Pflueger and Hothorn, 2002) ## One-sided exact Wilcoxon-Mann-Whitney test wt <- wilcox_test(I(log(asat)) ~ group, data = asat, distribution = "exact", alternative = "less", conf.int = TRUE) ## One-sided confidence set ## Note: Safety cannot be concluded since the effect of the compound ## exceeds 20 \% of the control median exp(confint(wt)$conf.int) } \keyword{datasets} coin/DESCRIPTION0000644000176200001440000000364414130001757012715 0ustar liggesusersPackage: coin Version: 1.4-2 Date: 2021-10-07 Title: Conditional Inference Procedures in a Permutation Test Framework Authors@R: c(person("Torsten", "Hothorn", role = c("aut", "cre"), email = "Torsten.Hothorn@R-project.org", comment = c(ORCID = "0000-0001-8301-0471")), person("Henric", "Winell", role = "aut", comment = c(ORCID = "0000-0001-7995-3047")), person("Kurt", "Hornik", role = "aut", comment = c(ORCID = "0000-0003-4198-9911")), person(c("Mark", "A."), "van de Wiel", role = "aut", comment = c(ORCID = "0000-0003-4780-8472")), person("Achim", "Zeileis", role = "aut", comment = c(ORCID = "0000-0003-0918-3766"))) Description: Conditional inference procedures for the general independence problem including two-sample, K-sample (non-parametric ANOVA), correlation, censored, ordered and multivariate problems described in . Depends: R (>= 3.6.0), survival Imports: methods, parallel, stats, stats4, utils, libcoin (>= 1.0-9), matrixStats (>= 0.54.0), modeltools (>= 0.2-9), mvtnorm (>= 1.0-5), multcomp Suggests: xtable, e1071, vcd, TH.data (>= 1.0-7) LinkingTo: libcoin (>= 1.0-9) LazyData: yes NeedsCompilation: yes ByteCompile: yes License: GPL-2 URL: http://coin.r-forge.r-project.org Packaged: 2021-10-07 13:52:08 UTC; hothorn Author: Torsten Hothorn [aut, cre] (), Henric Winell [aut] (), Kurt Hornik [aut] (), Mark A. van de Wiel [aut] (), Achim Zeileis [aut] () Maintainer: Torsten Hothorn Repository: CRAN Date/Publication: 2021-10-08 08:40:15 UTC coin/build/0000755000176200001440000000000014127575605012315 5ustar liggesuserscoin/build/vignette.rds0000644000176200001440000000076314127575605014662 0ustar liggesusers}To0N !$i;!ƩTijaWy)buO+ϋ&L99:24qLGϐޣ Pr &Wj"oJϴJ.TZs8:Z;+lV`1kA@# , ˞7wl< ZRmS~+ˀAOLa\\%|e`J@rX0m^(t$t{w%UH&q-hJpǠhϘv= >~z'!7j;M~5D3#|`A"|gns".r3f29stfj'0JZaCBŵ3^B'8Э\ZgO3:d"ͭGpkF!sY^&]_!8(2|bĪ<҅%YhhfR;?4v6#?VƓ d=TEcoin/build/partial.rdb0000644000176200001440000061502114127575540014445 0ustar liggesusersxɖ& B$e(GI%oC#%*(U޾]d^HT& c{3=~z{=~۷ow{Yݗ'O fR @.}8'N8+DWg۶DW7y;Ht߷yxǞDݳ/$=]܏v,?k{.ns-oOBmW;jLmJR>l.Vl{hX~~`槶/n o /.<{\%׊'tZ%h6CKJ O׍CK+UƲÙHv(g[Q^7yg@3MSFWjZѶom_*Nv}$gw{z61FZ۹(tC~P}ѤgL YT#Kݱl,Í)wv냊!Mh6d/l;+ NOB>Q?R/= )ȧگ*4x$ӥJg{"!QlKΊ]bkae̙.Wk|ҢTK grtsUXv)Oggiݾ4pn] [u J 젿ro~[eF[u*,;t^e\XJt7V&F!*3bL_r1BO*hb0&0{`*?r%BvD`#bwx 1mh7UF{"㐏7JSQ1qC{4ܪcR.q^z"<fUjcJV,{`߄x:>}Dψ!vmt3)xA`'Qv<;IesEYsQ5x1Cڎb;x4aYYU=^qR^@njC|snhdûVV5TJkl09Kg(Z!umG8 ;qΣϫʕg]-^*'櫹`ǻh[nŋIʰ ƊU*zw!Y^{\,_ui;")vuKנh]Yi Eggd .{mzP1^?2=5=,EF=!+1cQ20Mt,zrrvO P턷v(Vh | q &T #; i Nk&zL>}*$35Vlp=C2 b( \Ⱥ &]Q{ut&F |Y "樏PfUzxV1 =fx=f#<Yg7PqG!K~`zL֏60Yx=O Z5,} yA"0o2~LUIFm Sr-XJ޿'Z&Gi_Vub~hwt]VDJ<@6s((ľ ҫ^<-nv9*Zխ r @\U6P8؎'tnp'Ptz\oU0-ovev#4cWk=Ԍ^wNu)h`]&PmnU>s>y,eѥ.bJ !%kf:uo[غp晜7kR,Z)TB *͘l?aTzsI{.CԳ؋.YtI'=%ٌ'-zsoJ>cVQ:UNY1On'zqbZ8tz%]QLl*519,||2)@>vA-x3Cnvdlj, )ﯣm_uC>/5Hl92c'! bT3oa`+=Ǩ6F1j#'$]13S2fέf?tjԷJ/KHRSGy/c[jebz./BPm-<[d[ ote_$Eipg% y\;F_%dc? QfOJ+NZ VVh)8TIBAiGs+N5Wz`xz|B>-<8έEkMW`rZUSqǀCԻv2c8 Y\5NARFɦRSc¹j"3 |˔KG rՙÌ2cTmu?\5Xr\uEs+=W\6FUk#'45$3wtO-o4֚lCO}y""i_QGy/c\Ot䪿PU+/EE.\5_,{1™? tQ/0Q2V^XKnCaME,8#龚gt(oFn@xi 땕7le=6ؒ qShiBtJnݶ 2icdWZ~yRuoZ[QȣkW\ J/R%BTޕNG(6˵ QHr9ͦFSSŒ?{_ϔ*zRdSYѠ :ں9^v÷MwC{:u}qkOR̋UV 1 --l+ XZ^ap=^; zdğћs] >0Gj(&+JU}mpI; d0N\'eŞ][>!w̐bUf#Å?]gF%o+3<Ϡ1}/r%YIaIޱ{3O0y !k&.o|J7jHp(k}߶/v/k#ҳlrw>jﾵ/moeoh`Dr%ȽsQssyZ:&-\*=Z1g/]7.MW/bpQfsE= pRω%_7[՞eI-Tڳ_-m&]ˮin~,奷ZﲻQˮ6`sxdŢ>p_=R[pr딶M+VVshVm+Ep۱_ܷui[ܷ.DWagy:l60r-{fe|e>eϦ4\fSCx)x[~eѭYVi-߫w.nJL7mjSV馞Cw߱\orVon4fk6o1ߩrQn;zF} ]2}nO^8F>U1̤;]VKy_k_8ixuuYX)y5ۛF94̢a)(mvp(ҷ=:U;b|`)Zl,߲v.VN}Wh jysa8"-9d;kbT sX}'voFR~von ݷZg(7o WԾvtSc{Tg\{!vbӳ\~TCL?Z.^EDWXԉI\c蓽Z% Gw}/H}5ᶌͳsYj}ϲg7J>}~/?;?L?Imӟ#MSpŅgRoU]g`PZZr Zơt8 U%%A'p&?<6V6MjwzZVq_ټj$tqI~V6&kټ[gqiB6&e.m"ل1 Wg-kȷESo}+(!èa:z){`PlC\H.d#9FfӘ143;W5owR^+~ÛK!֮{9uU䜃<^oc'tO,V'P 䌊FdσtdTxuu'^M;Ev}a<,-?B[ ʏo#%bUoG=w.=\|pa^O[H8@F8 ?lqt4M&HG 5!꨷V5B- s}(aYUԤYqk[jNȽu)G~cLJC/feo"AO\nl"oyy`.UҚYmMxB6#sS73˦R\tlOSEAUmz/AUmz#V׵KUThRծ\q]fEAkRxG_nsC<ڜ"9BH΍?^綿qgcU ^I[5-2|4tM5N/X^| r/B~Eg8ģk)dFPa;GPDGG,ŮQ'T䨳 !l稳 !CşPSS̨ l稳 ਲ਼QQgCQw;8^Ps|4.1ozr?RNm5 Ű\ny)[?Y6`?i?3 Vft^A>~QC@Nq E# =zщDò,d\b;ѣ01݁q,*[췮p6o{ tz QM)TB8[wxXvx*p|'z<X.B^|ozi-iRQi2cޢ[̖3 yRz r'z,˴A9Ӓ!=nY-3 x'*6<ډDƀՃa,l"Šo[m%|.Š~?؞v b;be1dOc],Ġ 1( jĠTl?1(la *كH30=_M|P߇}NvΈ!($]d0.i*KCm7Jν>)RSڼOx|diiedH  i϶ |!vdxuel% mȷi䍌Fr>HF[ce*b]pq,/Gv)J\O%jZm+TAiK1bQXn,[wWBxY. !@uvCi+8T>2hF7!k?бunV%BUF48ģG~sU(jWc;h9B' A(d1N쫪({8 ^Hp_PU8!E=mvLX '`寮) +?pYf+&f>sՠOEştS 3COL c4ŗ=*O4LRP~YT.Dm.R>!J8\PgF.;5\ Tu/%Y^UCQBC4MעN\ !KJ]lβJ"o(Jst,g‰ LIvB"!2p %L#G\!1gaUDNTƁSZobYp&U,pjD| | Yn&UFe p42 !ޯ}AلmFtF#T|FFZz, TRU8ȡ0[MXu"o6]QA M~U^xAlRR(T(de3=vDMh{&̄ qad9!6 ⱇC< V8"vx V/}6wRWSC1v"ٍb;;Q=v*vo;I%}IKU4GGZu*^ gZ4K0_X)/1KQA0Do8 yVc.%,6N>wxvNʿ>v:}*CiY/(Zc` Ň%kw*Z⹛Cz v?e)~J j^7 Fż j\@Q?xNX>LԒ?[J(=~ ň xڡ .?'%=eZM E6񻖨L}-{z }c i&禦ŵ <7yl|Dx40Z2H :EلZ h}ݥ1vqGcY6?/Ŕ ,5f6Tn?(8ӣ*CJ7g{.0\!MEajh묿31< ,z1cʚ;6Hk_z/H@Vw[XKj3Wloepl<( ez ;w؋hS-YNM/BRԙ\#+`LmNԗ:Oe.=fJٝ򾒶o v"[5-CoLjuE>oKlo}[p\׮VZ$]1s-ߩ ^׮e`?笪A1oV+&&"Yb#jPQ ;&侠Yek,Q9`o$gJ1k)А+1[ڝ'yɓ^$ً}$JF7O%kuŢ-|2v [gs -8y^6J\~ 9ģHc7ߞ"Knm|,3fI]Qq{ kAF+9>v8&usxY1ڈI]Qqg ˝&z``t0FXV\A_oښxvL]x\ڝX(zRWaA4{dha&cwkk6̕ ] !jZr*.tPk8 Yj\t=HQxM~tތJ ]Ch?Ym:QASR0%he0{E'h{LѤŤ%,<2J4BZ3Ԩk;H%%9 0:63stLNK LT* /$2;(_yY wIЖ;ųdf(ɌdG2ciNLiQ !_ ښ#W8WdXǎ_ 3}[u|o$_My@u1jEP9& bS-$ɦ?t#?=*f<֓X&Gv~ 6Y_Tˋ,vTއ]0}9DWYt!>dCR:<+=_kG'48::WCXV§ٻCF!4S >d43c~=q9Jph}*#/$בU(""'/+ RKe¨c됯ws]Lظ{iFL& V?#i;mD dS16<2J wWj}y4%ܲr#12EU/25El/p/Ȱ~Wq߲ n鯈^:["PAoMiclZT:WָdYU5*fkkibIJzKGξi#/m&>;+q;C:5ԓZ``0M7v)JHÿvҧ$:oP ʕb,O>;fű[9[-ӧ\pMARqȍ=zкH6-AV_*vyfRtÒg D,u:X "b@H-E3jFL ;<6 ٩TjbtRk,׵Sm# orpz41n[&uGm1ZOM՚&WJ{2H/E mZ FNhڮI懗ީt|#RBD21ٔЇn[ |L+։[l^< }c( ů_T;,vه]0}Y;ܛ7԰Y;JҍPnv*.,o9I9Uvqy0_#Z@E /(W S^ͷ;g櫎D۠Gx 9JQŦ\歊y;b.@Vo> rF6b@>މE?!MgؤOhFLʎ;< 6 d@L*5Ɉqs ,>mpvtl*MnX&39!eFfSSֱeȶ~$_M<u1jE>O9ٽ&EWV-o9[[kk)OO$6kSҗm\E Kgz顎^ik9sX۷VHD#&yוwH~98r-L[xEbY~7:,+_4ޞe;crQ/JHvh!I_ߕم;w#Dpx.еr h_\>*:/.HreG3~ (|\+z3 ʼbHb9R kg$NşBKꗁ~I"J%~ͮ@|]aOAVK ',OOlp'~%8|B'U(;D=x.k(+vʱEp\ry0_ W z~1UC)Ē,g; y̓gwEӳGfدLal G tQ!N!ˎ*RRdSYeIRQ5=gl#o%B}C-'o^ R޽ΌZӛ%t:f?7:-ȷq(T́\e2^תY9EoI«*TQ/0, ~jP"3NĐMY0EkuoR&Q(fҙ1r}ʌJÇZ5slV' noC!qÙ`fy8p0eI]1ɯ7 Y\qYeQ&a#ƏF~[GAȃ;A}~~CÏjm ?V}Vn!DA!y^{8BO gf O>p"ԗtDs,opt+d ef"ɞ+i6Ύ?B}.O![@PTl <g+cIŝ VVSq"T[z$k%n ^#ng|@V? 2ӨRߣVuLg?|_B\ .YTqBu/\gOeB}[?ㅞ"tG]{Z>=8?V<e'hR'cx)'y^ͪ7O]9IB}aɁMJŝ)“OiV7? ߚi?bAkLS0?M"*86%bee<([.m%m[|\i䂌cVLa4 5fK=`(ˬUP"Ըf0YkBxA=s@vԛ{lv4&iAP4#Dqܣ8:Q¢1qVg0d%]@>ج _$oڌzf?>fu|d6oVfApl#zC+1Ip%ԗ];Ϯ. '7>Q=jk'8-e'nn"^OHMxu:K$ACP?B!QH%m&]Of(fǨg j9+rZh;ykKb9$LANiTG N?Xu_0]_?EB}fnv1PCg?eB};7iAhѼ_JjxpP"/@;U Aʔavll8=22,L_!:Q+Uq%{Yȳ3/,u xm O Sg#1J4ހ|}ߢ;w(i#f׍%Y`8k@?JoVB5 ߃5ǐ?VI[w()B}/{>ʁBZ? [z,w3 D QR"gA?(4 VH% ^;0!ܧ*>-*xZ[Z>Ң7GT yLքF&.*vSה`Kog͇Ϥ&d*;&?$ْD'NK}ES9PC<(75&yё1&ʵ8/?WPvzI֡ԌS-T.Aȟ/CR~ggvSЦ `Eo 筷&Jc$ɸLT:-ȷԍas1'x;QGc:_xgj=(uتkUքSECI1C{6Bz 7[!x$H$Ɩ,1%!7;ZXOzskz$&)_"< h ףEͯ_Bm׼x$; /(3nHL~†Fغi[| K8 yu $/ ri*c'02o<:g>}Ej,s`yqͶnjkJXŸp)A^O՝:7 u/qm7B}N!dĎY#Aw!C^Cω-]nيYym% {U#W[ay\Ϫ +l,MG>}b"Óx9AbL xn\S뛞v!lƵBao}Sz9! `)5s!وx`/>2N!j2:n O*M`ؼbU+Zď;IV( ymHH~1}e|V v0ulfqG=d8( (N8cP?{}_v>W8Wsf,>;3dܰ$>-7-}7in`^M-XO3#EF;΁9vc dP7}^M;9}Amˀ}l!Vv!e3j,*_ÓZ/׾mk}FnAJ}7p 2,uKsĔ _'{!\l&sğmiT;!c gg=/=]#{9SxmPXZWZxnZZZD67FC9* AkIyngn:lXm7ֲ^Tɘr`} 3Z÷G!s|殺VRԶcit\\x+Jh)_+Ul檵_{[NWWm_e1* cu Ur܅(;疽g[ 1FN.aȇeEc(XF`݅ X.t}x4iHf^XX A uC+!nOۥ!*,x4i|f^rc̢z!mvNyۯ-**x4ikϪn? <Pem>F.P9ģI/qzr;“OA?L]4x4u! rt/ڥ+*~C<ϫF1JR^n3zL;QG95hFa;^h}vC\=nhhʡhM.=a;9CI/:!lg4u>v0Os9A?Œ6a9Fs'!r*ÿICצ]93r%m=C;.sC">ǦԼY4s29/rJ?TikwDviAӦe/vVi-m@[)4ܛWzKwC1!\Ū^rS+ڥ*$x$ӥJfc9ģ*c7Ax$: T-c Ǣܴ(u.wzKѐ.M7Xe2 [D,j9M4ƣHc_x~w^p^Vtm.פY Z.+9u g_MG s5_N;gGU9̷uHv+J'_sy瑈YiFLk,]-)-H,ɍYYqMrI;@3$Yިxw+YaO$kRvk53bˀz0WrޮD%[N>L$%ρBn'N}$ۂqURiyѮmZҊn +0iKkQ&~e6.~E*,C.w/ρduA,nmePL9x/#R}tDh$z/fUr`b{uz*vNtz"|Y.hQg;R4 g [E:Uï@ \OtA;)Zc^~=^fm2Y>av&Tu N8"p8 yVx[AҼ٘9{3'2ǁm3(%>I<L⩸`G'D9xv>t1rOĎ:?g/lD? TO†%/"Ide~7ar}@!1Rn=S+35K*^{y 2Gm<?= @恊v4@-}^UCQIrC +NNQT8Lj^u)ްh>) y9;|S4dc97ŕp .J?6dt xڡquוu?JVB#7!֧72y!vhd#qLQK /X k.[KR뭆; R^lͳQ`td\`$ &WO!k \qy1WJ8Ot@O۵B˧TeC 2 f>nU>(*r:Fd9T1Rs9B1 5?mK peH6A7@p)7AgTd%C/vhP~OfG|l rF۞ nc4cwUZ^iW,NzXmڢ8 ]z#^j /]C;b݇0dcx;XaL""F.;5\GUuoP%^UCQBC۹ue{-tIx#D rT%`z,˛A}Z#9ģJkxaeOi-4-Z-n?Ƶp%#<<B=G[၃,Ll!]Dz$Y&=&Aȃ?>NFC(d1V\CDmv!cVJ1 '+;{G-7!WVk !_ȤZQO 1r  E2NjSE%&}O﴾X+@-g1&t4,$ 8-vpZ@pةiʫ(jrfYR%Z6\d-.@{!˽7YqDo8 Y Oťw K0sTܕD} ѕ0xz$namtQl>áӏ,ur͗D=xOd Nct!i{xžy[{w8\=FQ/Pi}PqÐ_mLczƛB(xqrOFE8>,c*2W7O{a7OMJFIȽ QC7fgH ر籼 ͸tFʫʆhuU |a BKJ4L?c0܊.>'nztH^/,\L# ]H<7~rVƲ'ďɨ PΚ鳖gVސtxZASR}443 dK8my.ω]3}~?g յ5OV_+|ͫU N_ ,GnbeymFխPF`PPX^U\z&ړ _M^,pc}nL2mGwF|\G* roOb٪7Ej|/ {U$" ?=X~A Vn`RV5?reGFRȘO"w 8ZW8D=l[(4i*¿Jr`^#ZeTlB K/P镭X聄!WV$[1+M;Jz/J5ⷿsiZNd_yҽn!IC#))eQşxQ$ <1P$dZ4ܱf 5 V}~Me h}ݥ1vqG_y)n`/^eMaL(gSLEhp8y^*W6•K Q7ɝQv6VI(6\ \t&>BQ {mq#aV*H ;9YȡlBw9/^xbV4_I O@>M7jv'LBnCJŝ ǩ;=L,uUbVRqNQ71DjJQNO!w|#ȟE' Ky81 z'!K])fT\7dc6Oo7,%@\N!jk]Q LY OMH*8~6Gq֪X脊P-:ٔZ[8;`+!~)eKsDeٿ=AkNGMe~1Ǩ~~M'g\DNnU%%D67FC9* yQlHI:lXm7ְatLW}5Nnqa'k&wlN*կOm76Cf³_UBZxos)#"-NMTkͿ;􏝞EZskdg_Pm6*v/x$hD3 т`DŽ avF9J%]h_%T|xtDK]=l5F2£n(HۭnXbd-2:<\;S&z`{dm$.f-N x+?aӒE7܊'WÞU v߱eAo!jCRrjۡ"«_]T5HK=9ģ*Y:L;FgUrtCcgα52+o3J9^nyYYmFw;<Ѷt#f2]԰i16 :KkQZIPmTm7GUFs)UZ^[u6i.比])鹉ĶDh3.*TUM(o_ Iܟ4@H~kXy|Xb|6f>-Gd\$l29lZ+i2ǭ:W4{aycߏ0ފѨPzQXL|Q t@TvYKzAR\̻ЗB>*]v }xmKŨT]g*ޤ<!<)iJ?K*42!D* p6lȨcC

[dE&D웘Pq{n p^[)g!Hq(=Q[SQGMع(0-["}ya;8*nP=ۥj3DZ89I'[o*TN)rTL0S3td: lc@v;`p D yhy.]ڴЋy+Q]r([a!hÝ޼hDm gQ'zyKG{-"Vy@Κ^bph70`LtܪP޷VRxkhm?}t[Rн O,U qLvi_E _Nɽ'\B+%t\[rU@w/@[ouIv,rjZuعDGU{nr+n(Uo׵ޜ7VpJapA +uۛU$]Ͱ]IQ_q> s wNxmXɮDEPTg{J?zGj=Ey^(jgю](“~"tCf&sab%ѳ.6sV= YjYqThlsC<ڔsVwx&Q8(*`eGRؔx_&6gF}9%Jiqt6d&Rãcӝd2c8}oyt/ \,7zt]X/ʰ}WQrz)8TNV*\t1mItN|g`^Y s5F^ik9sXzyo#跮cCe_T,vS?~xj% wi gbJK,õͼ,bϬb58WrbEG/6}[LBm'p4 j5u OI1Q7K ԗ .ΦR#i:x iNt'f23B{''#cSq2QG; 'ZoPOE5Vvrړuz)HicԊd6rBvM7=|~ЩFhhWf&;MU$6gk]:C_:D /F}QM4Ua_o&5ԓ#:sZUIݶ*t=v3,H3 j^tm,g׍O! nWIRD)$ۭ( GArcXc`r1G!(qp10T?d1X8EֳدW^? 6u/jpr2슗X8j~Du.$ !K3x$A}!> hYWV01 Yј#wxc({G)SD*5&3[\_2"I;'RS#;T6[fB~Cd˶fBmca4o vz)ȇjcԊ|6rB*Mb;Ν4ٔnb WZ߀EǾ^breL8brzxw_[G2Ӎ/EE.7|%2GSYc:f)g]ϠgRx$=֙w{x"X"!܅ l`Wc\0J92yűDz A>^٣8@U2!602>,8Ⱦ$l, w誟)ۖбIN'FXKRI? ĞSej@Ls,+vٿ^0i#< 2ɛ}2,7wO5^Ҋ_DS Ǘo<>A!y {3F\+VŨfx.z?ψS_l_p뀖9 ӨӍZ^pM95-B}W>?PsU6&uF{U J5eG5Oˌ5*y´VBoDP1鲁fz_.aE-->{>IՎeҎ$ LGp%V(A+ˮHrbٱa ]qӿ ʄjGͫ4ei4i7^B!g!\ M26٨8ƪY2<3 09D6UbC kp7~:~m6 n:kp32?jmmTJ~PqGl*3)HFsF~~M_smC6CKJ O׍CKln,;drU*!1mUWZcXbzȁ_ %$5NDPia'k\0a"N*ЯOmoM.ܹWr0V\MnnZnW6&E{%b/NKF15"۩CjbkHЈ2b(A1i8d)zX6 5DwIO@>~P'9ģI;'6i'MGW BAK yۯ%*C~4Cd&KuY)(ar - گ1*>!]Y2x=;U)DMAGO?jK9ģ*K̷ uZ￤.ɯ "첢iU:UsVc8އNwAÄKY\?mSRݶXH (ҘߝU[4ղ۪](دCi0H .24#|K@~R^9ږfeݎJ$qk ]P4Cg4pu6'8wQS#Kojv%*b_@~h]9q"W!rmrv@q57aM+BھDx 8y]0Bξ]i?t&[< LCvL *ZTcT rEUiEU#+GK,c#\׳sAejQ.;gAx5 RX:ڟ~󍑣%dʨF,>*n&Ѐ7#MV}o9)c:bMŚlɛݾ[f-!p'*#xrft< _C_fD^|( 6ckQ=h;.Ԁt$AxTB젣D{:̛͡H ITGUuF4qGQg'A-s|GT}-Aw؛ߔ{)ꕈy]we8x圝rJT)=U^7SԮ}9e2=dWL ܻFMԵ5"3*n;p}YtU*?]㋄!P3|TY~.cgg!mY|NY}*a/S)Oq *LAV/E!C wFGa 8y\Ye:1 M7qɿt-"EeZ~ݴ* U2 If;yTJUӝ .JkSZLEJ3s?AS.>G?j}/z!/hQbvg]gHPy L!G7!w[wZV F_V%|wiݍbbT|xڮfzhD}YDoBrZyˆFx(p~oK\u#U aSsH0#@ل~Y}V&b;;ΡϩjaK7#X$?Q{-vhʞ6;W?e3gn0UT*=yہ+6[1Y5i/Z->TZ;9r cjkYwj/{%hxyw*/v<.׋!kH ;~Xa  T|.|ez} 7z:#8ģㅆw{ɋ&Zkḑӥ.Ӑ*;j[f:^L_y3\zmeCdVlJ6Fn6Cb\P]m\'*)S71*.Q 4A6(,䳭8"9ut6I(J &=mb 22*c됯kSn!ϷGi7 1*kupJP// 'o}̳`k|&[n5$3 ǭ7Dmq:p챤F"pxD,aFQlF*NōY|VU [ƍ{ {J 3}fgUG4qGQqc.-,U -xCsFɋ,Ek5 .B^TU֯U<[`Ve $:ČH" !f/0C&v 3#P"wdZ \@]@2+M6k89KSZԖFa?j'hEҾ8D8]Co1Qq'uwl0L†D kpԄ~2Wa#96 6eKnI)ER+Cb1^,uRq}ː^<5-v Yp8ù 31,61kYGug)d {VK)+?J~rN#^`G@f(Q9czhvF|'KpةwU;={[)~׻UF4rGQod7ʶ3rk ߀v O=q} gRqc{P9ģH_N9P_'H& r6cS/j*7&ڶ&Hx9eɼ! x7;{dr8mhV.33,pU|,h6FT4vFTT|f3Zzgip^҃* ~I ,arQrizGAk<,M G4-q0y|amyTG{Vx |Y}Lz@N*$c*v;r4nrC KM*:x~;CߓY%|^jrʖ!KTn~d8q) p h1+Up%Hށ,7ԝӪ]8.dAk=So%>G=gFv 9a`x_q]9f x"Q :T|JJ|0F6NI) FR=vjJz-OU [OI7dqS{/:%-OdJ*~ayl㔔 䔔 SR*v;SR*7SR񫻈!`T^{2%%*Gϔ 8%CNICLI `[T8{OI*=6NI6NI]NNISNNIk9%؍b;8%{8Ԕ1ZryLvL!8էꙒ%i +V*Fn=Nޤ+\?|wVʴs9>1} lPہ!ON'2G [$u?Q L%jgz.Ӊo>@ "9 !/v`dcw(;a߷{S쭯[QOzxU"Ee2Λ0F}Î(E(0 Y};h?M=yyDk@:M#ԷR!{I)]Or*n;d(GԱ}\r]%!_3oMwT, kBť8YΦD%܆KdDz18!` m i$F ; >G?W¦PP $Q-=BģтNp?;e?^O-feλl WuޔZ+yϟBф\v='A@p("Kݽ\_ ^@!vmJ+`Ax/ |U_DM-nY%~A^ 'ZAQq_S{Q̒7Qp66sM^.jZp򢎑 hn%oTY*lW8?_zW 72EhIo$YG(m',[U-gR.6e{UCg/SF&_K<(kԠ FʆS͸B)8 c2PYy.ZeTprv3 PlGx%PtM/ 3 i NG!by==cՏaaÙ FJkt9*Wjga6EAV_y?L ^[YuoIs>%RGOk47f!Ki̍ <^&g#Dc{$uZ"D=!'֏~LJIiEC;(P,}`Ǿc_K/P) RqIbV^K$}㐥ڇ@Dd,ީ~*{b/  Hh4KD$ N(!#n׀#S4zL?P(0jEpMh[oG%S3"g)å44hC?>apc#4H/p7dX⺁{ -?K?I\BLAVY -r0-aLZ2\6dfz-M+V\yLsvDpwh99e $`E+*p Q(د]bMؕuV Zo  /(Wj|(ZpRm4/ih4^\ !>s qKcM'j7jK=祘RG7 .KdCMCu,Esvnթ9T1 YriٳgaE^$xJ`-c,wtRVM3] ~mKVdnץ S;UQH^ղO b5O/.i֨ZrG(> w v?=nIVֱWwn5Όq;QBUq |Y=5NAƼБyɠp=HznI.dlZ,P_1YGgR o[IK 5*ѫe★!Zo܍Z` zY-湩 d&ԎPwx7\ɫH-TpO;Bo65lKX/?6QOIcgjI){♵hZ|'Exl.]*cW2m8Z1+.hVPi^ȽJzef(+6Q.;hMrF#Qv!+W#F-e< Ha&?X7ҩf-<&'FFTadGyAH@Vw[X ZLe9/0٬lJqRƀ bZOn|X !wb}&YЉ ~S-V9T^)J,ԙ\GHNBw<^^'(>,հb>x㼨e aZƷ.\'ĩwbT\7P;&›,wi~ I< d5j9~ᆗa L,5su Ѩy(c,'\)bŁIOJv-?J J%@=YEaP]=t~(BN5glUZ7˟7H-a?~fnn6ᨙx rGS,zރ|O[/{ sTU};1tCoݱc\ u_訣8Ts{TDpF[x[7í\%~+jQV\.q+FG' ,_Ŕzxn2`l:$YT"?yǠWDZ>| YgK6+إ5O ,$+aa }lmÃMtpAԮCn *"zDng!˝:*U0.XBOZ[/ 3*xYeerlpk+R&#!磻ˤGSc%5Pi!_JѻE95G*DhDίMBģ* {y:)Y/'<`l.fXU0-7IJ.=1ׄ-A +u1wíK׃NʫXR< ^x}6.%*2.d3; CF0rcO|##ih#>Z |dW*ewzhnvֆ>m ؜AH7+itFַŬF.&cW+-oxnЩ64`^Yٮe`?̋M5_jv5h8ꨭ~ݿhEbw.[fʷ|76c'ެz#t-|%Og15ԓ4!=$qoBTxᙃK,W7Nc+Ub^pқlj33ނ|KW7.@|dWiohV§_g3WgM]oASslLcŞ|B C<2Gâ18ܯQ1#*d&,J KE`rFz&G&Wɴ9#Xr猈ֱ1ZhSo0]lJi饨#[Q+E M6It;N5X} )W6&+ЍtL#6sḱTˎCY(\ڙh."OO3D5 5ԓ!g쑽^rRH;$3ݞY9: %SS#!SI:6ԃpr}O wrRpYq]1Bk"B"]&#Zߎ>,qiQ6˿k\  r(ǜ maά`Cw]jۖ]4V*1>_Ǥ';9(_#.]k4#EQT\7P,-f/=ZuµLv|{R㙉odƦRcewx' ֱ1$W\Ko')/UԞKQGKVJmoR+t|;d_5F^ik9sXzyo-֡Z1~LNґrp:n|Q.-rvN&Jܨ?SP[ >Io^LABxDP5^Gwt`֊`ѠxwR'Fx#aH: ܯqdK ՗|u\^|Y_&xˏbTPBG}I626JL &2 p?(z䕷ɉ져11(q[Bu'ފ/oį17=JGQp-WF|^ZcŞ~h|;j;/U07e.ZIN!w`^B-hY%d~\uzegv66V" 0)D i# Gk D{/< 6,_6؋4MώQ `/ã 0pz|үWÞK?B39/` La 8 p2=9~O^x4 {O[`/Vlbe80/c~J?2x?IQU?G>a2ϱ {f3<.$_j/B :ǁR~x1'Csd؟d37Q=< x$Ku( rW5e'_s6S.;$lJNl\ة/BQ(X\@[mL [O&\7Ns SK8 yT}!V5ߩ35iH={ӻẃcc#1Gp'<ӊ׵?OG8',odSRx:;<%\j>,uJRdJ?_:HᵎT|x$hDuN^$3CޯM)_m'j@}گB#ћF7P턌97z_zGrεڴPXZWZxnZƲÙHv.f*\DƆ k+?t}O3-1;өwq a5MRXJcwR~f~jۏ?.ӷv..<{\%4z6H7Uw7+;cvz6j-JF1j97$1ߛ69* >4,|]2_m5$7J !Ye`Q47lUyD#N/U&ц~“OA? av释?!M9t{`u^| ~#Rd?!]>Uod|v肰>n;tAAGP"v@'qLAGi58^?>n'CNqTz}ޗAb]➏r2;`SG8`#zd)o#^(4d9 x4)5(H톂@r7 @/Jʢ9ģ+etAPntAP?̡PӋ 3 NrTi5r~}>臰\&`(G8*]jbd|~肰>n?tAAGP"v>脰>?͡fG~@?q58xe2> tANw 젏sqzqNA'qTi58^?>q>P;{rM'hUF?I,~x%QK/hRծ]-1%;X9ԛX8uۥԜQ*^[!#Pڢ(~@yRC}tһl:*'m_)TAH*픿_KFOJMR NlC6RK1|LT;s5l[(809qZ*\6b[ᾕvu*~C<0sGUotݝ`~^5 V?o/0H1ݲC[MWZ,Q u5pR tDSJ'v ݻ8#ɇlEvDL'Kս Wv%OnȆhr;--1oK h̭&mlɓ${mZkwQ##gO ?6D\y1bO!?Un4,gSgv%#.[< ,Ox!eO{oxx"WÐץNt)"0 <պa=@1x۲knCoz8Jd:r'P@(= 8J;:%` QvrK:q2:a[ltm٥մvoɳIpuIO;"{;*+e˝wD}le/-li[XL> < Y%іI^s+_4nhKl ϵS%KD9UoDlIo0 6ʭyuYۧpH; <ى>EӐ;0r6i;<9d fJd:m.,V*vi+Xp*ْ`ɖt6 hVa֩8ZL7^_):ԥCǍWcZljU e 'طdB[f!g:a8N"0 i  ﰋ7C %5x"sxa*"pb{؁xv4^ K -iIg/d/d x ~4D 21L|@< /}t">"0tbw( |o"s`*"pb{؁v4> Kml%MC|0F`-LFh}p chk T0* X}E{m>POWS]4strG,X\1 LI)5K܀"$^`>dΈ!($y>[WQ]NAVI]6p{~KQCSSڼ圝r>T)`:QۓM%3l':ǀW ˝RNÐۣd>| o5 QwQ>>_*ߨB!Fv×;0>@لmFh(FF;P?,hKѝ-8CFT;5,U堲 __/Cq#J/akq#V0!D'su|rmuD.wTMC;Gljڤ` @FLv%S=v%?C?S[^{[zUF4rGQo Oέn2Xly׍R`;[JkftyjO"ZPLQ?0 9; LAzIzHC ]h]n؄4pe!OeyX`+"m} 3l@^VQ#Z#w8 yTYq݃ B5\ *xqeG&IIIp6l϶P8 YjUd1+q莓R=ڣ+e5ydz 2ZU{ E*&2\vVJPہ!kXK/SGG!AeXar Qle;-uU-lʥ1"}IGʯqGQKɗV`!V-JA.=ː/+y({▬ɜFFg5v{ZSl xGT]w;{#qw No7ӧ{8v^'&~(>.YӷUni{XFVTE[;"F@xb!Z>?T#k@TR+#LOL>w1nKd@nqgT5urF͈T*&@>*X!F6T*IJΉ-sFJeN# d yy[fx& Yݛce~eMz&`-껮1vrM'hUFMXIa~bRsFznUJFsѺ+d}C]{ F`\^yU˛{aNv۱_{<^oQ/.B^TS|!["+xrs nͥ#׬W^uW6P*e o{{{]X5@vjjj0a'FխФ, Xf>8IyK mRQ6zB&~oq|nmpd6x}`Q:/3rY6KRG p]|g,;GOj/$uL< /Z%tEs|'ྋLr9Ͳ##TvdL|mKiy az3=ƎRP`eBo UHҊ][8H)`53gErg4'Dx 5 =*D>&e?ld{2rJwoqKc8^|A[ع6ͤ]f gtbJ=B*ҮE4b8yJ}F*/~e) ,+j8]_"L&\K5[KW?]3c!Dh/p?-*m'rjnmG:[Kn C׮m2C7Om uobWYv0Cô '=} Aeb|(j*!,GXc ʰ t0rpx qp3imBōBV_ocPfu q|2ʌ\vv6mTMZN ta<}ѭ+7֖&ڪ7v(7jd`sYJKhʶ]0%ϬU0Fr ]IATV0c^4ްU80dowDSAȃwTUrU^Hkb]k9ZP7gU0_ax*/IlKi<%N%^Im!; LAN)k?.wM.YԪ[zX9CLA3\'Xk/Zܮ_$>/nT\FnPnfyANio! Ũ "EZ]4e'YG.4?%Gx %i@Ḿ0Yj¬o38Q:ZRcRi5j!hQSipn,-DFQjØD!pZ>CSpZ_IBǑ1gY)=ҧ&RI?hdz϶~)QOI㷜#F6ͣ<{b_P_h_ 䊢h,@$:8ģ1D.@Һ{r7#q_@/*Wl2zřl4BTyqG,0 *~WMEr(C;l3-bx8 y3-*0p }"\z Yqnk4wcy2؜]lp 6mI>ͱcC׊@B}{'Y%X^5W ^V fѥIA '!k\D6._⦀x㼨e*0[aZ3N*aS/d\Pqj0%$d ѷ^HJ-W U*p]mԴĄ=z$ ?,cY/@>Qf3I*]Vc81k^ 'ZoT\7$d`I_BxچDuG/Ap8Yj%Y\BnCNŝAVߥ& ir뗶(#A>1d@M&fO >*cdi4*~C<4?W m`R>AӦ]yJ† zZ8#Kw tꭁF?c3%f !UZ7˟:vQno!K7[ws GcC,5EwnF,!/*9Eii)1Xh~TMgEK6,d)PiSÐ[1#'a*+Ҋq/\8v|Nt- FDmYʢcZdWZ7D{qšZ\t\'crBģ*s,8)='Vjr)kV\lcvKn1}Koc߁GBכ2[CCbkh:Mw-}6S.A8Yj5sL'5bV4 MqG'$@bb1NoC6<FFw6YC }ONRSpr}Yyvөg曲5t{'=of^_Z׿U;==Y޶/d_p6Ig3Lv|8;:6&ht2;<1SO]]Z~`pEس9 w# 9y詘oDC?b;̱a?Qf[5t4[TА/Ҷ6?x5Rᩢ_&:(z?8-9[j#3񵫕7IW:CZ.v{ek݂32ӣbj=ńYZl]:j_W].Z^d;UF%c>{]*݈-]K_T E d-? witV*.>+G=B%qW: wW${~JO8"OiW9m'*WiВZ#l1CД)32{i8OOMoM'j M%,?hGul3A%?>Ĭ؊[bT\7 3 <γܪ}c\LțE+A\CvcBql./ª+EN{@P}^4]*C, K!wB7gVhh,=oR(v/dШ2}s|;j;/#{^Xs]fx$@wse;LQk}*}ﻉ+(.~_gjG1Cѹ`;Pu{F)jWL]gf<9]AG\"]똢G!Km {7mcQ1q{N+^g8ޱVWșc.{P-zXQ,ya neDCS,sc%FAaT 33ʴOk-I半^k@'O(OcT9@&=鵠$˦'Qd?7'oǾ9͏!o_I_ 6Wݱ0H^~.ubjѱEY T?I֟N Lzz";7?ބ!_W(Pmr*hQO@}sUwӚ&gK9TJX*%/jUs,?z!K ^~*K^|Y):K1_3`Ev- ׾su^ĝПS!CzPӟ#CUx?{] 'Pe_ fS7P_B)ς!R4ᱝ cVFZ\ R p%ހ|Cj$l}s0пCc7Fpz7MYy`N6\TR)F,Qa {!'_C!O>znym78Su_ P gϫ^Y˿Hͥ^ wˀo# Ae!7ۿ ~jƫB!1Og릓Z*E\&'<<][z6(@V?N\?CԣaRodW,;yuPCVa{7{ feoqg p-žٌG&AP_&neǀO2Lir񟎅Ze| _0-OqG q(;D=ydzłzoZ u7- 'o}h@* @\qL\6vL#o a҈]ZoUVs{}, „Ǖɟ-v2Uz3NcK?1³*w7!1W Oxm<+RlfbXkԂPȁerX^xeG TMH1X?C3`iZy;?HֿUM7/8)($hM&O2oK$xEAP[}yɦw&މJIR,J?p.] ezm Q B}ޓ+ ob62߈IGgPvzt'md} qD-]:6P@;}ᦥo߅"P$U(v߾cNl,cgq6gg̒L2%o޼yMf28d2;U 8P@j~]$u|laM\Lv.|p{ջl-?44dOo Et0jQ?so(u-eBb7eH,` caMcaX`0Q+ɭI1 Z}v5>;o↕m7ە".۴9YUݎ"K+wegiW4tm#fU.˩_B}_[&:Fhrp}eT#۫zc4_)G7J>A;LNm3&X_Q6c$Lio\z!Bps7ܐۆm|lg; @M/ Fnab} Fx( 7Y+D#B}MN2[U&X?e'ד7n, ye,.6 l2@8 6U۳d3Pk|aġZ*m 5ԶqȄs S6_6 —69|/i5~F{=0hJcl~ٝ6;n-ݙGOxr!=5 Eryfv1FAgS N 4 ?2ci%{%K%%K0|iy%ܤ.GFv Y\P2˥, vەIENo3'^X wKk>4uM:=l7jZ+-2[6nʛPB|q쒏(֗/\Q1땯WNEV2AqZxnzh/9axbGq.A 1|44EMJI a"RSCMMQ%d;P"rY!5 )@33NA:vuds<$lA#,I"#^Y,3k[ˉ9$lu95 EgDŽ2h=hf0!^tgPtj'+O0|i , + 27#D H&3  n N7Ne8(^tgQtgsgsg\Wte#X} +a˄w0|iky>b)o eh>iA ?ĩ>;DLIO;Xc?ki"tl !B*мRJc j}"~VV(U'_KJ0̋H"qDGJRi?txXΛ^%H/E|G)ID GSpS/`__ [:i<{$(86IjSs2 Zu%5uj}lcCH;k!x^b7˾MU׺}V 0̴Ip 5]›_5e)KNUǤ $ /#Է]H}H#Q"Gz 9& 1|iDtx@ gP3/PRg|6:qD3N3"Quƕ( p 9$5 qu_j4i WT]ۗe[ 8mM:u,@b ڐz!M637 ķ9. <9q];v1kэ7*s-egg vr6N&U!G9ģ8+S'猗f>?(c "/ll-mgl#C@hHYHSUb@xrr|WsSC3:{8ģ,zDfx-g`zD`xԈ(옿B4<%~%7PodV0> 0 Y*G}v^!uǁ)r9M̂3L%3<>6dlrC<8dY6EoB"/e,C<-C9n:W4G TQ pCB>O"*75`}ԄO(2jdgn|Y5Ns(${ʄOvlIY#` V٣8(&5NzwZw0©r8}g uv3j@8r+p&vʻ(+԰%ehqG`#˛RaÉcQӥ:ϋ3/p̝&G0p, _m]a$J\`/disvUQ4㭁 sܒV6,é2on{_҉&K1v\1 :>Xv;lQw%B:M.i{e.&u4ARK7 ml.H}j.ɖf6<zsKdfz asᗐ#\3_.,u$c& 7Ȱ"pU^cV,yQ":c;("d}s`Y5]nR-n{S>-]J`^D ep-'nPT[@&w!9{VQ?6Gh Y=y(giE9|A:!G<}laG)PƎ.]]ގ  yt߶[JۮT2V ADۜDJj]YGF7 XP|R<ӆOooAՆP}la m C_W뮥j J;IMCu?29tcƹ^^՛`ؑdb) >eYɱ_X9\\[0~$d9͞8VQD:x4ٮku xTw׬$Zg{(oGO16U81&z׷IƸX9뚸W mlyͬ:Ňa9+5JBuzb%gk%J+;<[>"/'6 dbѷJMRZ#Ū9+5 s(VD%ܚiv7=5T4Z^R=YYK<{#ʈ0d5-At&9(j)e#B}ґjY*m]d£bX*+[Ī9 ܧl#A?nS=cExbO+Ն񘎓 NolS llȥI.0zft(Ym/'&5vCqBy/>&`Ξ?Ϟ&3n^^`;&+릳Rɳ|.Y(~ ||eEQ!*;e:;9ldL2l-le⦽ sށvMKr妽s^^})c6䙒%  >L-76Mφ {g}GxG۴TG)[Oߴ.R]Dg' u{ Ku7 #_1@RwP*$p//pZyϢCVWp .Hln2WslU=G;خZa 1(w.HAdKOq%%Z]"5naZ;<{al.Mvp6uhR^"쭋<|%u")ʻ+"/oTǁ' ]+vs^`vT`L ,pr $p z]j(!Okn8v/&Qp,dO\AS 4">rrfٰ$6< \>}Ls h@=YEaH.U:bA-D&4 #< ]l[M<*D<sf*fg⋝nLaqF]Մ^ރ܎[MH}[t ; |nS!PVZ/yB+ZRZ}%b0 b,`xR̆3يEJGyR#+ċʊho`'/ΪP0/:R2,ǥdkJ5"n?hCnI[Q |J`DxK ON'-nY@JgmяFҫCTf:FnmD4p&Bi-BQ$d&$Sfٝ`R^)XE^o/b͛4{hهV`S( "nhudQOq~݄"6J-Zoh"MR u;XF,ިŠv2l.ƪ2![{aj9JL:7,XxgC ~b`җiȋ{aXa#/|,E-&nd5y3Lmli>|Ɍ &d29<2Fgt*L3Ùѱ{Wcpsq304 j3'i5eX6D= 7&\} Y.N2<<)yL/ж$@rh|K0|box?pxC}@ fwLI.$di')c).sx+pa=(G = ꉸe2d23<*^>,?SKO͗%(/ל\-劕}m'{yd|lf`0_OgXf"9P9*/cS#MN=&M߃h~QV/UcZ1nw[1}co칚 u=_xiȮ/1^{0jTQO6cի>L{Ao,hX.|txOF~j`k;V;EM0gP nZ6e=7$x<Y繗;RxIu)Ǎ+y4Z#"yGN/BJt|dhjƓqIsNBVOqYm}!C[?552WHrG_ä\' 32 iKvpdXG I WW):/=E6FHi#'4N[$Q7*W3sͷd3sm4/٥*[e| cj 1ЈO :2_6\|]m|7ڙ_bfDi|Ԉ*ks&숩O[nس]^`S]=)J>qwK^<5z-M'pBL9r#aؼV#Ӗ]ʰJ:-2s:6j+y3b l>-1Qe Z>#Ó I&3#] %M7[oWRC<-k,jE}2jwÔ{$v7a2Aȃ7!VӰa4w>tğ4ݲK!+ tf8(.%' nj'r70z]| ܂M &NBV%Sѕ>pFkD̊iMM܎HZbS|2=MMx}̔'j+Sm굕#~[xɆS{ii1uKFmcaZmj4͏FOmM퓤z)$ƨ[$ *\*_{ם_ym^VD^v2d}Q=~%zVLh꜑T*=u3SFwфXVPpZ+Vz[^) eQKrW)aƬꡦeq%*|B!]bY/Iպk*-5(;TO!K-;"uGW ˝CZ*x43]y@DnĪ%7;yDBVOy#dD|&^,zmJC<;|Fcu!u)8qek'hfь DgxA_N{G/E9mFNhhH;$酦溙l]MJ]m.oUO"٣aLmA"+CGvƑ+ѭ_TAVLhgڣ}A\}>\ʦ*I%جQYn=L'ѕld:sA:ur8HkkD!/eb0r=ik]>맃eyUgߨQ6S { hEЊ~yO.vpƈ%uii-c xtuH|&S4Z#"KꆁӐvn^KGdrdT8KTAnGCo#IO eFãcQ+Vz:! oGo4KlpȰ^ S|F'xou^:Һ5#P:AotDx*r{K6i{f4fF,mI;t7$-л))%M{Nѭ~(oo;(!ɸMt?pN>JC<יg٢N@XMGg xάz˲pRl4=5(LG@cRe\ݯ#BO1O6>15`tHZT~eQ~OtH^ \Cޯ*::#NGAd7QQT; %${C<(;qAYi2Y%,{hm|u[k&%dgW&S1# Nx688#GK`g/cF 3eS?"jyp 2k[-j3^tZiG" &zSUza+fP2g[69ɱR0? +WY}P_E=1d|6,S~"LOZw\S*35ri/RMތ%[ @)H1Y]?N+AQX(Y"[t̤e˲c * 0?,ΈοRr^cvX~k`&nllݱ48/.U"nMon>$vLK%;yP҄Ӑ7jK[Ub|Pڑ` M%ˠDx­WB1=lxJ_zD@qpL_Q=ZWjH~ eD{ B W,?>BSv!^$\<[a ^|A#+)[ڕ,30#< tz9tzlsN+8S._^0}!o 2 hKQc2j7-'&g dLGfސQoK a OB>`nvjmj5ΛZeVq g6/ 4_N,(NI'B_39Q%}PZ醙_*]H@g?KwRfYGCKg|np㳇?1K引5}`g_OS6'ހ|C[ TV+ M{;oq}-[ MJJ{cmPߨp G qv[(S@wzzj-¾QV#LSEB}do8^D%m?Bw#GZyݎI0\mS@PLƴGUZ__OM꟭PrizCUwm:=䖽T)"3H%:p fv5P!c0"#``$\Z 3_,zE#JڑPaMF?鹀_~Tտ=+|mo DoH c BT+)~&ode]yo坳s[6*KmEgL8yJ#Y{ll\+*ڛ/@pdFe#_rB}#H@CB}⽷_RGF0.IM޿Q2isuUspcDb߂/UCwuщ԰FNsNqbLí8t,B n\T 5.~+ެ{%?R|" sc#m Fqhw3ܯ]@ƒj{SETm:S3offzKQq|(!OzaCPg~J$>AZg_2;>jzcfZĬҸٵU7Të+Vl7TK0i|ޢ0*①Q)/]t5jA"| 'ìKF2^U!8ģ0yäb DOrGl284OLBx &!.UWx\;73KW1k.:ga ‹ZAcu@u&[e,R?!Mu>5sdk\-hk2:m6YM3Þ>ZoRC<ͨL~: ;D+NIP[,[|NX09zaHZmu0t^(cvJ,^T.*0z=n.sYʎx;kx.1ʯu1cհtc\򆗴0]vgՅ=K9:V'{[C<4ϳgw},JC;9& fhfM%9NxvZ3_´<֗.x$MC"(>T ƒux Fx`z>.)ȧx(biJ0`v6MkuV2b{8yNbQrvp@~\hk>S3ުڶ5l_Sj[wÌJJ!Kx5kbƌWO^kk}$RPr_$<R 5'2nyx T:M-ÛOC>lnIsLR*R\*MrlSI 6RpF,ɸ5u[o(c?3i-=-s,^ V<b`l+vehW,k]& #Qou4p!N#3WKhR|򩛊2M4Ef3_w&3n+V֠τWCիxVK-+a/_`;k ]V&颩[ f==e1-˟Fx 0z_D_#U FՖ?aqJ H0#N؄!?lr+ZN>mc ]+ FɟVB0=X!.@ UMF4s(@|df F^a'8/`tf&f.msŨ NomO ±ޭ.Z)$ڽ<;ʚ]{Iv@> 3>!kH xa Pwqخ;N3zX'ASQ8!E^h;K=N1v~]bq, <09lS,gy:taοTԭp2!rpI-%KÐhë΃JYKNTƁSb. ,Rfs4B)wO*g52#ȏiyTF>+!T r47BMI'Զ7B8lWo?`uɈ~ ^/֍.8ve뚮YaJBkj,v D b@Z)^ BVb#B` 8 Y}J"nvL}%+ba 9ģa5,'bG!_{VQGhL@n$x]I]70Y}P!!C4tZˁ¾|Pƾ]}J>j} v=}vrBģh`qvvplt~Q N@Ct oJyM3 Q&'E7q Ja>mhOuhA| j~Ñ OC>l JGQ"gV( :c됯+&Gu! !w&mu b4aȇm9( co v=6v=H}zdPU+4+o^`TZ3;j8qC<[nYoI-}Q:'o5 .B^T~V}92_`+26_Cz-Z!J[o5 oClݵ~g; ʄʼ `svl[2 4 !5ME8]Co3s ʶ;>,>A1*Ӑr2AajۘD]9)/dRz}1ՅUm6"E= JtlviYߢN!kFle|Q/4 >Ъcz=!X]Cl: 7xxx4 rvOcŲd%fu AkM5 5GA, n` )]ݐ8P**<Y})@]tl#*C uSьL@c9Y} x=pHZ`NFRbYv'Զq%ww!mÈf`VFTbZtBmǵvkooZᕾTKC4z{!vZ"E+]#:3gis%_#poz _P ~"akҸ+RkH]"d.=x'w kC$la'G6}RštЯuR5&!v:6TP]!׋}zQ\k]&J=@ZbuAKlN3o߸l,>Z[㲑o0̛YT}zg[w?p2Y`,Ҙ5hP 2Xދ 4qߺ"F32IU(-O2T笴K]:ͬfSl \)w@3V,oߗKԳ Un?OCO}ӷk Gq4tL,d}NFI$d3ss%Qg'RS!i\]sbr<N]޵{},})./MK-DWQJl1ZW,ke#+VsxEȋouaKm.]j05)s_7}N'O$)M#4z=`Fɦ+[~tEA wwWC75Eĥ:맒N`/^eJT5H^UH,d-bHs8xax nn[fÐ[㖗#G!u (Q]ni|1lK Ynte?iq;@bq֓}ǑXl@Dz K*Ū, <( U*Ę$⏨nvv]k9OcNP _D/8Y=sѥ6+lձ+%_Fa H*EVƋ>~Hȭ o_&"wbyf$ YMCR!>AZF.@^hC~*AVl"la&u@}!vy3?%dyA+헭"]\ЯFBQϢ7\Y Q9Gj{DM՚77n ̛/h!vH>o.B^T~[H8wP"< 2=݇PcVز]^J&{֮Vs &HKȝ־$  7Iu^|=]px JC׉<>,H$gq 8Y7f^*puJjoW$"蛄*RS.&auM7x$,ioA{?Qg*dnYs}S\-TLMRgMxi³."r x9VaQԝ& _sW "jX%JYueDpT"n;9.JC~:1[)dB7[۾ 87b-݅Hcv! Hxi$Y|){t7A[M&<-k ODd8Yj8&A.M Am>ݤI4p N2 17{JAp\>7F ?P&FK >eS@Kb )N@SX$7DjC[!^ !_%L -4䴺=?),uR~o`*|S$wCxH8 R8߫A,O@>F|5V9 <Y=_d 76(fm$' ԣ">v@?{3`7u%<Y&J_4RpD08ͰK9 SS dɖ|hC=۸pN|hG9ق=UFp>G#mG Km RxQeU&aqה21`΃GBƀw \q ޅ|52YWiwѨB,bսlnR3^Edmɚh,ڕ>Ip0+}@3ڀh,/<Խ\(<%ǐgUW 9M8Yr#[b[,)Q8<Y.yiID/@^,??4.\Hh&q"Ee ^v \o[*ce˩۲m }|\xV7ϨrJȯy@)VbC<}b ܣl;I%eAlZjsfzRPA 8Yje!I^ gĊpbU$h756P+lA61<<>;,ٺqYC"5wjr/,Eپe8yzF&RW.Klֳင ?hC.A7(9h- J=J:8{BKgԝ\8D'L@ nc$dE;T|.Htù]D !d!Z"&!H#-؂HƀnQ>%䣞^?R#G!KE81%u=c5CI]'8dU Rlr8yP[Q\:!ΑACtqc3D&^-lz;f:uZيc'˰bZl27AY?=<_@&w!뛗ǹ!#_ރ>=/giv%ug kj ZhK~'"PhI}jv*޳C<HiN Vy Z}֫9ߕax#F@Ah}KZAmz tL*LJaatj1(MJW3D81d`h]\5z3D_pf.d)ty$g j _k~ACV}L@#OpB=I[xg'-ĭxr v N)ȧM޴֚ ן7AbT"E؞CVX:5S8.:5,z{U= *Dt |GTnj{b3-va'̽@=>E oBنmvLGA_i'p/d)[;A~fI['PϾ HN?8ixKWN rPOX x4YclLq R#lsjOB[x &Hf"N \"s ~Nx>}|:|Yrn*{%\Z-zmbslywzzI#G9ۊ ~eҩgT:Of.W橗;Ofn=YxN`BW ; jvlX A֑m7=ӯ-m4[+KАlguu`_1gR:)EhQS/;-Y{iEJE՝NVvϾ{ `Vy%7oklӧUvXJ76NDwRH9My+{پݱdy^VLس{fb18|=_xi_b.Di@P1gfW'س`b"8U8nҤİWhRbY^}_ >wEN h,+C>/F`3ޯ7\K4GlAֹ="GNg!/G*~C<-O%r.`3ЋH7N;Ň,3I&3#,0][$uҙ_ɩщxzx0KF&OC.4GlopoȰQ~XMEu _3ԞKQGzOf-AdR.|;ӐOk W d2V9!]=Q >q`:k)JR75GH2=%&\^,[1+CG3DfF3p:E!5NOMɭw;k"KzPudp57ѤW՞4KQGTf$M-Qa7B1esMdsM6o٦Oy""YdfG,o7t}Dz_] gbF;vK (_T*-2n dypL:n{]$y߮ko"V oByQ٥2ek#KZ+px^GGd+R>{ռ]qF^pQT ›oW.ߨx `dBpPr|dPvg0|uP^FGɑQ:^iJ{dzxh*|L六t5ћ! 7Xf%%֑]EqՏ|y= 6Fi#'4[$Q oV Ubul8U>&{ם͜)/~T.izhVVtjOA&UԶE[7퓙t+PE=!+_݄;u oX#u6hGrG[vgRq` #u'cI&'s*2ҜTHzbhxldxb4V )J ߗiZL!3֑ݮ+a2/, -ў>KQGDfO-1x*2oB*͛^0fFlI;t$L7$-LŻ)%fjOS$>Uԓ"؜S> R$ZsջM&$5T }»*6"}u$ħx:ֲmn_$dX xtIFD$#ljQ\̸p\so lciH OMNf"ުaʆ^xa6)b{c}Dl}mhFhO襨#eQ3R6 (QjzQL4׹dS6Wm2kنVu)/+{/E͜ۊ۝_Hiu7zR6⣣ ݄j(S}($An'ag\Ŕ$xO,f#v$zp= R{Voߣ@cu;R/5X\g4 Y,[+V?_Ce/oAE!\R[3-9غU^2Tʇ6F8f*eɱ](TV2]M6Ϗ~Fad-K$\+XG[G읊cL`seOL4c4vB"2n/pzk&c h2WgfxDuhT,@V l83LO 'bM"6t5~[`ZպbGCn&=2:>KF0%K/ <YxNҔ,XȰh-p[s]u/rӴz)HjcԌ46r] 5EP)׃vON–hUn&}k߼Uv?SdN i]M[cmm3FX/"=1e+ѭy_Tϻ&%j۽}tbt(VPb(5DK؋ar!J⑌UߔN[ ;b=!ԤS]x\˦ˮ3O 0$<ͫzrv/An 2xy =˞9JV*]D2LDARfXϸR٦c_l#IP<$RyՠطY~a:nv̍DPXٳo]K8YjZFY C3T4hV_({oyDچc ]PɗiW;#n0$2L̮&Y}WMpeWhp'<Jf6&R^A&ow8I/MnO+΋WW3_Wٝzfk:FL8 yRy(;Ɗ\Mx{?+sg[t} zE+7a&"+O^qBkpRӫ95PuA+އ| @w VWu1 ̲ak+55q${QҚ V2ύU*γ)p@t|N`o&}ʷOkDFmğ_B} ߹6O03xvClWiAmC{Fi.- UZ:jmðRlxr2FL[σ5;F$Fx?/׿b j%HhVVAzY EZo;9h䅩e%<\o 9-rkuIfzT__B}D43K 4;U۳dԛP׵V~ 8R! uQ޳ WQv.=77ֽ yr_m^x +:?kdܑu~K }ߍVgqmC^Y0T.xCOXf8 em8T0CmqOѰ>NaA߅'o Ղ( ODT}|9rrE,eCs~1]+1gwMno?8=nĕU=;>jzcfZnXckqUKG;<_fZQk=ЄעpDjpeǞվSS~^un_2Q@Y|f!=<̲(?c(hNآS| [p{r$ D. [WKץF",+.[rGE)uǂZ}Yioxm}(~?x4ӒW$ٛt"oG"<2r^o l G nrGn[7) ӡnm/ucuWIZi0Y|.Mvpa @~:.f9,ʯ1mοg)gY*ժ+&b:ǭCV#9?}Z~ݔ>M '/R'.f.<\}NuNWy](Uʛ'6MELP)%NNi}dih?7=mn>n -?|z!-l(huBm[>bZ3(3Vh %A'R5C!ʯ=? WFr7J&5 [ Cqf}5KX`Eɢބ,5 Ťn x -e;a\hGO7m䅶4gbQg!F jn`?~ +018 <YjRTC*g _hU/Blc\{ݲv;)v'Զ7E8lWo; n!^R,8GK;Y>3U`mB}c}> Ig0@|_՞{@ܠ)J uGcՉXb q*_ lakAjZ.Z UаȊOp]ME^( {c3[ZoDm^.lp]Qr'B;K1 dl:}ts8YjX%u灣M0ߤA" &Fid19 ;1e 1l,u>= <{~r2mK0:< tK,r 3eafZ`rBes{dr">ނ,_. Y}Mn2R4;Eȋʌvg# [vϴGQJ/p?d}!6QHN1V|8D@#7p8DNmpwqخP %RBжz8#9R^I4pgA 9䘴&Ԙ`3BnOEYsM4;ȒCsk2rx Pp [zNmc%]+fPU+4^X -AqՈAx\}_Xo%ݼPav /uoIU^}|Ѷ0yeH%dI+2ֹ<:;pZy7 hy*rVu4oCVO4G?vf,zIqM!)ne7ZNmc7p "vuQVh Zipxcf==ƹzDC<y %5"% Ń3BغדRۆ5Uv$A,dRw 8Y}O< ydnx(2 S6dRšt@uגV f1<1i() V baEm! " M+מ7P@zV&Y1(?<YC]woh F^$?U6q` 7pԁVI'!?=BWufRf[pb>{r?:oR  H]'0.@VMWNN8Yz:?߀s1lţr1浖_<9їy/>6ze3Ip$ ˍ3r1˟N㽚QBYΛ0eΆkUC~ZSt ñ-٤-W$<+y es=R=5MP& Sm܂nB=3H; rSƍn|\tu[t'#2L+r0Yj"vN`0{EGHIWp R7w ;94j;iޅ,Ս2^% ?R +2t;0{!ͪH!#6"sxWcR <YxS?<>4<عM⭱I d&u291p gg64pԩf^|EHU5Z?0zF10jpaWH^7RZ`;; aŜtCQ$2S bhee7˴ Oc @|hq -o/'>=@%bu@>lIdXPn)癑+Xk8d:,uxu*b!dVz" y-]ɗW>Q"s}"UfVc$I1B1~&0Fv-solGxL@̎!e$8]ބ|Scp2 pF#6?79bp.B^Tt`kXwܒKp >>(ruT5e˦I}V-&qW|<;\Nxr ; w(yݥ^[n)A

HPtq>,7#X,c=苮w^ K#_Ѻc}\Qyx\X?Ғ\KTӐmo8dJBіe!_W6>?[[z*` JK5f}gtBY>@9Xih.Ϊ2կ M86ٵp#RG K6%IҾ{5nZjWq%Xfjr{{Ÿ 6Z'z:1΂"Nʌ:9}hyqL&\,5Jz>KKhWEkje3al]̋8BU23"B] &_ JXK—|z-&k`m`ՀDd(Pd 14>&!τ1X]׉^ 8Y8˸jX`J=% A,B(% Bnll,ˮٖEË V' ۘtטD,p u'c7q Sj̛rDr33G@Q"rNԭM,dP%ACbMlz}%/k:Mf,uq9R+>-sxԡ)Cd.G!k+w.!1XGt`dkC<^zA n5 bcipFXf2\lP;*VQQ?(GESm?d][0:8eRd[olE<iR5 dnX%uW!Ovy'M !V;L>0IBdz{YJ'ؚ­3ޠ{"]q${{C%6@V, Yjt<3+tL2p&*ׁ!ǘLep -ө6<'ggQM9#f VH0d "V>u`vzp̬R'MG8[k@VC]OM 2வ`ڻ2_ZeUhuá" x6jXQ.@PzS19 <Y>i;<Y}ܸ>YȤF‘BRXg,,-mq>| Y}L7"ܭ͝rE[&xr O[,5Tq/e2w܍2<,{MO+vz'hQ8WOO E?^{95Z<ΜR)fi4/FfCRgfJ= 9֎%z- ).B^lkQq돔픥 )6 r|"<6_?r&!K J409l)┻E Vy#yKF!x,!ܡve- 셬/mտ%m!y|p?d}7$(,6 rr6cpxm6U`u,2CG,+X CV@4<#^)N2]EEB,Pa@QmNCqGSocxRXǁg!k؛LL29<"^9`:7>SKO͗%zKe/\[X7?+vޝ~Qζg38I2#CnEzx2e;Ofn=Yx dIdWNrK~ם0+/EJvc=+1fu?x2;;=4}1e;Cu;jTy;z{?*.;:gG\xޮ^$s@  )U>szk䜋tϛLYYdW;\R.}QK֊weCm=[j.i]t<4fз*RF% Uԓ!:Dcy: N!Rǁg 3mH"sHyb#jlB!_Rvs rt G<"U0ˎ^H Wf_88+=X[pՋz=N?Ip;<S8i49ȸ=@YbeHhLGfTO8Y_Վ̸%u/>:`#drdxLx"\NAR&%e`Y; wHЛˌ LO&әLf,:'!h4GlOqOɰ~+E wEs_J{O/E?mFN(=HRo^`uk(U.&{}tL#:r_VBݥ/U n+o3ǿĩڣ(;%;!w*ђtߺ:|kDu?ԗ;[ײ?"΃2yn-t]yFyh(ҩÎd6s*y]3Yl펪8kW<-!ܧK|bB6oy,~_ݷ಄F4YoዄcՏYrqh2UGfX5u5Z#"I&7 P30Lf&sD},6L~oA @d[A mt&Ax^6ԗi+USr" O+|b k;?'XݐK_7ĤH[g_]u@۰:D$ǜ]\t<_v$ ^,jL(߇b'I3MRol+2+C. !ks+4E?gO=iy{݆BO' K,]$u'[]$S]]q 8yER7 ].[ .@`*.zc: m^9o12s7 !,+5[xWAp;,7Xf*pN4NO tҋɑd9W +7ZXߓa92zT]sT:uGz)XwQ3i#1d6DotD7*2tlHUN&]Mk*t,% ۣӫ_1G/cЪy/hMok5!8ICplEjS|7ڹ@{GS^c:f1zIy1_Jb77_خ\Rx$Ԯ7yǂ(6dWϞe3[-&s [vv19e>y0f_n' ?^,ubQ QA(E'L SCxAejYNgGI*!To"5-}D~Y.]܂fhVbt,g vOLF1dyMXA"1{ gP58NAjC5|xsDWZE<2Ub4a,`y/tYh7=eZŜF4C@Q&~ բ]7{Na:[sO sGx򅷭G11R `L8 Y}}؏|k=*a R~9Ţ7 CGI-h&QO˟NTlS*.zIJ[6 B( ȉ4Z-bqw2ZV0Z-hu.P j}P@q OU"cwl a͝7!T~k׫ɪ sV2^TIzAvyME_'@kʯpFܣw\1.Qw`-! o@?w..&|O10> zGq`Zr5l^ټi#Jw" 75Cd׋;ZtL';T 33-Kɵ'[Ia_DC@P_Ҝ3G„^P`L/ݑ[g釠G?w Q~x \d09.ö֝K9Xv*:-MCdΕ_Y2_upLg$< G;8#A"5 ~~6d {!KMDsscvꭔY؁r_m^x +:?qG֙b]/+G}7V[qƵze]r4xXzd2HfL*šJ>kSa߅n ՂTKFT]OF|Fc8>ȜwݯDM'~'-NرWG˵r٪eJkU-][onW{+ 7]S4 ָpߘ - 9x$hힲf|Ԩ)pmjvA'CKF25(ZQUW+yC:GZ`x7C۶ئ m?ᖛ sf0Dcb֤knfAR]9Z`.X<!M\E0 0Zi;?ġ0F2#V0 a?ɡ0@aA- shar7<3 &.ƫ;<'ʚzp#փMvR29cB-apM9TUal;'c~آoo[937#77d,tV!<YuaX$dYBxtuß#+7͢,GPPd JDG`#(med"RC(R9 /K>Ga6II IoLOMz2;gW#Tc5hQH~HeQ=U]SmJlm[DCUÔ٪cWJ.3V H7uȗM, _mT${ru )HiO*C,DJTz"ӷPRMlz )T68dhKrw@/!/+ϰfg>BC:H0pz3-:p2B697]"Kz!K-a 2'c%͏[\Ѹ`b{8yu@~ҎZOA~Vնa԰6 =a6AR hFm#r Lx_f!gwFP#Ъ1=5l} œ)Sm2!6&'DJߚ.9 lia 6"|w 4 ]R;lk<6ˠPQƛR4tQ[eGm#ehBA"f xkoBf;*G?jCs]WU}z:z@פ^ C}-^UQ1 %nEmy#T;ͼ no[l9ogFt}v^!uǁ))e`kcg8Yn9Zݝ26!Vdx 5eSѪM\A[Ἑ'كt50{KQw!8>9H]H]ribd˶#s<9 YERAÐ[c8p򈲅*2lC[y-h&byRvˎQV_L'Z`{ & ݄JϱhU'v֞V H}xZn(Vh<RÕs.Fx sǿ.z1 &%DʆU u7~Lǖ+-:QNAj4p'U(fW+GjrZ֙WNez½pLAn5%P]G(GVhV=-v$:fI!,qd C:)Lb*g *yJqLA05y\g#X-o70796CR`L91!uCէ$eβ c&g64`r ¤80 YCR343kƨL)G%/\J ?f9I~Cqcݠ &YIdE_G}_0v+p䃂0L16y<˙nֱM\wé#N#Y^x/!:x(Wfp͇v~dԠ^wj}\q4: Q!SU`\SXh,9w}ͨ#yq{xanu炻rOǂJ[DZ2@t: p\6+5r㧬w~Z4q ErHmk-O!C)>RRkQ)ܗ&6@JdT{IdTJH23[6" T'83 +VyQMZb!TZͯ{]̜h_c g h ˝F\g!K9Ǝ wrpyfrˎ\ }%G!1z!f{ ;<Y}UǮ`׾:2f^|E\C O+tx z#G4Qyʄ2fVu/N({m ^U^Q(y_s_z숾xr1|\zFS(tf}%2l5;OnFA>r>wI1B~CN nI#`Y}N&wsx5N;U{WAA?!N KTJlo*A?ԇg`^t-Ev&A݀"Oj`[ioCZe ;Q&\ zK6&YnF=/9uva o덉~9-'u!O F[=uxuHz"Qu!?՟Ҫ)( @>Wtnx&!K͞ L2 hMANwG‡kF b1UoV O&X3&oixĮxJR d*)rߖAh,CV`ʼxv^PyUo@M 9&0ZSA8YB yw+ QkEֹ.?M-{A-[Y꧄eDZ+x%tjO(|C MDN7n}hMs\*kUƄѓ&(>܂-%n tsv^Գ>C !\Umy-~ GX<N`?~ NUu oSɎ? I "df9C+?jfFk­1^,u b]<0zrݍ>>G4:Nx+,Wy7yrQWO@>+vs^ p3Y(IIdԞE0,wgO#[ j Og!`8Ny(c('g +/bvR>AfKUG@dB;8#YKwXn Q:e[/{bsk x4<?XXMBz x[r6!fRwp%1,2,5ːa?^"3FS.բŹ !}_N߇~oB"ۗ\cm@:t~(܁"R9` 9lExڈVwpVED,"d97PZP{s;TNhn>Eԝ d4.2~6??z(cHFaxÌdXZb/(@4߱~E8 yXjZYKzqއV7 ǤAkoL"*@#\GEn_?MnIﲜ۲5NGTOCV?X*u`n:)`07p=ېTOuJ&,ߧy%lG6{_H]'p/9Z7a7^|Acr%~U=_ Q=JG#!+s,Xԝ`Sna[v*Y?]eZIkn`+_%ԷW<5fģvšaٿ,ϫOÒ>q];k V4",uX"uIr˓6 MqG:'$<v>vxMek숏L w-ѽON$Sp q} Y>xvө˒ tJkN.EUrYٶGr8L:IOҙTTK|Γ[O"޴,<$o~l<睘UlMa kkiָY'l\.CCա`_!qgR:Eh!.{nȚ}E.b/6r.ٕrӋ#Rb]%Wv[k;ܼs2~1i"Yk[Lc`+wNݱdy^2VLس{fb7t<4=NeZTQOFm6bS] $fMlSn~,Sfz&s?_ ԗ;c,UW#1!ܧ0}.*E T- GxYmݢZ.eʊ'J5<;~i)R?!Mm, h@ZyTLL2!FEȋʤs?XEITw' ;L`ӡc$$0OTG^F{{2?T*⑬xoJ'ۄGѵϞ|˩bY6U v|q#ʎo !53k7h/&@p2ѸS(Ńm8co@<qaP$CV?(Vܾ? !IϾw:LG$dP? -, ($ثR&h& ĝCwzRǟ?r,rYzb٥$ؼl;Ebx&'Ad)>@0 9LH),`Ŏ%#`{ LCa#94u9SI?d&qB}-a(Y~MKt$,8BT{H(b+/LN1Kq蘹Em &HX Vo{lZ $%ȗQAK&XQ|l(ov>9/wxO;D=qck>\`o+VyQ\eI|8y|9 ?[6ͪa)AVz\ָE?qB}#F#W YL f gh-:7A<p8MeEf>ӭۗ W0AOy~ # IꅚDmf I[ G8y ;D=_,X4 &^Kf8&ˆU4s )Io0X`^˚C?x~W!\ZڎcenʗByc [>h~1콒XKB>ou5/J޿`8V{7J8%QI.ރp;U۳dzK~Z#R! uL{`Qa/^mFٹXz@6{^x 6Wt>^;&+w]#9Yx ij\( =*.<^3ևLdctnxl$3P(I69w*,Rm7~Z2sdD%⼰0pix>=* s+RbWB&q4F G{VxDxÎŅ-XzV-W /jo^|5ue+Vl7][zJ 5 - 9x$h׳Gh'p}2jݾd-^܁ yBpGU`@00Fxئ4t.>< o*yC@]0 q[`.μW DOrG&=7 ꆁ/Bcu@uVX~C2-` {큍/A{큍,lH}C"l~ٝi߱ RiurB78ͬ麆2`3N;n-ݙZ\V-;*]R!ɸt"QC<|W#J0syT7.m@0$dP}7^ fF(F nɦO(`GG ˮI?MuZ]w?z= <'e(K9\o@~\hS3ު'׶&< <؊w;I'˴y-ʖ馪K񁂕K]:9}F5;e2eu wcIkMw@bc7ŷdwbyW@T; Q+%'ax9xn^{GG 4Ns+%? j-a"e*#}\Κ]mWB C‹_uHm,71* I` rJcz!7OebmgǙF&pG-OEP$۔%(9!R=>}ҽ6*Q1 wC 0QԖ%x`f/ٷrF]} ڢOR >80Y*mvgf:}cǴgۆMr6^|M&}3IdѺMdg!*Gu;qk {̹>OcyNm`vx 7Ky-tw6|r_/CZ$VH~`zr%KF96'QI$di~b;h3ORyz6 u:k^dZ6A&m%Fݼn Yu@VH֙WNez½ag@7a {#Tu:Raz#(QU+4znUV;#DU\3FC+jT W!MMDl T讫u?tԷepzwDLsivsN!ϫBᆑ/!/!$>c F kPƆwqخ/Ćq7SE`m+WnDC/SR1u\Vݝ@emL0YjXcBNσHPFnB&VD.!B#>"/M~o;Qg"Z 4ߙH^Ygϭ,qB~-;sq" .& ~uDt D_m )WDk?Af+Rxz f& aIu!neʋCy4 R'պc}\QNBV+>!Si9Nn>p0B66FH}\C_SBfi[YP})U>(RQ;|Øj!=^a$>T:솑]NCVz{X{u(brx]eF2 n=/r86aH]7d;"772q rW*ݝ ӜŪ;5[a4tLCfܹ 2ނ|5ކC8;Z кvZVy,wGfK?0d}WzruN[Š PI0jC {I^C$w[ucZ^I%ewBw RB ]x&!oKXG熉z  <ިlO!uOj- g e. NqJ܂v S~R_!(Ѷ[]}_%^{N`zvBְHxzCW!;4VՈJwBmnNخ;(;Vh8z!Ka:j/!E{.+ӱ܂ 0ZKb߯k#n!FG' !E COBV ѱn(鈼Nj}S15)8H]8Y^.:F&dl'N7[c ꍒ0/C~ܖ.>jIYSͦR < _o!Q@)S0\;>.( Wc9& CR[dr0 | =Q~`WߚD liv% ԶCCkۂNT.[#u)깾t  K50ϟHd,>&䛭4dE9ǒ(rrb>6~F;Dm7=XR ׃9(09򻶷i[Z"9޵-nd۴>wrMd91I?OrGM2YNNmcwqخd##U+4LwBIPWO鐪{!Qt,6kf|RCF$̉Q)9i;< YTLme1N9Q 阄,!eM%,N4km6-iI]wv;pʬ,b-ʒ`{ ;feI `aެ|`Wߚ, liVvߚ,9|KDYYRwVdePߦ'C<O+2 v@hDjPD]E^I"q6'oUGJ Rq gR0D7Aa= /(zvŝ3 Asx kE_Qކ,W,蓺;vQ)}x6'pLXI}A]KXRGS VS>Y{U<GXzQ7h 8udw(Bn{R <Y}8+9 +#+cļ= >1\fzq>EgkLaUޘbT\5vYy/Ngc$!XM`)]`WOuFoBdxOtpݡU+]x}xX+V˕2+ebI:N+X|oADoUWq\p<h04J!Ǝ/umqntAku' 6Jtf.ά]Y/O5 g eV弝}.: .N}9sBN.@V Z?rˎZф 4.ζ Q!iېKN?=VRr[ 1ן0emRYfz)cGig!_=!!/*3S^Q(MDVs&!| Y޵~gǖ7qҙbXOJ!s/,y%V65E!B ʿH~)ȧt뮿]FU$!VuRĂ/BHE>UQX ,c$!d}ƢFGӝ½pR?!Eۙ6L<=Dx~CSǩlQ6iiV&cqZ3[IMdn.'FG #v@֛>h˦S4PMWn'<gsNI'-t4赪U)8d հz 諆=ĥsn]AVBtSUg&ܭVwW IVÐf?J0+e3uӡ ø Xh%Gfl؋Jt[[,uapzxK8]uLGTbw܂I dVs"*Ѻ *9'R՗.FKTYת xD]?KxGT2-hy.k;91slȖm\kpZ" ,wHݥb|aA>܂Mn M o0.68tm'Ð]=phQ!2g!KTsRwxRKdG (;){g^4]'b 2ȬK:g KA7!1x %ZE=/Ը ^em 31Ū(2>X.X'hVbjHAE6qǵĞ4ƒ" dubFN/C\89Y0n`[ry#HE  LZ`9対/U2`nZfRjyїvL̯^evKfZTz%"< Y.]QsTLaX!uCmv-4+.RD+ Yy̗erUc֡u[l`ؠ_hKp~G8Y=}uO6/\LlKq7 NzAdքW!_m}2…$#36k 2c\ /d%R̗nT,ux}Y@Ҷx\'T.xRk,Z`Þt*B%t8y%f:TD?M0,yj o$.ې!^d̡zMM /B^ P}NjQo":I4ٛH[,՝ѲX !/2M%sxgx enˮ0s\L M)N6vc3?G ([XD^\qUYYl;,.a:ͲMZbk&8=Ek;qx\ch9˖=H~V$ Oru-[O!7c,/>.y { KJ6<\UFҰ/-e_?!p T/ғ#<>9. ȊE!v (o&&B/ZwAV?u9HnQGw :!&[2LBcp8Y(; .ё,¦9 x7{VC(iJةJFQe6%y\.. o/v؎Nvlq$vzS4w;qSI=3 \R@Z/{?r3L;3sR=Y_mDaxi KqtQ 8=v8 YGC6Lܗ pT~Wr=ƍWdfJce)z[! {-su~]/і #PzvCss\74r=@3.M۾m yE ,r>O =%>f{b.tYS+vҨ^[Sq:nDHd_1dq/NY:\[ m"k!k5Dl d%Vw`XwBo@@|I ~=Z~铏+? Gtle ƞ~Tiy}߀}">%@P/XF۽D˔J6kabF! Y?|Hukw@3cZ@c/]̥@ gYүl@.S_߃$ fTH{uU,7Na<.(!43Ǣj&o6Ag~B`ΑiR< YirDp0!bcdI(=<&%Yfg| Ŗ3:{Rj T2! &&&"txR()3.o@_ܬX@7ݬqbS@Y~p7ݟz!f~'<&VOSZU~U8-cXeY#և /7&8*mHw?#&VX~X>0/B)#!qV N! < Y)J09eQ[ZuGo#yMJsiE 2(&ҿ 69yl)[%igDͰ*Ƶ@'`܉C@VZn2jJm8 Y)j@Qt7ԦDf x~+ygl0aٹʄ}[ɚ0 y9I.^Jn9)z Z @<Q< Y=p  dxkSP4 LG p IF3vp#2>;z>?f̞|o4ǟVpQ-Jfk8 y0ށ4>J*.d}T{Yȳ]gz%gc- m!Dh3s')^Iiluh:o!7v $"5 rwID*&O^)-WV(އ=AB8W6UkDes{Jhnt?޲IVpG~ͻF("3 Ma?lcIavð">}JA{x8L*]#P1MܼPd7T`-" cY^ EDnm^xt^p*[ժǥF +絰K1Ј'469p,{TKd5B+FH[Qp#<`}ە".nj6ΊoD;P/n[m\ ij5lf.Ghf^S3>4TEeinarNHœ,R" m /F["%&O>t+HdGE]Hɯ}ߏ' Yi\̔|KgS[h4dsk8[Ϙz Txf +uPj} x=CwQ3tux4il\ }@q t_\Ʉl`kɄyVƛwZ»B]`9¦n.^M֤nmw>pTJ?/8žV&h:D/l nMn" A_h{Ŗj)KVY` 4XQ6pqː/b} 7 [ψMJ\=g!w+̔C#5^}aX]4SMfX) ̋YܗU6SG&"6-Z d?㜯^W9Џ=}R!Jm+p?d}wa4YE7tER{Eګҭނ'jQrې; Nޅ"R]rʼn!aD ],A.PBXG=ɚ0$[3Bc*#?ExQ=1/>.q; Bζ5ԎsVTJ'iv.BVԤ3v5W;hsv^ZtLejl!k5̨ÐlR<Y) ĊwxJtC-"G!?f:0bs$md}E+I< Yg1JmcښR:DOB>6z 0 9 wxpn-䢗+Y?mֺT@[&-Ns?0!? ! Y;pIŸBℽն4DUb.-=n.Qr{!Gkl"WhU{sd͉^y~diX1m &ܣ\/ GtBGxIL=㛏|"䥪[#|c #+~U9E^4:U !4rSO|rTmĞdɆjE`DLʑ2]G^W1]F̶?# 'mǂzt@Y\3iǩݺ@n'dHŘdC>.nN ;o!Έ,*M()w8L *N2,d1 ? gt? ̄=7'zO9>G>WPN*Z5M!fMm6+ $ܟ'_CCVtϿ>?-ϓ✜_B3síU: P j0b@+G +Jr J09]|0lTDgx ֎Y97˾搂&e\Dz:Y~u9NmQ~]mMqN_͌qn85T#%ZG<~ -JЯ#r%@l"k3:&Bhfs;2u (٢('?{(PBs JH*Yn8Ed8ׇphP +EٕU`UҷR)}v<`@A XzD$Jn%w%}Ίҟ>Pֺo#d3BVQSO450J ]j+]M` +EgUVsD+kSD4.d{GX̭)%#7ʏS&|ƩD/fƩOBTDrMĘU2&|I3i]7B3c֐!4|ն᫴)vY i3]} _0lD,"}?y}mMlʭMdѩƬmSj)!6E40Ymɧ]"8* GqSYн3cQgy`d.VckYx{V3fD- Yɭ/7sC?4u@ֲ~ugaY7XVjdȸI?T{W arRYЊMOe3Yͽ[ ~U.[%p/d37_;  ~QJWiKAzEm'7 ݟm=1|Y))J&p~%=K&LesPu FV8mFBmR'"xa~%K8yT$pPG4uMhWџpŷkGHQA!+ %4Y YmwMFx Y|qu귝t` F.&? VlS(S\TN1coPe'^7 +U;ioBڡ^1"[݉-#g΋]"kJv5});5" <vbP$Nh>6/ACĶC6)ACɭ5r_`ULAiGÐ@\!_6  +zΒlv|P)Q@wbq;+^M-R*(lr@8vdf  { (<(kx$eNzsl-Sds Z/ $W1C㐏7 *z8yȘlv*'Q=  OQzRAqx yԢb;giдrGSe/crZW]٢%~Yw*ڀڢ@DבJ,z#=]JkC|Z[;JpxVw )ԑVN 8Y fx x>BM/Q>w=;~#]Hu3d*4QnxV<"J}(j+(7v1-iO#1=Y@#?žD#vkz;!Nu' {!mOu'^ ;0߅^j!VHuh>?/O]Ҽf Y*ȑq@dOBVZN6nu;<Yɚ[@\kep ^x@9Q+>o|8YtnvqyOe_>, ͭo^ӏV> 7Seb RoC)\/ _Э fG 4sB Sc^0dV_(z}S9(D k* ؘqWY"'ų9˚jD<Η`)\RcsvmWTO0YZM0zIc"RyRJ- <ĭE>}W:d3ekhj2ѹB< =WVG# Tf~9e;XE+^YXE_uUQA_@g!Ϛ բ]%GU *z .}/|{AƦ M74H!;?vx'RֶM]a'K? 3I6CVZ2JmͼӺ&BOW *bu鈲Chd#h^Kh,Qu!OPqJ:jyTfo7&✉JT3W129@?lrjpA.CV H}]%l!6Z/FUۢ*K5Zg//B=-@0as WKI/Jhn\ $ Y3D%.-t< V{9o|s%QeZr"p..m DЋw!sAVzqxjQCg!v'8[O *l 9 YmKHxr}B&6WT)gxHȄiBJj9<#dN00)dcoPOdDUg4 .g각9oq?Ix0qRrCBV-V!XA:i[C A0yy8 r"8*dw/ 0ε,ce@M&l06q8#d>Y7OAGF?㳜]'b\c "! V(&b-]Kvln뭅c}1hW>㝯els#mF5Q3lbS)KO`g{-LhēLuoopEƤ~xKv?%wxG&I7]=!t7>~&DWZJ ]:tuSGT2M@Q#W!Y+g^Z% ^շnqx%چukolC_Y-\C_ ܶ*Vm<#d5Ӛbkhj-fऐ ƓKl  csٜőˌX~SSJ_s_JA&3sV+,Ou1*\B<ʹNzyљW`wȄ`9_(ʎ?tP'd5/~_6֚YqBv;K:dY 5Q9 ⎶XcU(^Fl!&, \Fohysٳ6q Dq+l<i甝/suڳ2?oW3E)̝6a+-a|ݚsJNm"{ڥ)N4?<ؒ]qOdW%6fg;Cxџ=bo*Fue[לEWeq͂ZDz2[ggQ44QHyΩXaʄ{]N!֤d-BVW_;B&lwJ/mbUXwR!!k32eUӸ-dn5Lc xGj idwlse[3z \f$?[%Lcf+>5*P(1FJ`X#zGl`#1t<4KKãڢUQ1cB;gGg+ B6*=Fg<4fiبGK)f]ڏ3c'/K\/k%y.֫g3B6~YȤ}&yf:O`Cy| 0)d vnz=j@ j 5[ ?VM{^t$[ڬ08#df7+++" f'{On)0/drr}/%x@FƴfA!_!wB'ۙJc U螑B\O| f]~3*o9!3Ķ6ĩ\\/p ӚI}AJVVVU[dT4ngXV~m!9X5MLP[LjkͱLٮ-EY:"|tL\ΠpFMM,dEb=xX2.Hot9$;w?d̩6O5a)WPq*Qݮp$CC6Waas5B%2U9t\ϩ m95݊mUK] +%ۓ2Ag.Tq-XP ~Y v+7 "E@x-ps<Ambw(JӐ|[SP^g0+Tp+kB6)z_vx]:maKU39B6ccPe%Tcژ5/r<kiQ!XKcX^=b|hKcBVofzlvL0P,\^mB6kJ(M |3BͻvD;S L @L̠A9!$m V My(:^#mj%}ߪ{~ӈA"}Hw''ȓ~{[?x;"'HNȪ0=t %v ! [C)#I!S^ڍ<ӲBӲd/馽ܾ/m*DGZ9SzX5_³_Y+[*`ݩɆ\?9%L3@#LݗLW~fWRaˤU`I_wj;0PiV&秾G Ֆbÿ*y¾S*v dWO[-TJ>g;Eb zg@Wm;7@,YU gD&yٴ'z>>ϳҮ3Q+C.2 Zr ܎G v/E)pYbM dЊzC WFZOe-Fme?њ3o*G.sbn"Y=ow"-kȽQƵW_rVժ݊,l+xWU}++F5}Jm+2MOyE m+vV*6_eWz\Lj>SFYgE=А6cWI}pKg1[M"W{ϬRTi c-$+rCA'lMTF^?Sr768PhhcyuzNZ5rp}pI-:Ksv\q 1fl#<x]Ѯ&Eɍo mVJj.a=c3*; }-BNl1h16JstztrDmBX5n1s9^F3?1[FY; zn7b;b=:v /pEr-g̸,En8c3FNabHfg^t8 8"F;mo|7L/_Uۭd/lcOYk;֒~Zm-25ܗowF7LL6N 2>hokVdZ&i>G#7ٽ) ({y"|<))WX>VY> 8'Q;H8]ilHs$ 5k1>:Jn8-dBM CJ;B6zxo :!ߘl& l|n$krNv!k7KPo|sd65=t Aֱ[ ݪ"^?gʸw,E9c3FNjnHVVn#ov lꑛ5*~ eҧd}1owv31|:ʋ!'=&#]n^g4<lLD(N׬9ܡl!{ȐtU~gxGAA[VRH>{-8vmYu0+dv{|(^`N˂o{U偐 M|G^c}>( ؟kst>D Җ٣٣5{g gar/eXn,7Sf'&'3q5?gQ5ytClυXSa;\5{-gК`׳k3d ϐ1F #'5{7[$qļ|Vo({Su07J/=Oӿ5D]nz*fZ?;azp&5͆TƘrY >JXT"7| daAUZOʏ v(ƁG%Gl![}6Siĭx$b8&dųZUs:4Z52v˪/*Uym z߱{ݘ㭻1k/fSUs !^eP:supʯ̩<۳) { 63.ydp>E+H^ oz% !X:͞8zIh@$Gl`Oz3$u%J؏oy E6HDjb)9<(dcAZic$?N WvbsxVsc əPvx,eDz9oU9!_Fott :v";<Ukz_vM|振)hbMv)#jclk׃nZSefK o}vnŌabfu@mY䥇QV{Lv _۝0M'u8wO=aDА'l["Es#æ3zltuR}V6Z9VҲl.#SԬv0F7ht=P~Jy q-c 텡BN+V2M S^QxDŽ-PrCq!'Ƶ;Ka3#dLB{&l?=2J>K3~qoMexB:"!*_U̯?|R42ƨ cfDn:(<8M 53Un_-*EL/zoV7~a6 i6=&|u[dk,nJÙh>!YWE0x4i<`[[to^~ij-h^z锭Dyzyvɷ Z)J"QPɍ =OO'l6MqM_*eT:R*c4}qE?5ϤqY&|çj\lMRu[_5K+{m,n;oZx&loƟ)Q̺5^1/نDŽWqE4]dk89nzWÙ|:2)jE9lbwyXrθWX tR{&o6as:-[kUd˕M F }.,V8}-K^^)X&/$g\1BlbTDy$;$dB͢:bOl6ٍC9SAVD- /dm=Y]vUzWpthamTF[sY5d<]NUݺJWi!x2dI߉~5"2P$}$<6s4dW`OZ,׈Pr u냊V<&{ى i#f僒^Z81n2E=!w%B:==<-spv|(?: e_Ȅ#.!TX1K._d %b>#ƗUR4bQ;UN5ƑgHzb+[EȽQƥ[Ub^a-VL(YgHW-ğUՍkVdkcn:Ù8|:y A<9Y ԛE7Go߷k?* 6 Y=9IpqܓA1ؕەBLB5e 7WKukJlTQ>%ٵ]a^Jn%}9ƹ7|=I.Fق/xJAxB-v԰"l< 5w_XXOknQ=%(B6oqORQ~!J')Mkf2!'Amĸ')B6ppgrd0F'sXvB`N rCOޛNO>7wUA?*Q Qa ;]Qk:]񮬧|{ R4)4ƨBc|:f$yy6Im/|o v ݽ&u[)1C'VcLLɁYCYjid t31|t4!g]fJ.Dn`#&Pr@s1al8΍g mCB6p=~LhMC概+-/wE>ýRIf;ǮD[T% } bӵ'[;. Hq{ ur&M, s׭W)sr8ɮ_eIଐ6f>2a %Ic=җdyXzXzcӛ=LD -;%CȄA,t:UClDŽLȪ [GFsq\l, Y$b;b=:!b+(Wmo v=#XR4bQ;XN5jHzb'~w PۋVnU-y[11#Y#1n_ܧԶ"]Év'Lot{HE=А6cvlD;۪ ط'UG_}5 !"LjF<{X~2a=5\/04еuibJϘ{xrJn/mݙq89'#0-d Gal4GS\MBY Y~enb{/ 1׽ ׂB~ւe&3fmb 1Fp#'55[$q33Y UdkLjF>yۭ[>KUոݚ=m=zL>kcZcOɺn™|t4 C\Wqaj?Á$>[%6<.dU r}9"韑8Z]p!7CP$< j5`q#)`Zj, FfV F51x iGz 91nP1n0J. rbB[`X.v`I-!jw`2\em1Z GY=q#6Ǎ}uHzKf>#ƽnf)c1rRoE7[+ PۋfWmżZڭY#11koee߬KҶd})owv3Ÿr2.ͧؓ +@x wجP|"b璵TB@;Vse35L"Sڙ:XA]E# >U)0~@s^'b:\ xAP<:#JqxCȄPr7L tWb[{B6h:=91&_uQu:Ѹku(K;B&|:dI֯֡}@d:3bܭc 1Fp#'57[$*35IN{Kխ[Ub^a-V۬p|Vt-Y۝p:Ll>vآhȭs[;sn`/(9vkܖPڕ"a+f5kd3 0K/#W__1>#>}݉>zIE4&?}Wsg^gvml|2;F1|,ݚZ>#B;q |ƌ;LR401ƨc䤦f$nk7Lm/2kdݺZU:}^ڭͯ֌lc£Yk;֒~ZmMv'LotDO-!J͠yZՙS競1Ӗe3 SԬv֋B*}  1ccuWyQV,F YWKuPJcH+=c# |ƁBV; W%N 91~it,΍@@dܕjPs {Ps{y#7BgGbrG <.dB9bB kI 5=rx[#g>c=rf)c1rRssE<\aj{ȵT=?ou|L/WUvkFKb15~}/M[Lv ۝0M\8*Ow])^DZ$PGol74M Qib(SSKgkoD)']Od7^Z奒-K%YeWk)fS=k.r|+P- 3@؅I?_vR z@OyԜ.B2b)6/a44[lȁʖ,TyPsɪNY)$SlbpP>Y {Zl<*T&XZ˷|]硽K`eOI{1W'ԇI@u _ fx7ͱ58%ɎK%v3?R+hSg[tXղ1`S3]dHǐI|5LznW;* b N~Hcv!߁rd4 ˔ڢ[$Pg48W7j<~x <5.sT&Y٪ԭR-\0&5+BsC%>k߾ !mgZoQ32OچGIZn||Rl3l[*un&c#4Ü c͇&70F'{+#[3C!ΦXϗs$Hs&p$< ǘβ"NP „gAlۦ﹩!BCCF[5T:1o5Z"|'Q Ɋ_1V,aFk6pljVn'Z5[tf/' <32پسCz %DVٰH-$q p )eg uG~褿:Q^cH'CҒ~ j!(y cP newBɿQ+}+ ~Nd;Ph%荕;zGw"Q6v!^_Tf-Z/sh.-GsCש 7֙ JեIɺQ~z+*۞,{kbg0x9oj+CF{gVYw3-"W~oyfߵ˛>B-kY}+8/URjkV[Xeٛ|˞k'D*V9D7οLsÓ?%hDvJp:ƶiT7>J1f /GvZ31-̻rdIjZ!<H4 Fo蔆(c!cHCjzCz0ÝzeGT3R?G[tO6@; ꀦ6@;8FiMQCT[wˮUFZ17B+ijN5N:i.u ^[24!R6 *8emMegvٮ<ܪ:<{EVd%E$ X%Qfs%mYdA2V+=i9;cRܒhOwnP=!ģI{7)i~wK%'E3c`{j6iӵٙ%JΗ.%?B<-n6(![Q9vH½f06bczh;~*|1 |\aMĺ-kQ'q=x˚!>VHZp;jO M~0'}Ym؎T k֠txm*j_ҝߝW#q xBQg F5")`rͪF:mF9A_iJv$[Q-hQx% N^S&խbժ9fVu@~2ȿL5y'~h&$ Yȭ_i|[w+arNVVfW+b$/ 79EHGPisː/kbk.^Q8[m;c0'{yH桰h`d9䇸nNrC / :qRi`*tD `hP8ڭ4·7+\αs,.ľ^>WٖNB4mxZpQ %w8yJ[}؋Ej}R [[!o5XA> Dd7݉>' Bm)86+ȷzq-YqNΉ" >*"x=m$ԜJݭ{N8+ϥAi uQq4n]MFG3̣V\sej.YݳƮ]H(:#M<+k @dl]d|fnȻbՇpd)|Cu@§ɻvv8?WT-O\?ҧ3;x4uvjea`m%t$aCnW F!+mkt =Ī;Uvy1w*5{2 g˚qއAݰJwmF iX s:QNBlQrYd])攗J|hTJVEtAwfhZ7*TjJFB{뢂tL"mFqE]PCح J~PW kO^&Ln}@]]!43y= Fx ۢ]uɼ[fy'Pl횝ŦU@ 6i0ds[b J p~|a)ހ|CʖJfBKJk\t$n.k.Dg+p7dѿPr@XDu+tvVtxIerKsC DjxMciɩ<{2ԃVuJ*B5SF ;!TnUZ(v_d.,ZUP)mすFǩ 3RɱSZ?e8% TNx˧r䜔$5"}Cn<X;!HxqmKn)~WEe x(m FTQu:KYȳ{,AnT+EZtl8%ɒԴ+8*kHDgx%^W~ rF,7%".)!ָ1jaqn};옮Tȱc,VRx,h VYj'|vЙ"[fNcSYbF@u${2>jd4Z&pY@ۭAeY4!h! +Ez]j vCҒ^ÆliKYRwx 6;"qL{BVN+g\?JR LYw\g.iJ # jg dyE!^blsF\A֟'9lS"~OY{qe֒X~ b܄I$Bm9Qr 4P[ 3)5mS5ڭ: :|9Vn; vBVY'Qr[ kRr!a?2}Vh*kp)6tw l܍$I=ahh(6D"*8d}ocwjtsem\냹ogP#Tdm:|Wk)fpdͮrBmg-}5q< YH\kS EdNBVꦧޣ[9!2)d5k.DdS1(f!އtNޞ@_ m0Yȳ]fım+".)!h&Jm/ĩ?ޥ4h{Zq݌#-[2ahkV·It:J*|n|$bs%ؗu>q |'ѱ|(m= SloLI&De/]$09 ui"HQJMN%uJd'dpj4GwK*#Tь;ؔ(|`URr;!l Bmv g[))ct.LBtrJJvqJJɯaPtKL Sͺ*#BhfJzULI)Pf_U1լ¢բM3d ^h$Ĺ dv;MP{ O4=Df/$ds[8t]7%w 4h)Kt*`SHo07:".vEja}?^>vە>]hj,ʽ,NxB9;UzGHQDoxl Cl;WbS($d@x 8yPT*G) Pw6|N7q)VmbރzKv^E.Q*> d526T$*Y0| K&I4.踫%Q:>yk Pz^$š %> OW kz,jWB3Y1, tm?}&.jLzzn#Eܠ za#/eLhhf_S/W? j( #xrXs[lqT3[xEAp~Uynj/zZR<}|]wm9} ^lCoNm : .'9vW6vW<*Dտ%պZXի++"}@}*'D7_I(XYx<,X#s{e=,ԫ~R+-3g| yi?5>&ૅidPCDiò"އO P|=[./&t^||[/Cf{$Z1vD{!3zz V$y;E@nbW G0/qzc#eYF&Oe|P9ǟ &-/Yx&AV~Vf8 N÷48̜HaX tl`/}ҟ>PA^`(B@V4Wrc7* q9 <x d ԋEVal_iȠ*2EKz8YgҌ2 nduhx#iځ!;?pcML-vk^ٙL*t[@B߄UTT6OϐBsρ%~ hqلBm^v' % yM򒸬BVH+:*ÖmTpTnU132 lJ60,ʦ2_sw2Y^[jPbNH>={nUqf IêX)69< hͫKhU֜eRǁ 2d=|ݡ4 3ݜl pPg2 BvgMrQODžFƀ!_;)2Kvi s4?tY;]ݐw`(Mw + 0QԊ5rSOuF-B鎆vVJ1iUW;c%l={X|YnLJr@\/p/d9WC|- Ik55h8 yV cs)i*XF؜[[dԈ[eXUJGVhHC3vT'¢(:]W1%"A<> S˗BL-omMU/5%J>m(~a.K% ӐӝQ`rF[9Vp& ~_mxu{"PsYh6یq`c-ȼ<d B> r%ȖOqՂ;@֟f:΅3cfea暫tF|g!w %wh2ljߥh(W _X7w V&SځA$B~M4[1;,zUlTF& s< t#B<J 0Y8ffYX_"vC'[Gړ0-GO q/× \ OKT>FDylz/B#i#. o{ZӐ =^ЌayŢ:Ž\j݊[s+N! J GJڧƙɽ|hW-@Z -`zyjJlL|%r1ffYp`dWV*8L Ѓ+*~lڿ._B.4e|u !}_4;/tfU-t}`|ѯ@.CW]t_+6a+zv)V̲-B}΂2 nAV4>dM@_vQBGFZJ0)db~ՖԾhƫ(J'xkz]:&!m*Zh 06]5̩,Uxyy @P.U1Gc0x u/#VoeȏR= ~MSiwOɝށ|G(Rw t7>~&Mt{Bnեm qv;@<ӟ֬*o\ IV|{}׉%h dsӻO-Ĥ xn=<P.KgSlSz9t:?[ŪEKDt^VzH>q|e%`WyܵF WwOBVem{T43YEJ[U JKfD.A}I~ zX꟒>QGo-\/c*ʶNY ;JД m^#!ǁ G0͌GOJz>UO~DWG߉j(K,Cx4K"c8^-c|e<$:zIx.G7"ߘ0p_<|1a5]^b_]$Mv@6R4mUL:f]^=w4]%/Ca$[ix?]8yn GQ;gU,THv'QBРglDAfιbL O'I'S,7:9NƲc"ttD B>j'?ŷO/_cb/Nk[򦦦?>,Nrdn`cl&escd G\v|2&}?xf٘OC>-Szcn/S;O\_8 9b}Ful/y[YbM Gƭ. ? v=k)bCmƝ ŕ Ib󦹪m=󖬂'#9cbFrn"rg*CJ.6ekz%[%gdoO3Z/fWY6nih VrWd}Z-/2MOyEm+vV*"r쥘0 gLѝ&^Q-h<˂;mߙVg)vϗ[V@v)f2l:WvJwioBFg!jg]Ƽefu} Y-zwTwHc^ xum[/P o@JB !*B竈ie@6nӢz[! 39&y{( @3[C,32@x i+ n5p̝gKv\uM|98y9WtQ(VG7MPY;_{aUe&cx0A뱬PBǔ(/;8&' j#sDv#$ NFD0 9Lɘh/z&ƆLJyDiyMe,Yzod}F~}ֱc[ Ѫ"^a]YoLh[dQ;EIMItת*HP|lLWWmc3֎ݬ+[\W┢)3YG۝p=DLo> 4!:mt?Ӽa's g mjR>p+KV*۵S`3vm-zL>H;oBor<)39$FӐsPi$!GoEn.Vk{fO܊|X1bw8 ^4Ijy]Mۢ^~`oDǚg+he([]^oCFg!jg?|G|Ar'gФp^8yE j1[ꅊ&Cǐƕ1?(%7<_yAϦѬtIdB~h,>t"}fw$4Kzc;acʖ Q !E~]:f~4!]Gx.3#);MLvt>~'NuFjr^#yf3c#oLv @F']b͢yRBǴ02Bo9b~)101JIjMdt Vzن=K JnR3KICB[L$Yg HZVH;@3Ab@QO.B)^[}uW 8B{I\w _G/Tm]sː/wAihF~Wr%'BN Ӽҳk 8#3$d~]E$Kqp!y6{2duΩ֜Y&$v"-dWoΟ@.]y%(gr.I0QeK\ϯ{a@!zwLU~N.eyqgGx p3,7c 7oOTivMi LsdnxtTNOi|Lamgyf'0)ԣn}Ds$+ D>}<Zsb#O:r:cDejOno>sYe1BsSDrn%Ijm>Gx )m R@_#UΒb]V"A?IBsKq R.7Vqs )m,-KQVށ S3'Y?`i\Z.UzNRf iȧNU?/'b:aUy&~/i){]'Wg@KfN rύg8NBB/vfڴki[=99V;j䝕i5+%t3{ tj$5x!9Oձ !Ok#&CW6L$[VmZ.9x䪬;%@OkE~MM2߉NݵWEEEa˿7BiMd}OmRGHls7R=!ģ@#bMOh; 0O/jԶ!w^'?ģVVGd;bl;^6v!^OTf-Z/x%h.-GsC=iȟ =Pn"v(T?9 d"l417߁څ{gV5w3s#W~oyfg+}pɝju_k[Ee<V&ߴ睒+{ bĞ&7lh7A(Ј2>Y|V?cmSVdZ%NJCޥ* %;x ieWC+Z/YF@>B#";JPW4v6a՝+eI-fd-f#֝%?B<)ܗp}p? % x f (rcu@GALxB r+fBv1M*zna[TXZOM?vj鉒?B<@-$>A6YK7;.{!4k' lZZfF ٶm#(& ^<[TGZ1at7W(!4*#5לc_ ܛh8XjN`']PhBBY1F5֩ @b8tbfE> 1E>.JΡHZ^Y!JT7=;4cƪ}TP>E>D1M)(ESL֤)eJ%/C]H 箈D+}ݮZPj;k rV|B'arBF  ܗBM2ST*% Q@8 y}w,P9XRC-np?dQ^G NT#PU{Mb7J*:%; F7*: ֛V& +fy7mghmQ|mhw~ٮBraժQƁ```P۳A\*%y |!؞ve԰ Q BVr_1:QCI&w\_^|s՜ Z79Yo[bR-KweZ!D5cZ6˪LG\dsQȣݨPD` 8y\|ڴ|}~1&4}ݐww$2{!+yTek4L0A}:MbwxqJB1nq"0 TN>lK1O^l_Bۨl1ǻ4tj%!Q0p1Y Q{ 4m@ +LKp[蚅m(uZ*Trr[Wgi MHFC vھvhnޏ\\-#4dV8-ŨƇ; @hl{hWm G!MnYE'B:^|Q[';57zVmr x=`sY%SR(;̙KYs!{CS\(~>U_=^8EV{ᲤӐһLTmJ.Yjo ek4Q YmؒhI&BCqF kZ <`-<YA%9]rH7c*0p1}mP>1d}ZCVD sa$[=5 b),bWq^sf*3ܲSޒjcssHPkcTN-ZF"i%>x:J>5g3 "a!Mfc$BfY,) F~Y f@& n 03( Md PCحf`%?5biJ[pd(QWeDcWhʆ@ μ%/S#`+{BEz9=a=oK5O6[YhM;!fF4&ņ¢U 5qH4Y*ŒySvW '!O6᠓lLloBނvOˤ(!ģIcT(&|G̃pd1`Q8Yk!B' hPrմw(:g+%ײE@~ZnTVsB>4vX(P2se4 $< F;smTDO?gy%s;1a5$}^Jlqyɥѝo %{ݪ-40]G.C_`wQrݐwke"M+ gn[rZHts P"'8FEޅ>Wl׹O{&N+թ&HdqlC$mL},AV yV5TU4NxWJn;c*7Zc,CVm-~Y+oE|B~{VhSnM 3~Vq_T;ײIz.Gh.*\ \~{H=N*anщ&wi㴸ԶD$A?ˤE!셬v$ʔ^ҩxrm%xq0ŊuԼ4?r`z# c֜?*GS)FM N5`UIWEif! m\#S$Pް)r.?~`_k#)acWa1 <5aijE\Q,} 4 @I<0X)\<1co(qW&DGz_ nƞe=;Z:s$O?;jNҁwƝ9R iqDAZGn<CkswUbRAϭRi9ZwOl^ ۄeK(y 9fR<YiRc81[(>Ao\/d{#WX+G yײ^ pҦy8 I4nYB+ c@ִ Qv x@M&!(XJ*b#t⾠!s8(kC<ǣvFPͱ=E"Fș%w 8YRe|AZsX>,M8 yVF$| VChmmAf/Z:&=YjɱA_EKz哸 /C?&i?@V4c̨Ǩ'"< t퉒 R6SA9EGuS$I+tJ0R[L؞ Af7 dFI~JOB6yܸ}Y  Poԥah9֌b3fTaXс ~l %jl@i*,A֟l{~fDfIBK(,­vvyi1RHvd3o)a7]ߐ/)v]б{fOt@xtz Lu)v#î86LUqRCv<šk5Y9%*ބn= xxgޯiilG\[ @VpE2*6dž]%: 1A~]L7OK!͡2H"ٝw^Y#whQ7)jз=vRk7j1\)quKއEI ~XsL.; 5GpL&rdz19MB~(Szc몲}XekKKb( kD1O|],SlV[򦆆#V͵d*ŕ+Ib}ޟCcgޒU?$\%cS}km/Un\m76?JK3v)fx_jͮ*lTW-ZP)d7=uJ}7|cۅ[bbJb€S'GͧӾ 4[e"JͰsiyẹX<(z8>^?sdpv,zVp&$r1$ -ƅ/ހeFP7CGK ac&3:Er$J WR~b|0FG鱱qN|BVL3fWrrLJNCiqWb}U+)T֯J O$4J2Kф+v-[IWR{mMՕY}rn=Ml WgM+问ztJ gj,yYTq%=bQ*-G~yXE*Vi<(XɮvOz_FVAw1{lisco2 ޥAf:-t۷*3cinUZa?~ o y~ 5"J~W oU/mUvnUl:=61,_ljaUi>#lL&/Qe}bݡJ~}R/ϦqY&KÿdlL*_ZLkk3vInofWNK5*_'y).nUDT/d-G)vSFT~BVF'nf%Ȧ!X[2cy򙑉p&;Fp6|Jp'<f&}8[>%u~23|>ܿh> W!tG}i)EqD;}~#x.6j=Iߘ–}]yY!%M@09M[ۧ@GY~3XE{ xPI^7eISՠEx=5[vfjN:,ePk0 9y"פO ʄzW ͭOkկW6 O)a ȳ60#<ɺB;h}{w _x~E;Xhܗd wHu J&}!n9~r(Eobkt~=h^P=<ihF< iQyӴ[r[%~Kbq*tqdd ͍&>i#9Sf"{%}+.SB)hɮ,o;ʄ:}(l0jj/%=[Y dPCnp&<MJ/2q'Bo7 `oVX+L&6;ߋ,ކt@Kv.FT%Za)|cɛoo‹/OQ;a7'ߏ4c}-ɯD7a6q0' v.1.~3^|M;'>X&~ /A-H;n~iQq+jLXr5ЭY6PU?@Z(T7^x|"ߊB՟;ɩ-Ɯ= Y֧؈)ی'+ ˏ{\gr%#Jզ}QcPiz @VZsftjNx43MQ%4j 23C3%j4XP4~4GGJQcc9 6T/Mwl/͑TLh.P]mwX nP)Me~O{i97 j4EȪVj)ZϜj4B5}D66 *"?j4Aa#IP{if:? j4ý㏀isih4?j?ޑTD'lS+GKs,)V?j4KǍ4*JveBs)M.ȇV*+n/$/QTrU.]Ɵ 4bK B .m^cGjTTZҗKa)V)%engDA L8yl'ؗGȥJ=?g /KNwC (%\'s('%w"ߜ| Ex~䅬 xIX/=]{~ I4b &~T ڴ5h) YµOUN -_Ci-t/+3C6?qY_CBҺeg8.ەe'=SVR1ޢ[^LQ ΖbuQy[ ,Y\ѡn͞b~wp<} 1bM# Bf/ewp;6'6s0TLhn}1ˠ˅%Qɦ`3{y@e/oBs{4VCrZۭ{v5\ ssڼo>(p^5+=_[  ͵k^ N KvګKtyv-9ݚUrK9`Ohn]#?6ʃ1OjUm%UknaGwCM5vC))f&6 uB3"4 N̈_8;xxflXc`J8y 떟q~׺`=Yҿ*~L(l|5/ aQ̿a~jo=2W\4 RSlexl%@E {d(A rJI߮ڵ>{!榰8a.tih h9l56ye r&Z5WjrN.z0B.¿G1VCh/bKθͮYՒ;al !q!ߎՍy 9vf:~ 5ƠZo'V Q_P"4w$ݘ-/#|\W\˳|12?|T$_~ihj}ER@gAS֭֡3Z-QQ:4wPվREWKg 8>@tr[VtLX3nQmgBs@\״ Jhn-MɨOJnQhݳ=Fna nUBss4Uڕ+b4>dؤ[ ]m{y˕zd;V~`(%\@‡jj;c=L?0'}@T=-^,1F͔"\<+gם2~> u;;إ-P a;zg-DGen&4PGߠKg+#@<2tp? qyv9of*,Ϟ[Uǚ+ٞtM]#GH_Ä ݬяf-I&LxX0TA#mD%]٨hT兲EjѴbMexb6VK$Þ#5;Mޢ[ !ߖ(s I(e8yʘRv 8]-EǪJ>39h>U }V]:Դo !Ra쫬CZ[SdZ+KvHҢ]qiGn(tگ'_1Kf2 [_YVVy:Ev/lQ7T> 7UD.C=len a10o'?Z\0q!*'UV$u8{ STBoT\&L65ߢ3 5fp`dcM/mEd>[*Gn[!JonR>n,|z-tؒUs33uѶJe v'Ag"CR%[tUpW;{ ;5܂׉xd3f0C).)ˣ0u ղf9Nc(vA}x:>!bKX]4< R;@0~ onZ/d}'d]Ϥ}US=v4gS}nmѭVW|i>)kD Pcw3귌D?=/u+*Visd#|NQ(ՋtpH"bn-WA:7NVu 1BdU}> _(^ ':?; ; !F BVahc-E:z5QSO'巈p ~Hez;<}Bsg)RͻX-`_ǒq'fSSS{]'9p270 \6N-E';XOng}/"kKC*c>)|YbM oe |U+TSwQdUm뙷d?#s0i[Z$2[$WWnV"j&{kSdy +mo0) SƵkp3p]/YQq@W-mmW}"ԙK^Ԇ;azcUm nb`b ?^΄։zUzDž7BD*+# Q !Ŗi._fBͲVm_r=_~nUXf8v)f2lZxvJw#4o/ %S1S2-{5Lo}ZtY%TpcЩ切C-l cUh!_78(Loh+RP7CGlBYX(*n/*b\/p+ؙLx:f0d<h̗fùa]\.7125#Iȓ*jGv*zJuz᧌*5Q,g͸,E>Kc4FNʋaH׭*Ho:v uͦsfϪ|.;ZN,YQ!hf.>p*vb3*΁ a JTs?#g C>fA,[@yjDBOLR d:oh,9 sQHVI‰R xxMc^i_U)giJ_::@ ĺN@ 瓔-[4 |Ј'i\NoC$QBZqc:?&y$]z%%#x MIzϠ6b\?p?ds$9>;>Ng'uTs!3cj[)OW _QuuHlCUX[Ck]ϊqWY&\Uh/l ^i*x.UnV-e*sif5ft`^5Yu_uDVLv ۝0MW`8Pm}#QN OdoN:B<-Ӂץdq(!Gq$\*5ORMh(Wĭ-M9P$u(S,7P +]Ǎvihhm5 iͭo\!_8la)Hy0#<6ɤS XS.Vcq?˵5|k_/+a}+7poU|[AvVe0Ťss 9 VҐ.eZZ|*7/r CV:Вkf~ceڮ]s0Ltr:\EhN ݂n807̳y[ő5# ѤzoAO1 .ihUΗ‼Cʢx)$/bҚ7.^dee߶Yjlo0ahI}kr_H1¼ŪӼ9}ɍ/H n' 06{jKHP<J'zU Ԃ5W68,D .czocR^ ywBɿBAt/&~M~*U..Fiqp Y%t8Y TWP؉_mX(.޸˄|%s43ǿ%=]aMg\,澕 L3Q[V3Zʖ7<=̱K*G-7z50Q}IFlnO4g{,&uwt^%|Rr;Cw6wBV2T7>J5@&z;J~w'ezO5hǮ;m땯Mv=Cxi~=C i]QQU.jGhy^m#[7|rcLEaLҁ=bԐ9 AΊRj0!Yn=;7C]l)!k~4Ke4Uk\J$ -xjR\\52$SԨeDc{hʕ]V[[x"^=?tTDq' e KW3Sbč_f{"CƁnERqJG9!<LBV/px6*N6 \eTBVUr8yK*N@0Ml:otF)oj+eSdW[{iS(WI.!_Qxd^R(]FrBm6% ΂Uk5cKv /Jp;Aȃ]JFr1ډ#l؝EW;Q;uz#μغL/vpDM/mꏨZ s8o܈:b~Duɓ 09~ӐQ!c50[[..ەcyJބ4WOx -m(B>TFs95ű*g[ < h%4wnJ)R҃8J8Af]<@;86$tk n~^kqWek-y_k-%Б&]!Bmi_ !+\嬇;< YْJ?p8nZƀ![_S-YS _JOcbj6 .vVX~v?Jr1-a\TviMިnz:VVTD>`Q L ,G=}.<1ԈbŬ*ݚ^^j.py vl-TR)l A~xV%\}d珫3A| oynWSaO3{N_ljnƒ{Ϛ˰#Bncyߢ, R; }8@ }!ģY*w [q}U&$rl~Cw!S?g`Dt,J cJͮV,܋v׭W eWraeǁ +- cb2\1jBτO'`4Z¹>Ī;ȴ"&0% LQQ ڈ6!y] hNo_ %ܹvg0Lrcc7SŸs=}ᓑKÙl|z8nVM@FG[!ַTX7<+}oKc5]"Fz1l#1rѩƄ5[$=1leVțbڢjni_Z9[?SMgycT.k2b&1v=+*?N3ZndkD7>[XynZ*c$NV aRO(xGO!gj%ˤ_YVmcRl&æłWNvN{cbA澽f*^81 yV;S2-{5/m+Q†}At"2* -Nȶ~7.ot:ŖӡFukD !MPv,e;B--t~lX&mPXEVV9d+_sv8 yR_ Ra;i_D+Qˮ9Ϛ5M9cԎ5c#f$n|jЭ2gFYjn^owٴ[Cr c YePVk` t31| +ny<%Aҽ7}FzBGzʱb[{'O'KNV,Jpڤ%Odɪ&+nJi98dfzZͩ,ȓ݀u"c%k$˴e27OJ- @0p6&9:OL=] }򗃥p6G^}. jmFLTX|g@p_B6Xk8 7z #.TS .QQ}Ҵrk5iVǹŪUIX]J߶eAlMS EqJľ6];yؘh+\Z{B7YSP‰z-fW8i)4>;JIg ~PȨ1:}\yК8&-ϊ]x@evSkR߳k/O N~mJ6b|:J?xLD _޴Fz7 %b#BMkSZM}lUj7JzpgbSJw! t n]p V=+LwW%=݀C5X A" Mr;5J>B9 x.- a;q7mI46]`@AMa[a,j򢰼EaF]/=*ͺ hJ8'T +L8 yZtU5׺ ҋvuԖqEW\zѱ<'25#mn=;=5"m+}M]r/Q3iس%+"m+prx1xcEyyݯ6;ٹtCi6s΂SJfXm;3vѵC{Zjfy^lnݶ^ab۳"r(.aĝKɱ! z!.]:4\ =2x!+Sщ~= g͆jY_C o mB ^jQ0"~(ǐ ʩ;WlSfp}]ƄzG oXTs4x g$]FLct5{D 3QJf>.4Q V;jQFHvG5̎ Qͮޙ k8j*-ȷdhp b{; gr% -׋-W^PCeh"T1Fa\t1 IO-*Zk5v+ i]on r07FI;Wͺ)#fl۳rHюMsOF&F;azq™|t\ ׅRCuhb={GtW/,+ vEujjcw*쮟Uf`I2Nfa*4M{E<)HɌ]tTҫ9pp%bn}27ݪU-I)2OڰnōYe؋dw@ޡ]---eh:=:bWKNe_*y5-KW0zЙ:y8_\ 6!+ջ"jv&v:s15RIxAmM+[!x=yQx!*Q C@#3ybta?N/w[zn8HVD޺%ɉQI9j\_Q ?ԱEvAvAm~ (V<nltPC޽FQɳ411(}ikcwr9ܚ1 Ɋm2Nfٸ5w8P!_W wtb}CuxN2~ƅ֗-R4vG0F.f4dbHVOۧ_t/f^SfWg4O̰%fì+-}VzuAӧ"]cENRZ87{ŕݡ7MzBGzo׼ckW\١ا=yRUJRTPDP.:t(xy[uc]w334[ӞS3a 5S*/]`ѩUeP42x/jtG SĤ, I `48Ⱦ"5ݣudqRo&J5ZMlFyąu5qru6&x>Tj]1ZhV[57Ym GZj/<ӽ#tQ fO'i+ [cs6-s4i15Zl܀ԣN8`EovٻM"`hn5/0*੠F]|>dl%T1htj+.Н߷ cʗhtJ-h@UO%f쭹DCf5SCJ/YgX5 B'ՠHWho+@ 2.OU&C 6:6( ~4vBީB*4vAyPCǐVt!fޭt;J~oRz2I)d=@m Y%FD8B(!\DR!+W߲+v*;j#I4|XsOEB f3{4p:7Dx:U{(Q43tBC(S.֫~ n̯Vq_T%9z3lP]Kv\Gy .Co(cwRrc3 RL?B7b5Mo7E <.OjU N~`?pRr: d}X^9 +U*p0 x׼%NpL_;_&uj3RVZ֦DSfʬoJΗ}\ʥvB]:.Q1C>qRj*9¶+/&ۤVOֆy;Ne˷@:eiCq~*ˁggoBsg^ܖbo3FI9RD鹥y;*^sTsp(.[\W-kviY~mrJ|? 5:H_ʔk{|*-S%p~0 djU5;s7*r]Gъq16>G|V_ki+]7Un(8?tWL~-W5wdKWK/x ˆdʹUsn,WX>Tc$:D/9qj|j,k 5g @~ ':C5RAVʵ7*+ϭ"zɅ*HlއXYcDu99)RU-eGNmYle:7,AvS(3RղcF 'o"+Ơ3>_m6fUK.ͅ: Κ!2L]]^1ot]ϋEdcz^kr:tJ׍]+;5?4:Cs#QK\Z8ߚ:2mT/8~ Kbnv쨏#mB#uM>>J Er^gJ._[%Wul7ԓE=:ϝ3۰H%ND }ZAqSe͍Ccծq9 <~sOBV6!18LAVZLuӐGHl{J'xs.ƾ,cu9eU,:4IpNM1>-Tc?<D$t MþܪW]|pq}.%0Y(AV۞әiݑݗG!+Y䦬Adfhw=ɭnϲt'>fHɄ OY?>+)~U^bw ņiĭ G /JW(`u5r4.<9*% g@201YAdϲ B$Zރ{Gަ(^Hj/ % )yD$ہ _|BO,eb%|YGG J Qjy0A뱬PBǔ(/;8&' j#sDv&-+›²ʔҨgblx|KyOdlQr{:3"C﫰SjVUzgʸ,E"c-2FNj:oH⦋VVEecݸn{ivffMu@_OYŏ,5\ڙNp&7N{&Dmh Di(Lk}"N-j.u+/DFg!jg@rAő ' 6R16|/>8l‹S0ʝ #T>kbI#۷+!nKu]_@݊l|6ΏfD*!J;'4KzD'xMvHf85+.㵋'fy1!vGӖKqC@~\^+>Ͱ<[v"afs>I*yS!4fuEZEjRt vy䲢SJ~-2D4突|Jt%qdepq̮ a(&[/"J6"4H5~oOض51 #Q@RMgj:f5{}Wo"Y(ܪ$ Nw;ݎ3'8Kq83'Ni;3V_Xq[_$pӪba%۬,C%'~> ,ޘM Dm7 =|9'7v E`R$xo׍ZsKF^;ZXFb>GB}~(ٺdXzDC&%*Ϥ֥֜zZ##bX(q-sgoOA ȸ|TmEJU߾~hv>&1~ %;E7e,ݶ ^R/Of:0FyNJ%B Qa&'l}MAVq5@qKѿeT;%cq;RU=M ɘĭ:Wˮ85p\*J]y\gߏ,M;N:+aƬs>0;R>HЈ=jC1̳xT$Fk~?!M*aPOd}J^dg-:fY^3j{(XcoFyS.("}rC뷢TԶ}ݒaP~t?]@<1je$PjӢ /Evd0ǣ,K)!4%r3ʿj'ƎQlZmlot&k'w\ST(Ckcׯ>Bqر?4sK;Rp߃`CM0UpBF-dиE+0}8M3{5QʊW0n+)2%֕ =V^{I 2:Aai督Κǀ!6~Wq#X-Gd=,8x-XjUcC(5'؊F[OgCgzEۏa{J+;qT/8ЗFB9ΡQtBgK2◂9g{>8JW5iph -&ޑKZ᤟C 5TZZ M:[N{ެĝKRZb '(-j8$jeM$vbCŝ^,?=2̪Q1'd_NC֨e)ނ|?ʙކ|[Y9,L#ȏ2{8ß;hn>6|}7,׳+h%~cORq#SO4^U!g9|h{C?qI@{ӡBQYwɞDjf&6hݍb^8ف[/B۟Rö QL(䣽Ln%BӁϢϪa{3?H6ˌY5lAzר2cKbW\`fTSVOː1t) `dW .|/-S7J l47klͱmp=KZ\$ 'ЎT[N jfl8<`Į !wW+c~t xyKT ̔u4d_ Za { 5Pm&} 0Y;RWaOXeBjYּnfэl"@0&nN".|㼯 ~c+F-lZL׳^*]X"K>UyYuRpp25;o^v vp g/b*6쩢/<3~:LTJvŧ?( #whAtY^捏z۝e , ߛf#syX4ƱڪVE<°,xd*S7⌹-TEƷƛc8jU,o'}:xKыD>U ڷSh$X>R&5#B*Y+gҫՊفϸy/1o3,[ IL_>w.ʎPDq,HhG-@ci[x?"T.TXeXЍo&5)?̛z0*qS亁FSe?pkE#!T;zm}e PJzr)[ϊ.V5>oS5͸O,֢lsh5;.mb;qv/Zyv= w؆+2JSNQ]aZ/Ae?c ʎZArGl5 gDWUt {|~\BEj -V+yOó,:X;GZkXMOu1R6iZy:P&w`OmsL }3S]:_,$џ6$[lļѨ7&Tx$hĞ> _WocǴ[f߂*!_-Ta5@-eF~jd,EgUI5'>2ao*|ziyA>WZ.s~`yG[Oib8#A#̼g0KgJCѤqFyG!KllKYjBŏsGV5_;VQ1W!1JT *";GV-6Зvkt.>.rZ{c jx,qtGNrGf4_ťPLLD%j%Mr(wԖt5TU`LE(ȨcC)Z7ne#)Y/Jbͅ fx fAU܁4Z@=8qw6-l+q`G ~i8/]ZpzrpH.<#d,s),s'MZ0ý)m4FXY85+z4;;fp3E ( qGr\Q[#tiÎeŋlݬ=۳Jqx-W0 B/ǼOH%}UF<*ƄV ]^EqQ/#T [VQiw8VQ/ݢr K-Ta;Ҋ5@_/%cq6J-k`SI;_٫. kn#u SU8JcVxٱQi[AvCRZB Nhưp͊+jK܎3.NԶ'}kP(Eؤșw8Yj>eer xumJٟ&Қކ|?@A32ޅ|WWar(m3*3`%ҁ䦤̄8|fB!gZ0Inw $ !צ;AG1 Wk[*XH5/ `~'DE\">Q~4-_3=#W^oӣ6|y4KŌ/@ >j>D>=SqXeOLg=odeቀ3gzoHT,,9ܑ{ny^KkA AfD daGqCv"dWq~)&geSQG׀_C?: 5LV%CԩP gyc!ZRRmw{e,TYgC>?'XZ9F폩a{NX^9TES3$TS~vNuh#jTL1褁bCŝ^|MY]RN9p8 yRbJ/˪exYk^ᩘʿ Yݵ/3Dy 80p*>сzb'Cia[ /k5@vTIeݍgdχe+(ns 3e^(Ҫ=s|a~`L57ogF_.TMvUaiXat\j "M PXtd@C?ġڐ|^PQhMeO2>&wsY ~=w9L-ysTxq<)w2˞Y1أ,ѵ#1*2e @2^hN;ZbuF|Z'JWhG')f  OeJU!%ܭ^nՇQ0TAhZ M#G |ɔ斊;<Y:Ź./rӅłx_&B' bݎ SU-5-:.仢uo5-]X/ɰNoq-WE{[uƨnKX&$[?ijxEV.x_Y̥ךIX$%ky?vl ZWl]"~7Rzy{)4fPT)(}C[4!ɑi/F^# D!ouǦPdeT VjV7s ׵KV#8 ׃sCZ cvɲEF@63535ě„xD\>SO#nQ00ER6{EE|s甹κ^fQ Fxye2nX Kf|[BJ[',PM5 |rm9ƚ]kԂЙ aթ*(~HYI|4>@&wքfìne L xށ|FLjfAu33MpF#Zֈ6'h%Uu)jP~zɟ4WcuU.JLpOLt Kg33?fYI&V60_nGba*mdU7m{8eՀ_}(&FBܧ/pDzc}y A\xQmLQkӨ%/@0cվ9ro!6[咉=h]8ڒC2{p+R Îb DRf/NS2疢}1=JqjT=Vp,=sq7"EM=GQf!H˷,|"ߟӸC1 HSj3J\HJCѤAOqƖ[3Q>hL/{(jD%GBŏqGR tjtƱj-߿1?κQc\;Ը2됊!Iv,ҝCU逽XW':Uf0k7)9VӬjdFdo' ːemT A(zFM& OSn*TR#ؼqر[Z ї!b )Ip*j{#(݀N@,2vljnFIEtT"cVT[QkƃT+'H-@ 株Q ԟfLl`bM{;rA{nCGTCyȅjAZ˴ǮuЗ9A_,mC>M#ܔJNA>O5#D% x*J$Bַ몒409

uƨ,KX'$I A5Ub: "Yl:/ݪ kbV$ P,ξu&m%ė]0}c,Jo=[FQ4QT9mT+5F'wD8|jKZAK':i`LZKƁ1im%MH[ZhcJ %$Ƥ mPKkK/R[JJZZ0&m7QԖrR9ģi!֖xKmIk+ wVRVbjIkKuMmIk:zIuL״ 76Fpj#'$[uiIutjkģmDg^+\K9;٪ҭ+./` ]|%ZQF1M MY8tBwNͨlVp+v -Z)0E5ŶZ\sy҆A VOX\8r%O4p zJ̣27#&?f RFm?Ȳܿ{*G"tE3a<$C'4&/sBF|8OڮwPw332Sl_:vc=!:q}_[kwtD>6Fh#'A$IhwT;#d@_}gw?vOrĜ(z!.GO/d׾?T-'.1H_֣F 1O!5 r7:S QuztΥQ.]W !ʦ'RR(5_R*d (;B=n&{Y3sU6ˡ'EAޛ,l<7=ۥ Ǩ喜Eސp-k_kQ 3oUV͋g+ iTnX)SfH7A+(]ڰ_4i w$I-& rg)W$j#mLͷZBaB?Y1RmsJ2蝷Yz1)eZлն9Yo v ˛wQv_pK)E~8I~ύw$G{`GxEe7@F-x-<<}`EOZG<<_F "H$槨Ptz~Hj/yAΈ?ާ<L ÍUy l,'$ HV#1a62>4K~,3'ϳ>}(Xr43O_dᔏeǮ,-=,f 2a[we4j kѨd#곉Kt*?!M-0,UΡ,s~KqGr `%zUᗩpB8yLe~on~gw!_-Ta5@Ɉ-eF8HFYAݮaulkdɭIZ|_ |4[*)~dɶjUnWZզy٪~yI ]ej:f85dD͞vo}(h_u~  7w}OwXCta7OZ"~Z >Y o5Ruū햰ŮvfU._Q;ōq͟`Cc{ŃAF4 |@Qʤ_&x?!M*Qk^8d)-wF2K; *酊?!Mzuñk {fr}AmTZ鑯Y^%wV$C<ܥJ2rbsĢެPՊmCm'RYVkXeY.DNXwޥ ~LA"]֡[tK%Z^8%Rdnr%kӸ0"]aݨ _ 1>NιgQSéNzc4!dp1xA8ɔ?¡dyOl$B<2CMavRӋ^uM=F'i8\4L"sў@*ww^PUz Ql]:C @ CMv`DƀG!6~WqcA8c4U!'9ģh3ޑ%vA XtCxiiS44iQ!>i5zo>Tuו[&9QȦZi;2)kX],yאfOJ“#@f;!* <0Ɨw~F;0Söf= v19^w[*fx 3Qs|aaC e^>0ݩfXA0;pp#U=lkD#TzF'!K 1D x6νuU(y Ǩ[G1˜}c(勍@(v#бtm\U*V-:p˚R{rSQ4I 066l$KxMddxSi' _PVD8+d7ٶpf5 O#j[D3 |2жZɦ㍞YƿN\7KOt>i4FNu9MT{[0eM;QoMEKye)x}8gd- FU}v\l#ꯂ#@Afߊٚ^|Q'K/)+*7$h*Æ d[OrD2WʔO2V_5dy!7Ok30Wć3370*p򄲶+Q+sFySx EoALLxd0/{[ImhT)"DqFWӺg:)kVͪ G|3RP—_T{(wDY.stY {Q:Cӭl TIkYlEZBwz E.RS0Qسb$H]f!geH%,ʯ7PtSVX<ʀSfL_Qx$"~yKꆅU_&BϮl6u7NK~ZV7];KP(wyVӦ-tښWMiւO?hu"uz\ZK£QI7lSQW,SƬ~G +inYSiWSQCmFTzkC<؛Mg=M?1>1jKMX6jnE zf-H.Oͪrg&Ml%\\iʀmlV>EgeJ5d\s䱇c|jzm&x fzB:2*ny!{ոx vZѬDcCA$(Qq; rf(t. އP NI["3AdP-N3кX(/f5 $o5 ɱ)úѷ --|21*jO>c"6r& $C  j; {4c_FYiE<Izl#q@2 C+o?NW2ۍ%ڗ]0}cyJl=ZϵN)2a7hr/7|#JCɡ~Q^26leoKA/wYɲ<[ ]ͿeZr3 /Mл\E+,eM3tΨ-C]{BAq$r/4NҫIJkMX2j4hf?4Ҭ9O_a8폫?-ftLu;\(3LlopoȰN\^/7quQiw0륨Q/ 956I:n065=`YYsK7/M5$kC:\hzmEP?Tk`}7:+q{[ ;DӼ];Ȳ<{<]݊.XmJpC&ޅ|WwaYvx8)@7^qm;Tm\F+G8ģ˫2[sxT01 wxܥDM-r3^bs~9CW吿(.ONNOO/$3ރ|Of3Xߗaغ9SMu诈v׉^:\'uVo$T"YK6|Zz^#(oIj[މ/AEJo=Zo 3:UD8#9.K'1EuE=ԌI!nMOEyTdw.V#8ma Fx9e'$DpUs3'['“O*yѵ,+f[͹)t/B4ewLɮiT݌8n J]5p$V߂$5Х~#ӥX}K Ga߁!̔i.U%S)r{Lzc T BqZWU_ui C8y\}i;4SqB}GqeGGmhl+f:3ʿj<Jty1p#2ϫmZ=۰4y-S/0 ){u(;B==zliЭf!Wfy9Yw ͮbʿ7ʘTҪLWTx$hĞ9 m>dmkl{}on~seP"*0x Ė2&HFAݮaulkɍIZ|_ |4[*f%۪MV iQ٦~iYc e_l8v66,%(і֢6Ow߾}ӯ:?LCUZ;~O;L!:?iɋ,#kpg"jfcWۭ`Mmzͪ]#b5w`Vy~F|`JQAUU(8!fIed nًd(:@>"C1as̖(2^6Q4F*Lsm2֬Q 4.Ae,J?j 擐p7IL߯PFzH;X51QR}^l/A>&=tNI(pWFɳpQ1ߛWԔ8_];eG-Y>u;IAwxue}6z 4':2 vRށ|G}+<S_連7g0p[~(vsxꙋ7CPlpu N\4wtjv@~#|CEDGU=vݷk{ 7F]m8tda!yV ڬ[r(-> 3:ӉP͌ҡ-0zd/YdʛP=ȳ7an.&t`:2NLVDR'^—_*Wj1ߺ(Gmskk\aì1`nc.o2<%ՙe oh|k!>r ~-Utv,Aj8Y}ϻTNxWQ+}lL<@$9 LCNkӑ|LU3!úhd%+5Cҷ&^nM-U/G2]1EhWmKM©I[.PϛJghlh/ݪ kbF 7P,ξu&m%l#~7ڕKL}"?+Qtft_K;ºJN]WO=U OPvzy^̜kxYMr7L'byU&f!I JʢQp֩di$A)sN!$g:)ԟiq\ڸ@DovҲ3SsL7L] u cb*oqw5.};R?ڵܲQ۰)Ǯ09>!`أ> wˀ\c`=1>eNJ]VJ@{]WB7}¸`ߟw}KܪFcנϭ=0I#f^M,5c~يHWsJXV˸q@XvXV5|Q 0: uL\52 >S Ox=,Z !tLyQ}SMϠ]RӸ)zD` XBRmt J9.$I?50d&spAuMLQ1ODST ? ,e)IKZ.섢wGS9J[pL&c22Lt "x m J"< dCşvsC<؛w̳KY56LM mTs ngF=}JTB@^QYKEHNL*N[Nm6Î}u'D>h[j3xR3gp*0j3rHx[%6N?uiVG&\Pg8JT航B?"9۽+5ɆJ}"NM{cQiSD#Ӷbi#'88*i2W ˔MWD_$pB鷯6 rxwVV~f{rMy,"8bf(vg1'.AҦu wȺ _aȺQ)< G8$kzH}vD֕sȺ*fކ 2#or; MWnjJ^SjDDtV KMmMp-PPR=vL)ϮɄL20 }m5eJ@Ѩ(xceݯEfPG%\,偉-[(@(*~(sDPCa( 2y:Rfqnu J3r*NpyhuzĂNծYAZtHwRŪY%:XFElG `que_H).bgSä/̹۠$xӐ)bxEe5 /qGvJй!mH L]f!gq  <;͉&*9"diOC֍Gՠg|P,sS3s"X,g FN vtF_#S-7%R7ѷQĖNL c륨#v6F\| Q^6PdE -0,M6nbm|VZz#mG|6!z}Ow\qrnP..WrQ*Eir_mȨT,="GJ.\JZ/[֚e7vjێ>j95}x%pL7:Nw]#B|z8s,u+aTNpSq''ԻVqGײtZtWI<)S!Kkwdf&l0M QDfx=eR`>!iH7;W,$Ԫ󗪴3u2dz[.^KQW^xr+m]lQ7p5.YnUmZ1bF:ecg:hoԶDC_vvLPz΅'#劢oo_JG!HITL~Q;ecYqY_=&ن˼"ـ.˭7td (eˬm\8 | rf2h?iP}+ w [>Il=~X^ހmn)K6i*-u0aiJ NA~laYC?;;CihnLL@ Ԭ> SCMێC5YZ%ŋG䱊咲MBO S&w-0eEiPP, ZLߍB63bk)=}kr=&_KGIjHRKBnUV*}v7зbe-fRCWw2O\k3 B4(jmeGGk#VrALP _nɇdt'tRb[l$CyeddHq6nqJ&f±Ԗ$Cʷ: -BaP9Rf/J{8 d(&M$C'I}%6R 5Q˥J.9v ]h^:HkhƘGF(aؗ-/ RT(CG%B K-u{8CR1hRJqQ, l%PR45dy^n:V59c<{ 4j/).h[U[{T HjO9<:!VyՑ&lf9kTm'lRQ]5J|6 SF Ȉ˜Ғ*0bhԬQ (;\Qy ںƧFQR`:?asN|{1$%&St1&c@%B<2 XXؒ gN!}bHYy妤FjhdD<ܢAai&8 aLl(1H-Ԗ/6haU!ngE$'8ԳEZ. §S[˩4.c if7r7E۟U6Rm6F~Eqn{QJǍ"w8ȍ"l$E*nox}0kf1`؛o,p2}8#G<<}2{D2**21T3e AuMQq'qTB tlug(O5q.v%Cv44<#!UCÎ ْ򂱷f1nSFcg\ւ7^th^c-bz1V?O^')N_(iUhuG 6 U{s*U`+k{t<׮rLgtXfyAM*%bNeUzKލ`i$Uk ľKJ0v?:ũOև, '1hvº@^Qe<{ $\`ELtk7k&-LQ. =qbm!KMX$D!ˤZ*RD Z7ΊQ!oQDg|vUᶂ4{58W:]+Գ;|˄|raE :uMWLQI"ؒf>-B\ƀR& ,TPm[,d ,Y\۷!h20^qhnMʲՆpO!'/!O~O6 /b^]=ng7m'{Zc%5 %Vg1r_nP{ o ~W7꬈?k  ǢʣyϚ#`4 NMm "J+ţ8TPCa(sEg2Q>oagOSF,[* n}/Q]m,%[ [琟X(nC<8(AnJ˄ zTp)hMMdb.7 ܽ=+#x uZ Szƿʭ[yҘ]q0pLI}o5ȱ(úy*ѫ(^B;''K&^n ʱb;{"Ǟ6r&dC$C smaPnx~Vv&nK70NuJȎ^:i{?fzb.1|||%.mvf)/&}C>>4!ɑjD!ũ%cOlovjY6pe:5,Ɨ6}g SR%-ӪssݖIdKJ]ft=,NTfE)QBNK⥪X_,OwTP8w_MdX |\VmVУvG (c43=eSܴxO&6!7H;AkdP.NOŅ$]wuQ!/̫}u2M7Z\+wq}]ԅj]hz)pic 6rBMl ͒h>dh_ynlz!1g^k>' ztz4'rfGAo?#QHujtN{;hKlcb{Y~:+p 29N)놓y[kMv v{Np35 $uJ$5AS&bl˓Lcxc:j%ӟO{A>yeo Z%}ofŧNMIrE *X5>?,Lc֯DLR fI]k^: ofl5$]>zn(I6/sx_1wOHlX^!**{#ԣ66a]nF=T ʴ/_Y^[+NYX[| ~jh 9?ΡXS+h}~oD"ģI;Ѵ f g-.eܫ~i!MںҖ%~)aYPgwpduFXg q:9WE U / Ax GP7˜\ Îܞ9ޡh _MF_G!]3T4*Ơ'~Pܪ|3_Otgqi|:"ԫ]ma(MUBѤq]I=W(HoPG9ģI1gH1!e`pmo[h3[QTehU[{UQ[A*^EǙM˿lFRcK~ۋ]j EcC/*~CLUQDӚ](,k8N>;2r-usq:%|E[!i~toOH![;V,:?s &Hp:j*t߽=[ԷߟW}:qMr x2Ta+kߍ'ׁYr"<GS{h+ vi'nW`\NB_b 6DfsfϢ?ч=OO|JpDO ˇS:vUi$ UDplzU:uԞ\W[z{E=U%N5Ӭsf&p?qB_w&*6,B.3)4db=LЁ.3O+'A0pD!ާ3d#cߐkfȭR&F7Kgo%$ׁAN\RPBFzlF(E6-I>@o_V٦n }D ʤ3 q>{6tEXe{.{ 3ޑH Wэ sJ W.Ir{(Sq;۰ /g$zGRQ{ Vǀ~LܦEw Lԯ OkSyD`yRЍK \Cg"Y_܏[ii ԱJy6ۃXDk_>::t,U׍=W]G7"7W;UdWb ,P*A{:Р;M9h,l& `¤0`&LŎGgc)Nyt|;ر<,pr_PQs"7j/OŧID6^N4T؍ B>̕j tDv\t٥J}r^[d V9(%iැ_b-ȿ5O~|gENq"%Vc@k+ uEbj Vt+U{]l_kz0*|SCQ5 =x@#3hJ͒4s nG}*#cQTYzGlXBlͱÆUڐK8 FKJkSۍ(sC<QT9%;Ty=}PO8Ye]Bbןjr |j$edӰۼMh;˄ƫ&nve˅s0BMߧv.Ԟ<0MD;[O{T.] hU-t]`a jmE4sg9|-X[Zj:V)~0jU1 EhP`8J,BV?"&Sk@{}]=9>@Y=BSh_'/ P泋 P..rsV3!:8c3vG KmLK-˕_YLsMh++wnD8--U-tw]uXڅ0PuuHUeDcC=pyU0wp;1 ,k,mhpe3!TZtne7iωX o2߁ WҸ!k.Jv9 xae9˔5Quy@;%]NAꏒpR!)g!˟LTwPF1 K9#3| QM|D {+vCVO4$3OOB>95]XawF4&DEpP;%aGGgqC<{?j޶K%>c/)M}dϿ6h&ӐOk @lNl@0b9w8Yzc ,wL"NAZ3dtt8\(CG ' `E?>oY|j5>h܉bwq8CCU-t?N% CzEUS8!,NAMR'F_fBtX%:#TߜTn>g[׿y+#<גDgC<=^KRiYr޺6m@5}0ݜW (R7,m)dNIho %:$Tk5b*.:ռu5,jWny4LO`#='j*f8YEPq㐥&-E9x[I<$*L+岊U3{B)THY.Z_ |#&t\|HdF)b} p Y]V+q4X.SEm؏_A~\SAO&]|+#TPkqFG|.' KČ.J&Ex z _5q\,"gi޳rr?Դ|T2k_uK&2G KcT!irOoPgg!զO殺K@ej9A H-ydJ%NZr ?r B)JABr*KD *@cIbA,nFNˮD d%O-DqǮ *4 Q %BLd^z93N;iF,f ˧ժ{jnC-#fx|Y}Elgc.dcuzEެl ;~ r5P+-[yG݃q_2Pq{!= # ȨAfx.BVﾘXFB5$d}[faXk(<ۏNT>~'q\q(<>~F'!2[d8VLS>Xz6\.YuqwYAN&ZK/CVjTNu _y_Ek s,+#UUmTEk5!\\y\dzVmRWIJ6uJkrrXc(:B=wͨZ뷝v|fG=|M=&y]vӠ3Gv#Z_/ Pi66͵,f>Y ?R!Ti|/( a߬7=YjEk\h& Kކrog'jRD*)DGX 0rŵ.xzģ!K*; M2_l7;hm]/3v?@ą( | Y}~êQdu,\  M9IG1ȉhvEȝsTs ۫+;E7N)b-x! & K}۬[%Ek9_RWV se^=Gv&m/7o8w㬿u' Aer XuMխJަ pԡt1ˣEȋalC؆]) 3~H| Fm=ˊYVT.73}ɲ'k;eSb1+Z#&GoD8='O}68αjAx}&Z5ԃPz bXcFs u#YnEi~,muX$.A^@]ރ|OYU]Ugf\1G6H/Z0;Bb,?ҍR.= 742OaȯPtz< n v B-[;+5LCRA^|Q}e\P`K~DpXWΚc!&7w ~f_ҔQ30h&"w \6P~F.3a\6T~xJfYz5W=SA^|IJ(xկE\bu.m),^Su}bR A6t5N {mJxKJ6wZ,wD#&J^t xC]sx]+(b^,7)G%1ނ,u~P\5YmȷUs9pDY"tyE}fl ݬϥ=qrklchBD$d儘 Qq!KݠcdI֚O6eXp(PԴ duӺ\CR SpɆ&694d}- ~{<d C4GQ">GfjUw*)j;u d͖hDdVbCō)gR[;\|xڹ5+y9>HŇ0ͲVМBװ79sҶGvL^0~`/@"R ߕ!{')A!i^ߞVJ(u zr,Oډ7 k \2jt2ZP؍ud(pUR@U*:pЭ`U,ߒtwظ0!C*a0HJ!Pq;G!U֌g|RB[.2a+డNBVwRGd29rK SW^&yUx]K7V[C<3/=(+<O?9J58|YPSֹCak ::SXkScQ贒(m0CxES  ӷo8ALdqp;Y2DGZԦf =%ڡ Yc[ 흸I,J~۰?Ypʤ҈2OSRev|j6!}H;P B}GvE|gWQteO&C F.xe's»*JaYq<]#Bf<#&9`rwX\TVڙ,lD͊M!/c ų9'Ph]0:•_h " ,5k;ڿVbۿEGg{{okg. <YncuwEǻ\* d)G]5:vD.%Ih(ph+HiP餡:ɭF KjT\ dD(~hᡆ\>5PMI2w;ɓ),9< YA.fT1rTӱ8SqUr~i3q3!ut )Ph?'WݙXHŠ3At8*m?p>7Dg?yM{= 4,jWѾL, ]]f!˻MW瀹'J(*Y.^/2p%KRsN \1!Ewlnh3L'pO Hq' F^?5kzpXE2B}(cz|Y 'aƄO!?UV .X<J5+9D1j gC ~~':G9c{=cսjf'B'ʹwG!%Tv8yNZeC *So#[{ɐABmi]P?;+Ĝ(|| YjfE,5>?^xzl'Tp WTB8V{ҋ b6A[IbQQP4pԽas_1,*RycI{c!CDg/xzl+TN0ae<mEՊɬ5Vi!ϳ*}xŃ=;0.pQ_BVEnxmg--91mHo@V}1LsC<=6L*&p aNO{WwH+,[7㫈YJ݆7] 822 EwG?̅pr0V5 iz~V*~on(47]9@ @V|1ZYkVɠWYCx MؗD̟B*~W&+Q9xb!]7U;Rˈ?K"w1yX1~>Ur?{|1OCM\Jy5܇DJ{oR=g_f.ckF Nߓou{ ].-ϣ^ս`":Y)s ro&3dHw74cJvZ_34\G 'a7Jp+xfK۔W`#V(ب i%_A>Kf*.| YeJ%_ m(`8NCv踏cɗr@oW@{զZV_5(qi#'"j۵-2rÔG,_tE#X5ʍRmS =EW$py׀7!@GrTȣ~1Fso;ՆU)=ۮ7nx]%}eʤ/?pX ̛N B0f -KO<]Y,ܙ_ޜb7_//25vAbEٺ~0r3?&o8ȰNtlE lImg}RO )tw}(ŝ6FXv1ݺQ2ww%%J&J;̠Z7pG>=}V w㏜!kgw?Z9۵FQ:U٨fGaPHػn_;Թ0 5?*knwCb̊ o[%V \I+C) |ߴaW*:Mf\ /szϫK'6v/6Wfˉuzf:tgަضxLby yY ?AҶ%nOa $EvOB>>xt-g |.Ӑ; Yj E_fRYp7im,fJo.iuUm  D__Gۗ24_G4rw 1}qb_襨Ł6FxqWCo$mn һ>+#}[id5V}?$}tV\AzǍ!U*jkv}7v+EigD=n9,{ϲ'a;,{ gޚQdJ,IA9%<2T]wVbvn8kׄju<I!^ ϣG h[TYeԶv8=d׆gnt+/ƞXί,&tǷsZγeŠC._7 ʅ1G)W' Z] Ü2|٪EAoJ *%$ U-YgNLe ?'rGA8yH~X3 Y*WU$8˩R3JǕyqPiL|B>+KXtµ|q:r]TsEȋ2ˉ ։;mGۿ,-_-rux˵1ꅷ\Rgz$Kse{`P-k`G{kc/ݸOnhzeKLv:?vY]lCbxItzkawh }z:Y+W,{FyPrmPE*dzp1uպ5-߳9A8gvé ǁ'4_ n*n x 5 n>H<Ӑ5j#Be3^zę\n~vV}Ndf!K9$]rPAjUKafv.r]}>TsL}2ioO|ڿ,_->u|1G9m&mkTyd}>_qܞZ?b;q:c珴^+q_ C{ήY<{?[>nb}鿆zG^:C׶T8IQ<FM^*; ,B' Ow%MsGG Y*ނ,4ip/u:IDnCH_A I9,a Ba8]jf~zv>~QWp' +2l_?* ĕZĶJDA6Fi#'e$I¼XgTu ->+[ }FzLxz']^q(/Z.x"W[OE[4Q(/ݨ1_+A09'=~zŪYnD!/+76+,+&w@p2!q"" S:<]ￋ#Գz-XE)(fi6ϊ2KH^~+H@xJmο-5 C8UrD7nR$>ZUóޛ,l(o8{6ǔGa:˫5E oAV?3EU+u?^~XMw5NC;%XM cbhшR|K,TUԁ)0 ʎPQFbR|p"L 2h%oILw`Ao%/=ʎPʮ*{fKvӧ3zf=Reb\D$Y6*Ŧ.2GXb;‹/@'O$o\P ' O(ሮ~/Fx_C_o_A 3B[}AUYjF%u |Gq_֌eYW#B}>tMarz(;A96uk7fm`˟o~c8ef(R1EӼ c,T@!tWl.?-7Û 6޾ޣmVeBN)3}6#1z D:w75'\-s鷍ʹpkwP;Gv` P83?ŎKO)?ƪkzn=byr{˦{iezB=ƽbߙ8e3(zV jtjtIQ2&}l'sP2P-MZٽAs = ADꬋN@'Cɞ{F\_2Hߎv*%1H7:vtlkrIZ|_ 2|4[*f%ÓC펯V]k'/ǟdd) aA 1Z2]}Q{:?LCY;~O_=a Q@=+/HeW6ݒcZ_tlXe_{Bhbdžqso/b8nz\6{TnU:bPn }~W]>łS>0I,\<w0/B*hb" h BnƕnmYӼ":1 ߕrP!< Yj|Id ( ^FtL,ٵ;!# !bKͰj5~O`;}`v+TBb# 7<Yjk4U!'9ģh3_d%vUF|O8 |OC>m<ؕЗk|Kg!_W༞f6͌=4H1R.A^n{﩯{c}2po9`p>@=>h-O-u.ո.&aj{ޭNՈ:NįZP}PmqGU^utHje[Z5<9fɤӈv +n4Xɤ㇕ʦh8ou\:QZm_'b|4j;N ,fkbtxԒFlN ;6[oGQj&s{MD8 $v2ao&>{o3T. g=$r€eI1z+FƧ.zIď_@VV84P +o6|+?U VV'`+WkȚ͝e UMm8>FfUVQL 4IP&\E7+h\<$ӶzEUpmEVւ0?|y G 8GA!U1N,)Y jU)Zn٨rmX^ X1]X5vt֫WO'Ut7:FyձMݶvgA<>3J܁(X9+܃!ՖêtH{8ģ*86P[aNE!V0x3h¯f\&ѱK yYJ];)USquRdz/ArS\>SJj.Yky7?Ȑ(J4|m'Df/ XƮjݳ}cMꢶ okDgC<=5**5!WDkJk*Vb{c}UuN'TmmTmMRXR<)U^bF.a%So %ϧ/ngyL[[M11鵞VX 1Px-ǡS"jyvɈeLd*V1X[ϵN).CGП( qGrڷ]:]h>aG>s'/BdDŅ9`Y&5! nWaҊGˁ/HZW$PvzLnIpV3̋7'~&u]j\ۮ]ceR }jUNq6o?㜛hTxp 6tL8yjsG[ʌES2}1bIӬ[u+t j),jnt?a ґDZN?t-tib8#AO(a藎M/P8ģI%҃ nƖt[+ԖZ[l#CfM]j E6zJ.S. [D{D7zeK{v v7arVҒC F9M5F9#1bb{@F%!fͥtB+,-9&]y ghaYĉ1LGxqb$8ģh4·4UXLb<0}̉0eH|y$"EƗcek6@<`H HCŌqxFqC<ft~o:$6iZx oL<2gG/q!Fxw(U=lk) [t:j!h1 7QPFBwXv(Tl@=nIrb8 Lt&n)ЏIz)$vc>NTP}P^rwN{Գn_o`|>7lnaٽFaJD6<ڒW 7jYH,8RqC<6%09v7nFI*gK&׏%Y\D+8!){c+غc Ԡ_PzA T(vh 3hy!Cڴ5{.N[E_a#h) ~ pHXS8ģ^I W 7Lȸf>H(!AW0* /g$q =䮐:َѩ{Fpw,ivmͬmV5a6' fTdbMs|C ZN7φOjpf\62Q3T0e 7DiC(Juèy\yUz7h.p-s3=sСESlϨdœhO+)]B0ןi$;bx օϪ`L 'čcA`aVg'~_gU6(pȮ\XUWWƅU.W7+uZD=uwఱA',RrZ֌g;Nkj;SB7PZ^&[5wFao:SCMTNK}|R\'oO^\V)60)Ij xo!T TPN ⦚ކԲ-лeJm;JQΉI3p% jb n%| 5GM}v*5k. %ZQ_B~\gmNjD3+{׶BF͢44uEbIg?v yai ,(RgϿu:p #`צkҚZa,dP 0AT9UF]Ѥ)4D.Ց[r:e'lMM-/= ,5 Pm1INY n0=3>&ԯk;ND+Ik;bXeX'.^5swqߟx5T;;_dƨYﴑKX'$$[J'h8OL6ݗn_vYe]Fv]Gu|6Elc`H%D;u.#eq5ˡB-[l]2a~7DhjwwLǬbrA>P}CN4!ɱjۗO>Hg"H)EJUW>{y!L!AV|'I ua\A댋-hF`ׅkqz_&K,w:.RmKu D;! C#K`3x'`FxymCR<PӔ€>PC >[y>XjK@3y~qy*0x ~BRf/:ȸ)~ T\5S੄n{m&Z72f8j9MHcx>1;RiHЈ}?G% 9*x4Dn{Q-GTN!B*E@E$R1hRokFZAtM'];6R|NcNJMMtD3HhH=9Oo3ğd Ni8!6lKt.cyU>ħYvSEg;6214c)2я0 B# CéΑ!HF@%B<:y<fgMFWm~f~~K¶)|mѝPBxRǭ%5WUѿ"+",2ֹ}(ݺ~Ma7cOVN~AW³Q͌%p(͊+jN> iV;~e3-jD* ,@.ވ3" (ʟNC֦7&]9W cȏO4F&S3ϔy|lA.Bf'o7蒓|k3OAڽ&5 |^c/~na4d!F\= 8yFK(AȺ.NJE$D#"쒢_3=#/_o{kRkWLmZ53tD-zD-UXHmy=M[^ u"0,7 `}Mn@Z+g,7Q!vyl?5>=ig?y5ǀ\_#C]_ uWkZNrh}}GCikOrD1>wi.>4ᐬ>U:2vDlWIX2 q[.' gd i,[C9)T+,d%W\`FŵnA勉oX(3|X٬ڵWQO@fמY7k//iϡ;rw4)[(|j *~Cψ* 'EG}NYDQ,3́Aj+cɮ r35uo#Xk,te ) SV0[`IDUL!LwWc}/z"j]<; zߔJC<24S3 ,57%h#!v"BUX895el.W,3|2-qPAG2T9z!I SB1V]c&RvC>.Z5F_c&2׳7|&GJ51h">6r {pPzd3OX*ֲge\QtjS'׊IX%~kC#L;A{~[l^_vA+qhk=n8c.Z !ňx$Ǥt.~Qb\ZjM QFGpCױV}=&& TFu:d%u6{^=8(">iTmOrQqgYr x4ieH85Br7%h#Es电1ȲT.7SrycR/H\PAGS\aՠOLs3yE WMs2\f#$>0KQL^Vm-0<Ѣ#19B?+3}ih7?3.ȟVSSk$l4zz!>'GE;i o1~[lw]0}c~d֣1&9&9β'y#@p KH5:<IHT(_toBJ^oɊ&t2ȐsՁ<>nOQZk X5$_ހ|C+_t}n %NK_(~l?2ұ/&=Y?!]{i4(cCV?r83UȲB.7]X,e"t"NTJm^0CԤkUsjuug B+*s.qdX'䷹ܭw5QWhw륨ÕQ/\ p6ֵwO*<)KSU[|\z1g^+\K9[nwACbxtXj=Zj/ v7+%JCnNbT|* }aGZJ{Z\IW6+sF' +(=[Ldʱܺis0x|Vhu#L ´Rl:syL/[S4FCee}\\_naa3`FxyNFʛ2Y"ys5d`PvOh";cz7>/p"\/dSNx]jL͆Y[g 7+>{'\& r n`ѫ޳۬~{)XporZ"Xr:YDÆUnu'۔>q" c_}(N{E\>eS>|_Li5xJĄגTjk-SaA±Ԗᑒ߆*!_-Ta5@lKѿ;vJ"vKq2n=i]eU5*7fŤwT_4*Gޔ7 ިt;*^R0Z?7*ZªTkp)4W7JfˮjިUlS㿲W]jZoUro0,]mlOp6,wk2~)Y6# ۣZ0s~{le}]9YWaΎScoin/tests/0000755000176200001440000000000014127575525012361 5ustar liggesuserscoin/tests/regtest_correlation.Rout.save0000644000176200001440000001066713016767030020247 0ustar liggesusers R Under development (unstable) (2016-11-01 r71616) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ### Regression tests for the correlation problem, i.e., > ### testing the independence of two numeric variables > ### 'x' and 'y' (possibly blocked) > > set.seed(290875) > library("coin") Loading required package: survival > isequal <- coin:::isequal > options(useFancyQuotes = FALSE) > > ### generate data > dat <- data.frame(x = rnorm(100), y = rnorm(100), block = gl(10, 10)) > > ### not really the same, T = (rank(x) - rank(y))^2 is used here > cor.test(~ x + y, data = dat, method = "spearman")$p.value [1] 0.8474266 > cor.test(~ x + y, data = dat, alternative = "less", method = "spearman")$p.value [1] 0.5763332 > cor.test(~ x + y, data = dat, alternative = "greater", method = "spearman")$p.value [1] 0.4237133 > > ### without blocks > pvalue(spearman_test(y ~ x, data = dat)) [1] 0.846517 > pvalue(spearman_test(x ~ y, data = dat)) [1] 0.846517 > pvalue(spearman_test( ~ y + x, data = dat)) [1] 0.846517 > pvalue(spearman_test( ~ x + y, data = dat)) [1] 0.846517 > > pvalue(fisyat_test(y ~ x, data = dat)) [1] 0.9155477 > pvalue(fisyat_test(x ~ y, data = dat)) [1] 0.9155477 > pvalue(fisyat_test( ~ y + x, data = dat)) [1] 0.9155477 > pvalue(fisyat_test( ~ x + y, data = dat)) [1] 0.9155477 > > pvalue(quadrant_test(y ~ x, data = dat)) [1] 0.6906339 > pvalue(quadrant_test(x ~ y, data = dat)) [1] 0.6906339 > pvalue(quadrant_test( ~ y + x, data = dat)) [1] 0.6906339 > pvalue(quadrant_test( ~ x + y, data = dat)) [1] 0.6906339 > > pvalue(koziol_test(y ~ x, data = dat)) [1] 0.7825737 > pvalue(koziol_test(x ~ y, data = dat)) [1] 0.7825737 > pvalue(koziol_test( ~ y + x, data = dat)) [1] 0.7825737 > pvalue(koziol_test( ~ x + y, data = dat)) [1] 0.7825737 > > ### with blocks > pvalue(spearman_test(y ~ x | block, data = dat)) [1] 0.8901013 > pvalue(spearman_test(x ~ y | block, data = dat)) [1] 0.8901013 > pvalue(spearman_test( ~ y + x | block, data = dat)) [1] 0.8901013 > pvalue(spearman_test( ~ x + y | block, data = dat)) [1] 0.8901013 > > pvalue(fisyat_test(y ~ x | block, data = dat)) [1] 0.9061762 > pvalue(fisyat_test(x ~ y | block, data = dat)) [1] 0.9061762 > pvalue(fisyat_test( ~ y + x | block, data = dat)) [1] 0.9061762 > pvalue(fisyat_test( ~ x + y | block, data = dat)) [1] 0.9061762 > > pvalue(quadrant_test(y ~ x | block, data = dat)) [1] 0.7489036 > pvalue(quadrant_test(x ~ y | block, data = dat)) [1] 0.7489036 > pvalue(quadrant_test( ~ y + x | block, data = dat)) [1] 0.7489036 > pvalue(quadrant_test( ~ x + y | block, data = dat)) [1] 0.7489036 > > pvalue(koziol_test(y ~ x | block, data = dat)) [1] 0.8408785 > pvalue(koziol_test(x ~ y | block, data = dat)) [1] 0.8408785 > pvalue(koziol_test( ~ y + x | block, data = dat)) [1] 0.8408785 > pvalue(koziol_test( ~ x + y | block, data = dat)) [1] 0.8408785 > > ### sanity checks, those should be errors > dat <- data.frame(x = gl(2, 50), y = rnorm(100), block = rnorm(100)) > > try(spearman_test(y ~ x, data = dat)) Error in check(object) : 'object' does not represent a univariate correlation problem > try(spearman_test(y ~ x | block, data = dat)) Error in .local(.Object, ...) : 'block' is not a factor > > try(fisyat_test(y ~ x, data = dat)) Error in check(object) : 'object' does not represent a univariate correlation problem > try(fisyat_test(y ~ x | block, data = dat)) Error in .local(.Object, ...) : 'block' is not a factor > > try(quadrant_test(y ~ x, data = dat)) Error in check(object) : 'object' does not represent a univariate correlation problem > try(quadrant_test(y ~ x | block, data = dat)) Error in .local(.Object, ...) : 'block' is not a factor > > try(koziol_test(y ~ x, data = dat)) Error in check(object) : 'object' does not represent a univariate correlation problem > try(koziol_test(y ~ x | block, data = dat)) Error in .local(.Object, ...) : 'block' is not a factor > > proc.time() user system elapsed 1.07 0.07 1.14 coin/tests/AIDS.rda0000644000176200001440000000040412116365565013564 0ustar liggesusers]9@Em4i8"@^YB$ HB Ųp$QŤo*~Z߽w)RE )<,QAWOd޾!І,=4.7 LOtĚ*O>!r*O{uf5{Z5% P7$sdf r]{+c!b34 -s ### Regression tests for the distribution functions > > suppressWarnings(RNGversion("3.5.2")) > set.seed(290875) > library("coin") Loading required package: survival > isequal <- coin:::isequal > options(useFancyQuotes = FALSE) > > > ### generate independent two-sample data > dta <- data.frame(y = rnorm(20), x = gl(2, 10), b = factor(rep(1:4, 5)), + w = rep(1:3, length = 20)) > dta$y5 <- round(dta$y, 5) > dta$y3 <- round(dta$y, 3) > > ### generate paired two-sample data > dta2 <- data.frame(y = as.vector(rbind(abs(dta$y) * (dta$y >= 0), + abs(dta$y) * (dta$y < 0))), + x = factor(rep(0:1, length(dta$y)), + labels = c("pos", "neg")), + b = gl(length(dta$y), 2)) > dta2$y5 <- round(dta2$y, 5) > dta2$y3 <- round(dta2$y, 3) > > > ### check 'algorithm = "auto"' > > ### scores that can't be mapped into integers > > ### two-sample with block > try(independence_test(y ~ x | b, data = dta, + distribution = exact(algo = "auto"))) Error in vdW_split_up_2sample(object) : cannot compute exact p-values with blocks > > try(independence_test(y ~ x | b, data = dta, + distribution = exact(algo = "shift"))) Error in .local(object, ...) : cannot compute exact distribution with real-valued scores > > try(independence_test(y ~ x | b, data = dta, + distribution = exact(algo = "split-up"))) Error in vdW_split_up_2sample(object) : cannot compute exact p-values with blocks > > ### two-sample without block > it <- independence_test(y ~ x, data = dta, + distribution = exact(algo = "auto")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (van de Wiel Split-Up Algorithm)" > > try(independence_test(y ~ x, data = dta, + distribution = exact(algo = "shift"))) Error in .local(object, ...) : cannot compute exact distribution with real-valued scores > > it <- independence_test(y ~ x, data = dta, + distribution = exact(algo = "split-up")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (van de Wiel Split-Up Algorithm)" > pvalue(it) [1] 0.9417069 > midpvalue(it) [1] NA > pvalue_interval(it) [1] NA > > ### paired two-sample > try(symmetry_test(y ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "auto"))) Error in .local(object, ...) : cannot compute exact distribution with real-valued scores > > try(symmetry_test(y ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "shift"))) Error in .local(object, ...) : cannot compute exact distribution with real-valued scores > > try(symmetry_test(y ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "split-up"))) Error in .local(object, ...) : split-up algorithm not implemented for paired samples > > ### mapped into integers using 'fact' > > ### two-sample with block > it <- independence_test(y5 ~ x | b, data = dta, + distribution = exact(algo = "auto", fact = 1e5)) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > > it <- independence_test(y5 ~ x | b, data = dta, + distribution = exact(algo = "shift", fact = 1e5)) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > pvalue(it) [1] 0.9247 > midpvalue(it) [1] 0.92465 > pvalue_interval(it) p_0 p_1 0.9246 0.9247 > s <- sample(support(it), 5) > pvalue(it@distribution, s) [1] 0.9608 0.1270 0.0178 0.3248 0.4035 > midpvalue(it@distribution, s) [1] 0.96075 0.12695 0.01775 0.32475 0.40345 > pvalue_interval(it@distribution, s) [,1] [,2] [,3] [,4] [,5] p_0 0.9607 0.1269 0.0177 0.3247 0.4034 p_1 0.9608 0.1270 0.0178 0.3248 0.4035 > > try(independence_test(y5 ~ x | b, data = dta, + distribution = exact(algo = "split-up"))) Error in vdW_split_up_2sample(object) : cannot compute exact p-values with blocks > > ### two-sample without block > it <- independence_test(y5 ~ x, data = dta, + distribution = exact(algo = "auto", fact = 1e5)) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > > it <- independence_test(y5 ~ x, data = dta, + distribution = exact(algo = "shift", fact = 1e5)) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > pvalue(it) [1] 0.9417177 > midpvalue(it) [1] 0.9417069 > pvalue_interval(it) p_0 p_1 0.9416961 0.9417177 > s <- sample(support(it), 5) > pvalue(it@distribution, s) [1] 0.29646669 0.07164043 0.29003659 0.11804759 0.92572907 > midpvalue(it@distribution, s) [1] 0.29646128 0.07163502 0.29003118 0.11804217 0.92572366 > pvalue_interval(it@distribution, s) [,1] [,2] [,3] [,4] [,5] p_0 0.2964559 0.07162961 0.2900258 0.1180368 0.9257182 p_1 0.2964667 0.07164043 0.2900366 0.1180476 0.9257291 > > it <- independence_test(y5 ~ x, data = dta, + distribution = exact(algo = "split-up")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (van de Wiel Split-Up Algorithm)" > pvalue(it) [1] 0.9417177 > midpvalue(it) [1] NA > pvalue_interval(it) [1] NA > pvalue(it@distribution, s) [1] 0.29646669 0.07164043 0.29003659 0.11804759 0.92572907 > midpvalue(it@distribution, s) [1] NA > pvalue_interval(it@distribution, s) [1] NA > > ### paired two-sample > st <- symmetry_test(y5 ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "auto", fact = 1e5)) > st@distribution@name [1] "Exact Distribution for Dependent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > > st <- symmetry_test(y5 ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "shift", fact = 1e5)) > st@distribution@name [1] "Exact Distribution for Dependent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > pvalue(st) [1] 0.8828659 > midpvalue(st) [1] 0.882863 > pvalue_interval(st) p_0 p_1 0.8828602 0.8828659 > s <- sample(support(st), 5) > pvalue(st@distribution, s) [1] 0.1002541 0.9401989 0.6883831 0.9741554 0.7955475 > midpvalue(st@distribution, s) [1] 0.1002531 0.9401960 0.6883802 0.9741545 0.7955465 > pvalue_interval(st@distribution, s) [,1] [,2] [,3] [,4] [,5] p_0 0.1002522 0.9401932 0.6883774 0.9741535 0.7955456 p_1 0.1002541 0.9401989 0.6883831 0.9741554 0.7955475 > > try(symmetry_test(y5 ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "split-up"))) Error in .local(object, ...) : split-up algorithm not implemented for paired samples > > ### automatically mapped into integers > > ### two-sample with block > it <- independence_test(y3 ~ x | b, data = dta, + distribution = exact(algo = "auto")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > > it <- independence_test(y3 ~ x | b, data = dta, + distribution = exact(algo = "shift")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > pvalue(it) [1] 0.9249 > midpvalue(it) [1] 0.92475 > pvalue_interval(it) p_0 p_1 0.9246 0.9249 > s <- sample(support(it), 5) > pvalue(it@distribution, s) [1] 0.9362 0.2810 0.3439 0.1093 0.6951 > midpvalue(it@distribution, s) [1] 0.93605 0.28095 0.34385 0.10925 0.69500 > pvalue_interval(it@distribution, s) [,1] [,2] [,3] [,4] [,5] p_0 0.9359 0.2809 0.3438 0.1092 0.6949 p_1 0.9362 0.2810 0.3439 0.1093 0.6951 > > try(independence_test(y3 ~ x | b, data = dta, + distribution = exact(algo = "split-up"))) Error in vdW_split_up_2sample(object) : cannot compute exact p-values with blocks > > ### two-sample without block > it <- independence_test(y3 ~ x, data = dta, + distribution = exact(algo = "auto")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > > it <- independence_test(y3 ~ x, data = dta, + distribution = exact(algo = "shift")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > pvalue(it) [1] 0.9419451 > midpvalue(it) [1] 0.941826 > pvalue_interval(it) p_0 p_1 0.9417069 0.9419451 > s <- sample(support(it), 5) > pvalue(it@distribution, s) [1] 0.95437225 0.02408582 0.32436294 0.03146853 0.01959341 > midpvalue(it@distribution, s) [1] 0.95420988 0.02407500 0.32426011 0.03144688 0.01957176 > pvalue_interval(it@distribution, s) [,1] [,2] [,3] [,4] [,5] p_0 0.9540475 0.02406417 0.3241573 0.03142523 0.01955011 p_1 0.9543723 0.02408582 0.3243629 0.03146853 0.01959341 > > it <- independence_test(y3 ~ x, data = dta, + distribution = exact(algo = "split-up")) > it@distribution@name [1] "Exact Distribution for Independent Two-Sample Tests (van de Wiel Split-Up Algorithm)" > pvalue(it) [1] 0.9419451 > midpvalue(it) [1] NA > pvalue_interval(it) [1] NA > pvalue(it@distribution, s) [1] 0.95437225 0.02408582 0.32436294 0.03146853 0.01959341 > midpvalue(it@distribution, s) [1] NA > pvalue_interval(it@distribution, s) [1] NA > > ### paired two-sample > st <- symmetry_test(y3 ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "auto")) > st@distribution@name [1] "Exact Distribution for Dependent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > > st <- symmetry_test(y3 ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "shift")) > st@distribution@name [1] "Exact Distribution for Dependent Two-Sample Tests (Streitberg-Roehmel Shift Algorithm)" > pvalue(st) [1] 0.8830051 > midpvalue(st) [1] 0.8828602 > pvalue_interval(st) p_0 p_1 0.8827152 0.8830051 > s <- sample(support(st), 5) > pvalue(st@distribution, s) [1] 3.814697e-06 9.809170e-01 4.500065e-01 8.348274e-02 4.754562e-01 > midpvalue(st@distribution, s) [1] 2.861023e-06 9.807472e-01 4.498701e-01 8.344555e-02 4.753208e-01 > pvalue_interval(st@distribution, s) [,1] [,2] [,3] [,4] [,5] p_0 1.907349e-06 0.9805775 0.4497337 0.08340836 0.4751854 p_1 3.814697e-06 0.9809170 0.4500065 0.08348274 0.4754562 > > try(symmetry_test(y3 ~ x | b, data = dta2, paired = TRUE, + distribution = exact(algo = "split-up"))) Error in .local(object, ...) : split-up algorithm not implemented for paired samples > > > ### check exact tests with weights > itw1 <- independence_test(y3 ~ x, data = dta, weights = ~ w, + distribution = exact(algorithm = "shift")) > itw2 <- independence_test(y3 ~ x, data = dta, weights = ~ w, + distribution = exact(algorithm = "split-up")) > y3w <- with(dta, rep(y3, w)) > xw <- with(dta, rep(x, w)) > it1 <- independence_test(y3w ~ xw, distribution = exact(algorithm = "shift")) > it2 <- independence_test(y3w ~ xw, distribution = exact(algorithm = "split-up")) > stopifnot(isequal(pvalue(itw1), pvalue(it1))) > stopifnot(isequal(pvalue(itw1), pvalue(it2))) > stopifnot(isequal(pvalue(itw2), pvalue(it1))) > stopifnot(isequal(pvalue(itw2), pvalue(it2))) > stopifnot(isequal(midpvalue(itw1), midpvalue(it1))) > stopifnot(isequal(midpvalue(itw2), midpvalue(it2))) > stopifnot(isequal(pvalue_interval(itw1), pvalue_interval(it1))) > stopifnot(isequal(pvalue_interval(itw2), pvalue_interval(it2))) > > Convictions <- + matrix(c(2, 10, 15, 3), nrow = 2, + dimnames = list(c("Dizygotic", "Monozygotic"), + c("Convicted", "Not convicted"))) > itw1 <- independence_test(as.table(Convictions), alternative = "less", + distribution = exact(algorithm = "shift")) > itw2 <- independence_test(as.table(Convictions), alternative = "less", + distribution = exact(algorithm = "split-up")) > it1 <- independence_test(Var2 ~ Var1, alternative = "less", + data = coin:::table2df(as.table(Convictions)), + distribution = exact(algorithm = "shift")) > it2 <- independence_test(Var2 ~ Var1, alternative = "less", + data = coin:::table2df(as.table(Convictions)), + distribution = exact(algorithm = "split-up")) > stopifnot(isequal(pvalue(itw1), pvalue(it1))) > stopifnot(isequal(pvalue(itw1), pvalue(it2))) > stopifnot(isequal(pvalue(itw2), pvalue(it1))) > stopifnot(isequal(pvalue(itw2), pvalue(it2))) > stopifnot(isequal(midpvalue(itw1), midpvalue(it1))) > stopifnot(isequal(midpvalue(itw2), midpvalue(it2))) > stopifnot(isequal(pvalue_interval(itw1), pvalue_interval(it1))) > stopifnot(isequal(pvalue_interval(itw2), pvalue_interval(it2))) > > > ### check support, pperm, dperm, qperm, rperm > y1 <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) > y2 <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) > dta1 <- data.frame( + y = c(y1, y2), + x = gl(2, length(y1)), + b = factor(rep(seq_along(y1), 2))) > > diff <- y1 - y2 > dta2 <- data.frame( + y = as.vector(rbind(abs(diff) * (diff >= 0), abs(diff) * (diff < 0))), + x = factor(rep(0:1, length(diff)), labels = c("pos", "neg")), + b <- gl(length(diff), 2)) > > ### shift without block > it1_SR <- independence_test(y ~ x, data = dta1, + distribution = exact(algorithm = "shift")) > supp_it1_SR <- support(it1_SR) > stopifnot(!is.unsorted(supp_it1_SR)) > stopifnot(all(supp_it1_SR == unique(supp_it1_SR))) > round(pp_it1_SR <- pperm(it1_SR, supp_it1_SR), 7) [1] 0.0000206 0.0000411 0.0000823 0.0001028 0.0001440 0.0001645 0.0002057 [8] 0.0002468 0.0002674 0.0003085 0.0003497 0.0004114 0.0004731 0.0005142 [15] 0.0005553 0.0005759 0.0005965 0.0006376 0.0006582 0.0006787 0.0006993 [22] 0.0007404 0.0007816 0.0008227 0.0008433 0.0008638 0.0009050 0.0010284 [29] 0.0010695 0.0010901 0.0011312 0.0011929 0.0012752 0.0012958 0.0013369 [36] 0.0013986 0.0014192 0.0014603 0.0015426 0.0015837 0.0016454 0.0016660 [43] 0.0016865 0.0017277 0.0017483 0.0018100 0.0018511 0.0019128 0.0019334 [50] 0.0020156 0.0020362 0.0020773 0.0020979 0.0021390 0.0021802 0.0023036 [57] 0.0023241 0.0023858 0.0024681 0.0024887 0.0025710 0.0025915 0.0026121 [64] 0.0026532 0.0027355 0.0028795 0.0029617 0.0029823 0.0030029 0.0030852 [71] 0.0031057 0.0031469 0.0032703 0.0032908 0.0034142 0.0034554 0.0034759 [78] 0.0034965 0.0035582 0.0036199 0.0036610 0.0037639 0.0037845 0.0038050 [85] 0.0038462 0.0038873 0.0039901 0.0040107 0.0040518 0.0040930 0.0041341 [92] 0.0041752 0.0042369 0.0043192 0.0043398 0.0043809 0.0044632 0.0045249 [99] 0.0046072 0.0047511 0.0047717 0.0048951 0.0049362 0.0049774 0.0050391 [106] 0.0052242 0.0052859 0.0053065 0.0053682 0.0054710 0.0054916 0.0055121 [113] 0.0056355 0.0056767 0.0057589 0.0057795 0.0058206 0.0058618 0.0058824 [120] 0.0060263 0.0060675 0.0061086 0.0061497 0.0061703 0.0062526 0.0062937 [127] 0.0063554 0.0064582 0.0064788 0.0064994 0.0065405 0.0066434 0.0066845 [134] 0.0067051 0.0067462 0.0067668 0.0068696 0.0069519 0.0069930 0.0070547 [141] 0.0070958 0.0072604 0.0073427 0.0073838 0.0074866 0.0075483 0.0075895 [148] 0.0076100 0.0077334 0.0077951 0.0079597 0.0080420 0.0080831 0.0082682 [155] 0.0083093 0.0084122 0.0084739 0.0085150 0.0085356 0.0085973 0.0087413 [162] 0.0088441 0.0089058 0.0089675 0.0091320 0.0091937 0.0093172 0.0094611 [169] 0.0095434 0.0095640 0.0096257 0.0096462 0.0096668 0.0097079 0.0098519 [176] 0.0098930 0.0099959 0.0100782 0.0101193 0.0103044 0.0103661 0.0103867 [183] 0.0105306 0.0105718 0.0105923 0.0107158 0.0108392 0.0109626 0.0110243 [190] 0.0110860 0.0111271 0.0111682 0.0112094 0.0114151 0.0114562 0.0115796 [197] 0.0116413 0.0116619 0.0117853 0.0118881 0.0119498 0.0121555 0.0123406 [204] 0.0124023 0.0124229 0.0125257 0.0125668 0.0125874 0.0126697 0.0128137 [211] 0.0128959 0.0129782 0.0129988 0.0130399 0.0132250 0.0133690 0.0134101 [218] 0.0134513 0.0136569 0.0137186 0.0137392 0.0138420 0.0139449 0.0139860 [225] 0.0140683 0.0141506 0.0141917 0.0143562 0.0144591 0.0145825 0.0146030 [232] 0.0146647 0.0147882 0.0148910 0.0150144 0.0150555 0.0151172 0.0152818 [239] 0.0153023 0.0153435 0.0154463 0.0155286 0.0156314 0.0158371 0.0158577 [246] 0.0158782 0.0158988 0.0161251 0.0162690 0.0164130 0.0164541 0.0164953 [253] 0.0165775 0.0165981 0.0168038 0.0169683 0.0170506 0.0171534 0.0172563 [260] 0.0172768 0.0172974 0.0175442 0.0175854 0.0176265 0.0177910 0.0178322 [267] 0.0178527 0.0178733 0.0180173 0.0180995 0.0181613 0.0182024 0.0182435 [274] 0.0184903 0.0185932 0.0189223 0.0189840 0.0191074 0.0192513 0.0193336 [281] 0.0194981 0.0195599 0.0196627 0.0196833 0.0197038 0.0197861 0.0199712 [288] 0.0199918 0.0200123 0.0200740 0.0201769 0.0203414 0.0204237 0.0204648 [295] 0.0207116 0.0208556 0.0208762 0.0209790 0.0209996 0.0210819 0.0212053 [302] 0.0213287 0.0213492 0.0213698 0.0214521 0.0215138 0.0215755 0.0216372 [309] 0.0218017 0.0220280 0.0221102 0.0222131 0.0224599 0.0225216 0.0227273 [316] 0.0228712 0.0229947 0.0230358 0.0231592 0.0232209 0.0232415 0.0234060 [323] 0.0235294 0.0236117 0.0236323 0.0238379 0.0240230 0.0240436 0.0242493 [330] 0.0244550 0.0245578 0.0246401 0.0249280 0.0249897 0.0252365 0.0253188 [337] 0.0254011 0.0254216 0.0255656 0.0258330 0.0259153 0.0259975 0.0261621 [344] 0.0262649 0.0263060 0.0263266 0.0265529 0.0268202 0.0268614 0.0269025 [351] 0.0270671 0.0271699 0.0272316 0.0273139 0.0274784 0.0276429 0.0276635 [358] 0.0276841 0.0278281 0.0279103 0.0279515 0.0280132 0.0280749 0.0283011 [365] 0.0284245 0.0284657 0.0285068 0.0286096 0.0287742 0.0288359 0.0288564 [372] 0.0288770 0.0291650 0.0293089 0.0294323 0.0294940 0.0296174 0.0298643 [379] 0.0299260 0.0299465 0.0301111 0.0301728 0.0302962 0.0303579 0.0303784 [386] 0.0304813 0.0306047 0.0306253 0.0306664 0.0307075 0.0309132 0.0309955 [393] 0.0310160 0.0310572 0.0311806 0.0313863 0.0314274 0.0314685 0.0315714 [400] 0.0316948 0.0319210 0.0320650 0.0323735 0.0326615 0.0327643 0.0327849 [407] 0.0330934 0.0331345 0.0331962 0.0332374 0.0334430 0.0336281 0.0337515 [414] 0.0337721 0.0338338 0.0339367 0.0340601 0.0341218 0.0341629 0.0342040 [421] 0.0344508 0.0347799 0.0348828 0.0349856 0.0352941 0.0354381 0.0357466 [428] 0.0359523 0.0361168 0.0361374 0.0363431 0.0365076 0.0365282 0.0365693 [435] 0.0366310 0.0368984 0.0371246 0.0373097 0.0373509 0.0373920 0.0374537 [442] 0.0377417 0.0378445 0.0378651 0.0381119 0.0383381 0.0385027 0.0385232 [449] 0.0386672 0.0389963 0.0390374 0.0390580 0.0390991 0.0391814 0.0392431 [456] 0.0393254 0.0393871 0.0394282 0.0395311 0.0397984 0.0398396 0.0399835 [463] 0.0402509 0.0404360 0.0405183 0.0405594 0.0407240 0.0410736 0.0411970 [470] 0.0412176 0.0412382 0.0413616 0.0414439 0.0415261 0.0415673 0.0418346 [477] 0.0419992 0.0420814 0.0421020 0.0421637 0.0422666 0.0424105 0.0424311 [484] 0.0425134 0.0426162 0.0428425 0.0431510 0.0432332 0.0432744 0.0433772 [491] 0.0436240 0.0438914 0.0439120 0.0439531 0.0443233 0.0444673 0.0445496 [498] 0.0446318 0.0446730 0.0449404 0.0451049 0.0451460 0.0454545 0.0455574 [505] 0.0457219 0.0457631 0.0458453 0.0460716 0.0463390 0.0463595 0.0464212 [512] 0.0465446 0.0468737 0.0471000 0.0472645 0.0473056 0.0473262 0.0475319 [519] 0.0478198 0.0479021 0.0479432 0.0480255 0.0482106 0.0484163 0.0486014 [526] 0.0486220 0.0487248 0.0490745 0.0492801 0.0493418 0.0494241 0.0496709 [533] 0.0498149 0.0499589 0.0500411 0.0500617 0.0502674 0.0505965 0.0506376 [540] 0.0507404 0.0509461 0.0511107 0.0512752 0.0513163 0.0513575 0.0515220 [547] 0.0519334 0.0521185 0.0521390 0.0521596 0.0523241 0.0526121 0.0526944 [554] 0.0527766 0.0528178 0.0531263 0.0534142 0.0535788 0.0535993 0.0536816 [561] 0.0537433 0.0539696 0.0540107 0.0540724 0.0541752 0.0542986 0.0545660 [568] 0.0546483 0.0547306 0.0548951 0.0552448 0.0553270 0.0553476 0.0556355 [575] 0.0558824 0.0560675 0.0561086 0.0561292 0.0563554 0.0567462 0.0567873 [582] 0.0568490 0.0569107 0.0569313 0.0571987 0.0572604 0.0573427 0.0573838 [589] 0.0574661 0.0576306 0.0579186 0.0580625 0.0581037 0.0582682 0.0584739 [596] 0.0587824 0.0590086 0.0590498 0.0594200 0.0598930 0.0600370 0.0601193 [603] 0.0603661 0.0605101 0.0605718 0.0605923 0.0606129 0.0607569 0.0610243 [610] 0.0612094 0.0612711 0.0613945 0.0617030 0.0619087 0.0619910 0.0620732 [617] 0.0622172 0.0625668 0.0630399 0.0632250 0.0634101 0.0634924 0.0638626 [624] 0.0640683 0.0641506 0.0641917 0.0644796 0.0647265 0.0649321 0.0649527 [631] 0.0650761 0.0651995 0.0654669 0.0655080 0.0655903 0.0656726 0.0658988 [638] 0.0661251 0.0663102 0.0664130 0.0665570 0.0667215 0.0671534 0.0672768 [645] 0.0674002 0.0675648 0.0678527 0.0681407 0.0683052 0.0685315 0.0687988 [652] 0.0688811 0.0689634 0.0690045 0.0690251 0.0691896 0.0693542 0.0695804 [659] 0.0696627 0.0697038 0.0699095 0.0703003 0.0703826 0.0704648 0.0706705 [666] 0.0709996 0.0712258 0.0713698 0.0714521 0.0714932 0.0717606 0.0722131 [673] 0.0723982 0.0725010 0.0727478 0.0729741 0.0730769 0.0730975 0.0733854 [680] 0.0737557 0.0739202 0.0739408 0.0740230 0.0740436 0.0742081 0.0745372 [687] 0.0747018 0.0748252 0.0749280 0.0753394 0.0757919 0.0760181 0.0760387 [694] 0.0761209 0.0763883 0.0767380 0.0767585 0.0767997 0.0769231 0.0772727 [701] 0.0776018 0.0778075 0.0779103 0.0779720 0.0784039 0.0786302 0.0786919 [708] 0.0787330 0.0787536 0.0790621 0.0793706 0.0796586 0.0797203 0.0798231 [715] 0.0800905 0.0806253 0.0807281 0.0807487 0.0808926 0.0809132 0.0812012 [722] 0.0813863 0.0815714 0.0816536 0.0817565 0.0819622 0.0823324 0.0823941 [729] 0.0824558 0.0826820 0.0830317 0.0833608 0.0836076 0.0836487 0.0837104 [736] 0.0838338 0.0843480 0.0845742 0.0846771 0.0848416 0.0850884 0.0853353 [743] 0.0855204 0.0856438 0.0857260 0.0857466 0.0859934 0.0864048 0.0864870 [750] 0.0865282 0.0867750 0.0868778 0.0870424 0.0871863 0.0873303 0.0874537 [757] 0.0877417 0.0882970 0.0885438 0.0886055 0.0888112 0.0890991 0.0895105 [764] 0.0895928 0.0896750 0.0897162 0.0897367 0.0900658 0.0903743 0.0904360 [771] 0.0904977 0.0906211 0.0907240 0.0909914 0.0911148 0.0912793 0.0914439 [778] 0.0917729 0.0920814 0.0922871 0.0923077 0.0924928 0.0927602 0.0933566 [785] 0.0934595 0.0935418 0.0937063 0.0937269 0.0940559 0.0944262 0.0947141 [792] 0.0947552 0.0950021 0.0953517 0.0954957 0.0955368 0.0956191 0.0956397 [799] 0.0959893 0.0961744 0.0963184 0.0964007 0.0965446 0.0967297 0.0973056 [806] 0.0975524 0.0976553 0.0979432 0.0982929 0.0986425 0.0989510 0.0990333 [813] 0.0990539 0.0993418 0.0998766 0.1000411 0.1001851 0.1005348 0.1008844 [820] 0.1011107 0.1011929 0.1012135 0.1012341 0.1014397 0.1020156 0.1022830 [827] 0.1024064 0.1025915 0.1027972 0.1031263 0.1032703 0.1034348 0.1036816 [834] 0.1037022 0.1040930 0.1046483 0.1049568 0.1051213 0.1052653 0.1056355 [841] 0.1058001 0.1059029 0.1059852 0.1061909 0.1065611 0.1067256 0.1067462 [848] 0.1068696 0.1068902 0.1070547 0.1075278 0.1076306 0.1077540 0.1078774 [855] 0.1079391 0.1081859 0.1085561 0.1087824 0.1089675 0.1091732 0.1093789 [862] 0.1100165 0.1101604 0.1103044 0.1105101 0.1108803 0.1112094 0.1114356 [869] 0.1115590 0.1118058 0.1122172 0.1123200 0.1123817 0.1126285 0.1126697 [876] 0.1127931 0.1131222 0.1134307 0.1135130 0.1135747 0.1136158 0.1138626 [883] 0.1143768 0.1145619 0.1146647 0.1148910 0.1152201 0.1155697 0.1156931 [890] 0.1157754 0.1158988 0.1162279 0.1169066 0.1170917 0.1171740 0.1174208 [897] 0.1176882 0.1179556 0.1181201 0.1182230 0.1183464 0.1183669 0.1186549 [904] 0.1192719 0.1196216 0.1198684 0.1200329 0.1205060 0.1207939 0.1209379 [911] 0.1210613 0.1210819 0.1215343 0.1220485 0.1223365 0.1223982 0.1225422 [918] 0.1227478 0.1231592 0.1232209 0.1233032 0.1235088 0.1237968 0.1241464 [925] 0.1245167 0.1246195 0.1248457 0.1249897 0.1256684 0.1259153 0.1260798 [932] 0.1263060 0.1266146 0.1271288 0.1273756 0.1274578 0.1275607 0.1275812 [939] 0.1278075 0.1283834 0.1285891 0.1286919 0.1288770 0.1288976 0.1292267 [946] 0.1295146 0.1299465 0.1300699 0.1302550 0.1304607 0.1310777 0.1311600 [953] 0.1312834 0.1316125 0.1316331 0.1320033 0.1324352 0.1326820 0.1328260 [960] 0.1328671 0.1329083 0.1330934 0.1337104 0.1339161 0.1340189 0.1342246 [967] 0.1342452 0.1344714 0.1348211 0.1349650 0.1350679 0.1351296 0.1351913 [974] 0.1354175 0.1360140 0.1362197 0.1362814 0.1365899 0.1366310 0.1367956 [981] 0.1371658 0.1373920 0.1375566 0.1378445 0.1382764 0.1388935 0.1392225 [988] 0.1392637 0.1394282 0.1394488 0.1397779 0.1402304 0.1403949 0.1404977 [995] 0.1405389 0.1406006 0.1409914 0.1414027 0.1416495 0.1416907 0.1418346 [1002] 0.1419580 0.1424928 0.1427190 0.1429042 0.1431304 0.1431715 0.1435212 [1009] 0.1439120 0.1441999 0.1443028 0.1446113 0.1448581 0.1455780 0.1457836 [1016] 0.1458042 0.1460921 0.1464418 0.1468943 0.1473468 0.1473879 0.1474907 [1023] 0.1477581 0.1483546 0.1485191 0.1486014 0.1488893 0.1489305 0.1493418 [1030] 0.1497738 0.1500823 0.1502262 0.1503702 0.1504114 0.1505759 0.1511929 [1037] 0.1514809 0.1516865 0.1520362 0.1523858 0.1528178 0.1532086 0.1534142 [1044] 0.1535993 0.1538873 0.1547306 0.1549568 0.1549774 0.1553270 0.1553476 [1051] 0.1555533 0.1558618 0.1560469 0.1562320 0.1563554 0.1564171 0.1565817 [1058] 0.1572810 0.1576100 0.1577540 0.1580831 0.1583505 0.1588235 0.1590498 [1065] 0.1592555 0.1595023 0.1595228 0.1598930 0.1605306 0.1608186 0.1609420 [1072] 0.1611888 0.1614151 0.1619087 0.1621349 0.1624023 0.1625668 0.1625874 [1079] 0.1629371 0.1632867 0.1635335 0.1635541 0.1637598 0.1638215 0.1639860 [1086] 0.1645825 0.1647676 0.1649321 0.1652201 0.1653023 0.1655286 0.1661045 [1093] 0.1664747 0.1666392 0.1668861 0.1671946 0.1679761 0.1681201 0.1682641 [1100] 0.1684903 0.1685315 0.1690045 0.1693953 0.1695599 0.1696010 0.1697861 [1107] 0.1700123 0.1705265 0.1708145 0.1708968 0.1712464 0.1712875 0.1715549 [1114] 0.1720074 0.1723776 0.1725216 0.1726450 0.1726861 0.1729124 0.1737351 [1121] 0.1739819 0.1741259 0.1744755 0.1745372 0.1749280 0.1753805 0.1756479 [1128] 0.1757713 0.1758947 0.1759358 0.1763060 0.1768819 0.1772110 0.1773344 [1135] 0.1777046 0.1779720 0.1783834 0.1785479 0.1787330 0.1790415 0.1790621 [1142] 0.1794118 0.1802345 0.1806253 0.1807075 0.1809749 0.1812012 0.1817770 [1149] 0.1820650 0.1823118 0.1824558 0.1824969 0.1828260 0.1833813 0.1837310 [1156] 0.1838132 0.1840806 0.1841218 0.1843480 0.1848622 0.1850679 0.1852530 [1163] 0.1856232 0.1856643 0.1859729 0.1864253 0.1867544 0.1869601 0.1873097 [1170] 0.1875566 0.1882764 0.1885027 0.1887495 0.1891197 0.1891608 0.1896545 [1177] 0.1902098 0.1906006 0.1907034 0.1909297 0.1909708 0.1911765 0.1918552 [1184] 0.1919992 0.1921843 0.1925339 0.1925956 0.1927396 0.1932127 0.1936035 [1191] 0.1938297 0.1940971 0.1943645 0.1950021 0.1951872 0.1953311 0.1958042 [1198] 0.1958248 0.1961333 0.1966475 0.1968943 0.1970588 0.1972439 0.1972851 [1205] 0.1975319 0.1983752 0.1986425 0.1988482 0.1992184 0.1992390 0.1995475 [1212] 0.1998766 0.2000411 0.2002057 0.2003702 0.2004731 0.2007404 0.2014603 [1219] 0.2017277 0.2018511 0.2022419 0.2022830 0.2024064 0.2029206 0.2032703 [1226] 0.2035376 0.2038462 0.2042781 0.2049774 0.2054710 0.2055327 0.2058412 [1233] 0.2060880 0.2066845 0.2068490 0.2069519 0.2071987 0.2072398 0.2076306 [1240] 0.2081654 0.2084327 0.2085767 0.2087618 0.2088030 0.2089675 0.2096462 [1247] 0.2099136 0.2101399 0.2104278 0.2104689 0.2107775 0.2113739 0.2118264 [1254] 0.2119704 0.2124023 0.2126491 0.2134924 0.2138009 0.2139654 0.2143768 [1261] 0.2144179 0.2148499 0.2153846 0.2157960 0.2160016 0.2162485 0.2164130 [1268] 0.2170506 0.2171740 0.2172768 0.2176471 0.2177088 0.2180173 0.2185315 [1275] 0.2189840 0.2191279 0.2193953 0.2194776 0.2196627 0.2206294 0.2209585 [1282] 0.2212464 0.2218429 0.2221719 0.2227478 0.2230358 0.2233237 0.2234883 [1289] 0.2235294 0.2238379 0.2244755 0.2246606 0.2247840 0.2251954 0.2252365 [1296] 0.2254216 0.2257507 0.2260387 0.2262238 0.2265323 0.2266351 0.2267997 [1303] 0.2276224 0.2279515 0.2281366 0.2285891 0.2286508 0.2289181 0.2295146 [1310] 0.2297820 0.2301316 0.2304196 0.2305224 0.2309132 0.2315919 0.2319210 [1317] 0.2320033 0.2323324 0.2326203 0.2331551 0.2334225 0.2336487 0.2339984 [1324] 0.2340601 0.2343891 0.2348622 0.2351707 0.2352735 0.2356643 0.2357260 [1331] 0.2359111 0.2366104 0.2368984 0.2371041 0.2375360 0.2376183 0.2379473 [1338] 0.2386055 0.2390580 0.2392431 0.2395311 0.2397984 0.2406006 0.2407857 [1345] 0.2409297 0.2412793 0.2413204 0.2415878 0.2420609 0.2423900 0.2425134 [1352] 0.2428630 0.2430276 0.2436446 0.2439737 0.2442205 0.2447758 0.2448169 [1359] 0.2452694 0.2458659 0.2463184 0.2465858 0.2468326 0.2468737 0.2471617 [1366] 0.2482106 0.2485397 0.2486220 0.2490745 0.2491156 0.2493624 0.2497943 [1373] 0.2501645 0.2503497 0.2505553 0.2506376 0.2508638 0.2516248 0.2520362 [1380] 0.2522624 0.2528178 0.2531469 0.2536610 0.2539079 0.2541958 0.2545866 [1387] 0.2546277 0.2549157 0.2557589 0.2561086 0.2562937 0.2567256 0.2567462 [1394] 0.2569519 0.2575895 0.2579597 0.2583093 0.2586796 0.2587413 0.2590703 [1401] 0.2597491 0.2601193 0.2601810 0.2605512 0.2606541 0.2608597 0.2615179 [1408] 0.2617647 0.2620938 0.2624023 0.2625463 0.2628137 0.2634718 0.2639860 [1415] 0.2642328 0.2647676 0.2650350 0.2657960 0.2660633 0.2663307 0.2667832 [1422] 0.2668655 0.2671740 0.2677910 0.2680173 0.2681818 0.2684903 0.2685726 [1429] 0.2687577 0.2694776 0.2696833 0.2699506 0.2703620 0.2704443 0.2706499 [1436] 0.2711641 0.2715343 0.2716989 0.2720485 0.2721308 0.2723571 0.2731798 [1443] 0.2734471 0.2736940 0.2744138 0.2745167 0.2748252 0.2754216 0.2758124 [1450] 0.2759770 0.2762032 0.2762443 0.2765734 0.2772727 0.2776224 0.2778075 [1457] 0.2781983 0.2782188 0.2785891 0.2789593 0.2791444 0.2793706 0.2796791 [1464] 0.2798026 0.2800699 0.2809338 0.2813040 0.2814685 0.2820856 0.2821473 [1471] 0.2823324 0.2829288 0.2833196 0.2836898 0.2841423 0.2841629 0.2844714 [1478] 0.2852735 0.2857466 0.2858906 0.2863019 0.2866104 0.2872686 0.2874743 [1485] 0.2876388 0.2880090 0.2880708 0.2884615 0.2890580 0.2893665 0.2895722 [1492] 0.2900658 0.2901275 0.2902921 0.2910119 0.2913204 0.2917318 0.2923283 [1499] 0.2923900 0.2927807 0.2935212 0.2941176 0.2943850 0.2947964 0.2948375 [1506] 0.2951049 0.2959070 0.2961538 0.2964212 0.2968326 0.2968943 0.2972439 [1513] 0.2977170 0.2981489 0.2983957 0.2988071 0.2988276 0.2990128 0.2996503 [1520] 0.2998355 0.3000823 0.3007610 0.3009050 0.3011107 0.3017277 0.3021185 [1527] 0.3024476 0.3028178 0.3029617 0.3031057 0.3041958 0.3045043 0.3048334 [1534] 0.3054299 0.3054504 0.3058206 0.3063760 0.3066845 0.3069107 0.3071164 [1541] 0.3071781 0.3074249 0.3081242 0.3083710 0.3085561 0.3092143 0.3092966 [1548] 0.3094817 0.3098725 0.3102838 0.3106746 0.3110860 0.3112299 0.3115179 [1555] 0.3123200 0.3127314 0.3129165 0.3134307 0.3134924 0.3136775 0.3143974 [1562] 0.3146442 0.3148910 0.3152818 0.3154258 0.3156931 0.3165570 0.3169066 [1569] 0.3170506 0.3175442 0.3175648 0.3177088 0.3183052 0.3185726 0.3189017 [1576] 0.3193336 0.3194159 0.3197038 0.3203826 0.3206911 0.3208556 0.3214521 [1583] 0.3214932 0.3216783 0.3225216 0.3228507 0.3230975 0.3235705 0.3236528 [1590] 0.3240230 0.3246401 0.3251131 0.3253394 0.3256890 0.3257507 0.3259358 [1597] 0.3266968 0.3268614 0.3270876 0.3276018 0.3277458 0.3280543 0.3286302 [1604] 0.3291238 0.3293912 0.3297820 0.3298643 0.3300288 0.3308515 0.3311806 [1611] 0.3315302 0.3323118 0.3326409 0.3332785 0.3336898 0.3339984 0.3343686 [1618] 0.3344508 0.3346771 0.3356232 0.3359317 0.3360963 0.3367544 0.3368367 [1625] 0.3371452 0.3375977 0.3380090 0.3382970 0.3386466 0.3387289 0.3388729 [1632] 0.3398190 0.3401687 0.3403949 0.3410531 0.3410942 0.3414027 0.3418963 [1639] 0.3422460 0.3426573 0.3431715 0.3433566 0.3436240 0.3445084 0.3448375 [1646] 0.3450638 0.3456808 0.3457014 0.3459276 0.3465858 0.3468531 0.3473468 [1653] 0.3477787 0.3478610 0.3481695 0.3488482 0.3491773 0.3493213 0.3498972 [1660] 0.3500000 0.3500823 0.3508433 0.3511518 0.3513986 0.3520773 0.3522830 [1667] 0.3524476 0.3531469 0.3536405 0.3538873 0.3544632 0.3545249 0.3547306 [1674] 0.3554093 0.3557178 0.3560675 0.3564994 0.3566022 0.3569107 0.3574455 [1681] 0.3577129 0.3578980 0.3582682 0.3583093 0.3584944 0.3592143 0.3594200 [1688] 0.3597491 0.3603455 0.3605306 0.3607775 0.3613328 0.3617441 0.3620938 [1695] 0.3625257 0.3626080 0.3627520 0.3636981 0.3641094 0.3643562 0.3650967 [1702] 0.3651584 0.3654052 0.3660222 0.3665775 0.3667832 0.3670712 0.3671329 [1709] 0.3673797 0.3682024 0.3685520 0.3687371 0.3693953 0.3694364 0.3696833 [1716] 0.3701152 0.3703826 0.3705882 0.3709996 0.3711847 0.3713698 0.3721719 [1723] 0.3726039 0.3728507 0.3735088 0.3735705 0.3737968 0.3745372 0.3749074 [1730] 0.3754011 0.3758947 0.3759358 0.3762443 0.3773550 0.3777664 0.3779103 [1737] 0.3784451 0.3785068 0.3786302 0.3792061 0.3795146 0.3798437 0.3803579 [1744] 0.3805430 0.3807898 0.3814068 0.3819210 0.3821678 0.3829288 0.3830522 [1751] 0.3832168 0.3840601 0.3843686 0.3847799 0.3853764 0.3854998 0.3857672 [1758] 0.3865693 0.3870424 0.3873097 0.3877417 0.3878445 0.3880502 0.3888935 [1765] 0.3891814 0.3894899 0.3900247 0.3901687 0.3903743 0.3908885 0.3913410 [1772] 0.3915878 0.3920403 0.3921843 0.3923488 0.3930276 0.3931921 0.3936035 [1779] 0.3943850 0.3945701 0.3947347 0.3953517 0.3958248 0.3961127 0.3965858 [1786] 0.3966886 0.3968531 0.3978404 0.3981900 0.3984574 0.3992184 0.3993213 [1793] 0.3996915 0.4002674 0.4005348 0.4007816 0.4011312 0.4013575 0.4015426 [1800] 0.4024064 0.4028178 0.4030440 0.4036405 0.4037022 0.4038462 0.4042369 [1807] 0.4045866 0.4049568 0.4054710 0.4055944 0.4058618 0.4066845 0.4070341 [1814] 0.4072810 0.4080625 0.4081859 0.4083505 0.4090703 0.4093377 0.4096051 [1821] 0.4100987 0.4102838 0.4105512 0.4111682 0.4115590 0.4117647 0.4122789 [1828] 0.4123406 0.4124846 0.4131839 0.4134307 0.4137803 0.4144385 0.4145208 [1835] 0.4148499 0.4156109 0.4160633 0.4163307 0.4169889 0.4170506 0.4172357 [1842] 0.4179967 0.4183052 0.4187371 0.4192925 0.4194159 0.4197450 0.4203003 [1849] 0.4208556 0.4211641 0.4216578 0.4217606 0.4219663 0.4227273 0.4229535 [1856] 0.4231386 0.4237968 0.4240025 0.4242081 0.4247429 0.4251337 0.4254422 [1863] 0.4259358 0.4261004 0.4261826 0.4270465 0.4273756 0.4277869 0.4286919 [1870] 0.4287536 0.4291238 0.4297408 0.4302962 0.4306458 0.4310572 0.4311806 [1877] 0.4314068 0.4322912 0.4325175 0.4328260 0.4336281 0.4337515 0.4339161 [1884] 0.4344508 0.4348005 0.4352530 0.4356643 0.4358700 0.4360551 0.4368367 [1891] 0.4372480 0.4374949 0.4382970 0.4384204 0.4385644 0.4391197 0.4395516 [1898] 0.4399630 0.4405389 0.4408063 0.4409914 0.4420403 0.4424722 0.4427396 [1905] 0.4433155 0.4433978 0.4435829 0.4440971 0.4443028 0.4447758 0.4452900 [1912] 0.4454340 0.4456397 0.4461744 0.4463390 0.4465035 0.4472645 0.4474496 [1919] 0.4475319 0.4482723 0.4485808 0.4489716 0.4496298 0.4498560 0.4500617 [1926] 0.4508638 0.4513780 0.4516865 0.4522624 0.4523036 0.4524476 0.4533114 [1933] 0.4535993 0.4538667 0.4543809 0.4545455 0.4547923 0.4553065 0.4557178 [1940] 0.4559852 0.4564582 0.4566022 0.4567256 0.4572604 0.4574866 0.4578363 [1947] 0.4585767 0.4587618 0.4590086 0.4595640 0.4599136 0.4602838 0.4608803 [1954] 0.4609831 0.4611477 0.4621555 0.4625257 0.4628342 0.4636364 0.4637598 [1961] 0.4640477 0.4646647 0.4650144 0.4652818 0.4656726 0.4657960 0.4659399 [1968] 0.4667421 0.4670300 0.4672768 0.4680173 0.4680995 0.4683258 0.4687371 [1975] 0.4691485 0.4695187 0.4701152 0.4703209 0.4704854 0.4713698 0.4717812 [1982] 0.4721308 0.4730564 0.4731386 0.4733649 0.4740847 0.4743727 0.4749074 [1989] 0.4754628 0.4756273 0.4759564 0.4766763 0.4770465 0.4772316 0.4777869 [1996] 0.4779515 0.4780543 0.4785891 0.4788770 0.4792678 0.4798848 0.4800905 [2003] 0.4801522 0.4808309 0.4812423 0.4815714 0.4824146 0.4825381 0.4826615 [2010] 0.4833813 0.4836898 0.4841835 0.4849033 0.4851296 0.4853353 0.4859934 [2017] 0.4863225 0.4865693 0.4872069 0.4873097 0.4874743 0.4881942 0.4885027 [2024] 0.4888729 0.4895105 0.4897367 0.4899424 0.4904977 0.4908885 0.4911970 [2031] 0.4917318 0.4918552 0.4919580 0.4926368 0.4928630 0.4932949 0.4941999 [2038] 0.4944467 0.4945907 0.4952077 0.4957014 0.4960716 0.4965652 0.4967503 [2045] 0.4969148 0.4976347 0.4979227 0.4982517 0.4991156 0.4991979 0.4993418 [2052] 0.4998149 0.5000000 0.5001851 0.5006582 0.5008021 0.5008844 0.5017483 [2059] 0.5020773 0.5023653 0.5030852 0.5032497 0.5034348 0.5039284 0.5042986 [2066] 0.5047923 0.5054093 0.5055533 0.5058001 0.5067051 0.5071370 0.5073632 [2073] 0.5080420 0.5081448 0.5082682 0.5088030 0.5091115 0.5095023 0.5100576 [2080] 0.5102633 0.5104895 0.5111271 0.5114973 0.5118058 0.5125257 0.5126903 [2087] 0.5127931 0.5134307 0.5136775 0.5140066 0.5146647 0.5148704 0.5150967 [2094] 0.5158165 0.5163102 0.5166187 0.5173385 0.5174619 0.5175854 0.5184286 [2101] 0.5187577 0.5191691 0.5198478 0.5199095 0.5201152 0.5207322 0.5211230 [2108] 0.5214109 0.5219457 0.5220485 0.5222131 0.5227684 0.5229535 0.5233237 [2115] 0.5240436 0.5243727 0.5245372 0.5250926 0.5256273 0.5259153 0.5266351 [2122] 0.5268614 0.5269436 0.5278692 0.5282188 0.5286302 0.5295146 0.5296791 [2129] 0.5298848 0.5304813 0.5308515 0.5312629 0.5316742 0.5319005 0.5319827 [2136] 0.5327232 0.5329700 0.5332579 0.5340601 0.5342040 0.5343274 0.5347182 [2143] 0.5349856 0.5353353 0.5359523 0.5362402 0.5363636 0.5371658 0.5374743 [2150] 0.5378445 0.5388523 0.5390169 0.5391197 0.5397162 0.5400864 0.5404360 [2157] 0.5409914 0.5412382 0.5414233 0.5421637 0.5425134 0.5427396 0.5432744 [2164] 0.5433978 0.5435418 0.5440148 0.5442822 0.5446935 0.5452077 0.5454545 [2171] 0.5456191 0.5461333 0.5464007 0.5466886 0.5475524 0.5476964 0.5477376 [2178] 0.5483135 0.5486220 0.5491362 0.5499383 0.5501440 0.5503702 0.5510284 [2185] 0.5514192 0.5517277 0.5524681 0.5525504 0.5527355 0.5534965 0.5536610 [2192] 0.5538256 0.5543603 0.5545660 0.5547100 0.5552242 0.5556972 0.5559029 [2199] 0.5564171 0.5566022 0.5566845 0.5572604 0.5575278 0.5579597 0.5590086 [2206] 0.5591937 0.5594611 0.5600370 0.5604484 0.5608803 0.5614356 0.5615796 [2213] 0.5617030 0.5625051 0.5627520 0.5631633 0.5639449 0.5641300 0.5643357 [2220] 0.5647470 0.5651995 0.5655492 0.5660839 0.5662485 0.5663719 0.5671740 [2227] 0.5674825 0.5677088 0.5685932 0.5688194 0.5689428 0.5693542 0.5697038 [2234] 0.5702592 0.5708762 0.5712464 0.5713081 0.5722131 0.5726244 0.5729535 [2241] 0.5738174 0.5738996 0.5740642 0.5745578 0.5748663 0.5752571 0.5757919 [2248] 0.5759975 0.5762032 0.5768614 0.5770465 0.5772727 0.5780337 0.5782394 [2255] 0.5783422 0.5788359 0.5791444 0.5796997 0.5802550 0.5805841 0.5807075 [2262] 0.5812629 0.5816948 0.5820033 0.5827643 0.5829494 0.5830111 0.5836693 [2269] 0.5839367 0.5843891 0.5851501 0.5854792 0.5855615 0.5862197 0.5865693 [2276] 0.5868161 0.5875154 0.5876594 0.5877211 0.5882353 0.5884410 0.5888318 [2283] 0.5894488 0.5897162 0.5899013 0.5903949 0.5906623 0.5909297 0.5916495 [2290] 0.5918141 0.5919375 0.5927190 0.5929659 0.5933155 0.5941382 0.5944056 [2297] 0.5945290 0.5950432 0.5954134 0.5957631 0.5961538 0.5962978 0.5963595 [2304] 0.5969560 0.5971822 0.5975936 0.5984574 0.5986425 0.5988688 0.5992184 [2311] 0.5994652 0.5997326 0.6003085 0.6006787 0.6007816 0.6015426 0.6018100 [2318] 0.6021596 0.6031469 0.6033114 0.6034142 0.6038873 0.6041752 0.6046483 [2325] 0.6052653 0.6054299 0.6056150 0.6063965 0.6068079 0.6069724 0.6076512 [2332] 0.6078157 0.6079597 0.6084122 0.6086590 0.6091115 0.6096257 0.6098313 [2339] 0.6099753 0.6105101 0.6108186 0.6111065 0.6119498 0.6121555 0.6122583 [2346] 0.6126903 0.6129576 0.6134307 0.6142328 0.6145002 0.6146236 0.6152201 [2353] 0.6156314 0.6159399 0.6167832 0.6169478 0.6170712 0.6178322 0.6180790 [2360] 0.6185932 0.6192102 0.6194570 0.6196421 0.6201563 0.6204854 0.6207939 [2367] 0.6213698 0.6214932 0.6215549 0.6220897 0.6222336 0.6226450 0.6237557 [2374] 0.6240642 0.6241053 0.6245989 0.6250926 0.6254628 0.6262032 0.6264295 [2381] 0.6264912 0.6271493 0.6273961 0.6278281 0.6286302 0.6288153 0.6290004 [2388] 0.6294118 0.6296174 0.6298848 0.6303167 0.6305636 0.6306047 0.6312629 [2395] 0.6314480 0.6317976 0.6326203 0.6328671 0.6329288 0.6332168 0.6334225 [2402] 0.6339778 0.6345948 0.6348416 0.6349033 0.6356438 0.6358906 0.6363019 [2409] 0.6372480 0.6373920 0.6374743 0.6379062 0.6382559 0.6386672 0.6392225 [2416] 0.6394694 0.6396545 0.6402509 0.6405800 0.6407857 0.6415056 0.6416907 [2423] 0.6417318 0.6421020 0.6422871 0.6425545 0.6430893 0.6433978 0.6435006 [2430] 0.6439325 0.6442822 0.6445907 0.6452694 0.6454751 0.6455368 0.6461127 [2437] 0.6463595 0.6468531 0.6475524 0.6477170 0.6479227 0.6486014 0.6488482 [2444] 0.6491567 0.6499177 0.6500000 0.6501028 0.6506787 0.6508227 0.6511518 [2451] 0.6518305 0.6521390 0.6522213 0.6526532 0.6531469 0.6534142 0.6540724 [2458] 0.6542986 0.6543192 0.6549362 0.6551625 0.6554916 0.6563760 0.6566434 [2465] 0.6568285 0.6573427 0.6577540 0.6581037 0.6585973 0.6589058 0.6589469 [2472] 0.6596051 0.6598313 0.6601810 0.6611271 0.6612711 0.6613534 0.6617030 [2479] 0.6619910 0.6624023 0.6628548 0.6631633 0.6632456 0.6639037 0.6640683 [2486] 0.6643768 0.6653229 0.6655492 0.6656314 0.6660016 0.6663102 0.6667215 [2493] 0.6673591 0.6676882 0.6684698 0.6688194 0.6691485 0.6699712 0.6701357 [2500] 0.6702180 0.6706088 0.6708762 0.6713698 0.6719457 0.6722542 0.6723982 [2507] 0.6729124 0.6731386 0.6733032 0.6740642 0.6742493 0.6743110 0.6746606 [2514] 0.6748869 0.6753599 0.6759770 0.6763472 0.6764295 0.6769025 0.6771493 [2521] 0.6774784 0.6783217 0.6785068 0.6785479 0.6791444 0.6793089 0.6796174 [2528] 0.6802962 0.6805841 0.6806664 0.6810983 0.6814274 0.6816948 0.6822912 [2535] 0.6824352 0.6824558 0.6829494 0.6830934 0.6834430 0.6843069 0.6845742 [2542] 0.6847182 0.6851090 0.6853558 0.6856026 0.6863225 0.6865076 0.6865693 [2549] 0.6870835 0.6872686 0.6876800 0.6884821 0.6887701 0.6889140 0.6893254 [2556] 0.6897162 0.6901275 0.6905183 0.6907034 0.6907857 0.6914439 0.6916290 [2563] 0.6918758 0.6925751 0.6928219 0.6928836 0.6930893 0.6933155 0.6936240 [2570] 0.6941794 0.6945496 0.6945701 0.6951666 0.6954957 0.6958042 0.6968943 [2577] 0.6970383 0.6971822 0.6975524 0.6978815 0.6982723 0.6988893 0.6990950 [2584] 0.6992390 0.6999177 0.7001645 0.7003497 0.7009872 0.7011724 0.7011929 [2591] 0.7016043 0.7018511 0.7022830 0.7027561 0.7031057 0.7031674 0.7035788 [2598] 0.7038462 0.7040930 0.7048951 0.7051625 0.7052036 0.7056150 0.7058824 [2605] 0.7064788 0.7072193 0.7076100 0.7076717 0.7082682 0.7086796 0.7089881 [2612] 0.7097079 0.7098725 0.7099342 0.7104278 0.7106335 0.7109420 0.7115385 [2619] 0.7119292 0.7119910 0.7123612 0.7125257 0.7127314 0.7133896 0.7136981 [2626] 0.7141094 0.7142534 0.7147265 0.7155286 0.7158371 0.7158577 0.7163102 [2633] 0.7166804 0.7170712 0.7176676 0.7178527 0.7179144 0.7185315 0.7186960 [2640] 0.7190662 0.7199301 0.7201974 0.7203209 0.7206294 0.7208556 0.7210407 [2647] 0.7214109 0.7217812 0.7218017 0.7221925 0.7223776 0.7227273 0.7234266 [2654] 0.7237557 0.7237968 0.7240230 0.7241876 0.7245784 0.7251748 0.7254833 [2661] 0.7255862 0.7263060 0.7265529 0.7268202 0.7276429 0.7278692 0.7279515 [2668] 0.7283011 0.7284657 0.7288359 0.7293501 0.7295557 0.7296380 0.7300494 [2675] 0.7303167 0.7305224 0.7312423 0.7314274 0.7315097 0.7318182 0.7319827 [2682] 0.7322090 0.7328260 0.7331345 0.7332168 0.7336693 0.7339367 0.7342040 [2689] 0.7349650 0.7352324 0.7357672 0.7360140 0.7365282 0.7371863 0.7374537 [2696] 0.7375977 0.7379062 0.7382353 0.7384821 0.7391403 0.7393459 0.7394488 [2703] 0.7398190 0.7398807 0.7402509 0.7409297 0.7412587 0.7413204 0.7416907 [2710] 0.7420403 0.7424105 0.7430481 0.7432538 0.7432744 0.7437063 0.7438914 [2717] 0.7442411 0.7450843 0.7453723 0.7454134 0.7458042 0.7460921 0.7463390 [2724] 0.7468531 0.7471822 0.7477376 0.7479638 0.7483752 0.7491362 0.7493624 [2731] 0.7494447 0.7496503 0.7498355 0.7502057 0.7506376 0.7508844 0.7509255 [2738] 0.7513780 0.7514603 0.7517894 0.7528383 0.7531263 0.7531674 0.7534142 [2745] 0.7536816 0.7541341 0.7547306 0.7551831 0.7552242 0.7557795 0.7560263 [2752] 0.7563554 0.7569724 0.7571370 0.7574866 0.7576100 0.7579391 0.7584122 [2759] 0.7586796 0.7587207 0.7590703 0.7592143 0.7593994 0.7602016 0.7604689 [2766] 0.7607569 0.7609420 0.7613945 0.7620527 0.7623817 0.7624640 0.7628959 [2773] 0.7631016 0.7633896 0.7640889 0.7642740 0.7643357 0.7647265 0.7648293 [2780] 0.7651378 0.7656109 0.7659399 0.7660016 0.7663513 0.7665775 0.7668449 [2787] 0.7673797 0.7676676 0.7679967 0.7680790 0.7684081 0.7690868 0.7694776 [2794] 0.7695804 0.7698684 0.7702180 0.7704854 0.7710819 0.7713492 0.7714109 [2801] 0.7718634 0.7720485 0.7723776 0.7732003 0.7733649 0.7734677 0.7737762 [2808] 0.7739613 0.7742493 0.7745784 0.7747635 0.7748046 0.7752160 0.7753394 [2815] 0.7755245 0.7761621 0.7764706 0.7765117 0.7766763 0.7769642 0.7772522 [2822] 0.7778281 0.7781571 0.7787536 0.7790415 0.7793706 0.7803373 0.7805224 [2829] 0.7806047 0.7808721 0.7810160 0.7814685 0.7819827 0.7822912 0.7823529 [2836] 0.7827232 0.7828260 0.7829494 0.7835870 0.7837515 0.7839984 0.7842040 [2843] 0.7846154 0.7851501 0.7855821 0.7856232 0.7860346 0.7861991 0.7865076 [2850] 0.7873509 0.7875977 0.7880296 0.7881736 0.7886261 0.7892225 0.7895311 [2857] 0.7895722 0.7898601 0.7900864 0.7903538 0.7910325 0.7911970 0.7912382 [2864] 0.7914233 0.7915673 0.7918346 0.7923694 0.7927602 0.7928013 0.7930481 [2871] 0.7931510 0.7933155 0.7939120 0.7941588 0.7944673 0.7945290 0.7950226 [2878] 0.7957219 0.7961538 0.7964624 0.7967297 0.7970794 0.7975936 0.7977170 [2885] 0.7977581 0.7981489 0.7982723 0.7985397 0.7992596 0.7995269 0.7996298 [2892] 0.7997943 0.7999589 0.8001234 0.8004525 0.8007610 0.8007816 0.8011518 [2899] 0.8013575 0.8016248 0.8024681 0.8027149 0.8027561 0.8029412 0.8031057 [2906] 0.8033525 0.8038667 0.8041752 0.8041958 0.8046689 0.8048128 0.8049979 [2913] 0.8056355 0.8059029 0.8061703 0.8063965 0.8067873 0.8072604 0.8074044 [2920] 0.8074661 0.8078157 0.8080008 0.8081448 0.8088235 0.8090292 0.8090703 [2927] 0.8092966 0.8093994 0.8097902 0.8103455 0.8108392 0.8108803 0.8112505 [2934] 0.8114973 0.8117236 0.8124434 0.8126903 0.8130399 0.8132456 0.8135747 [2941] 0.8140271 0.8143357 0.8143768 0.8147470 0.8149321 0.8151378 0.8156520 [2948] 0.8158782 0.8159194 0.8161868 0.8162690 0.8166187 0.8171740 0.8175031 [2955] 0.8175442 0.8176882 0.8179350 0.8182230 0.8187988 0.8190251 0.8192925 [2962] 0.8193747 0.8197655 0.8205882 0.8209379 0.8209585 0.8212670 0.8214521 [2969] 0.8216166 0.8220280 0.8222954 0.8226656 0.8227890 0.8231181 0.8236940 [2976] 0.8240642 0.8241053 0.8242287 0.8243521 0.8246195 0.8250720 0.8254628 [2983] 0.8255245 0.8258741 0.8260181 0.8262649 0.8270876 0.8273139 0.8273550 [2990] 0.8274784 0.8276224 0.8279926 0.8284451 0.8287125 0.8287536 0.8291032 [2997] 0.8291855 0.8294735 0.8299877 0.8302139 0.8303990 0.8304401 0.8306047 [3004] 0.8309955 0.8314685 0.8315097 0.8317359 0.8318799 0.8320239 0.8328054 [3011] 0.8331139 0.8333608 0.8335253 0.8338955 0.8344714 0.8346977 0.8347799 [3018] 0.8350679 0.8352324 0.8354175 0.8360140 0.8361785 0.8362402 0.8364459 [3025] 0.8364665 0.8367133 0.8370629 0.8374126 0.8374332 0.8375977 0.8378651 [3032] 0.8380913 0.8385849 0.8388112 0.8390580 0.8391814 0.8394694 0.8401070 [3039] 0.8404772 0.8404977 0.8407445 0.8409502 0.8411765 0.8416495 0.8419169 [3046] 0.8422460 0.8423900 0.8427190 0.8434183 0.8435829 0.8436446 0.8437680 [3053] 0.8439531 0.8441382 0.8444467 0.8446524 0.8446730 0.8450226 0.8450432 [3060] 0.8452694 0.8461127 0.8464007 0.8465858 0.8467914 0.8471822 0.8476142 [3067] 0.8479638 0.8483135 0.8485191 0.8488071 0.8494241 0.8495886 0.8496298 [3074] 0.8497738 0.8499177 0.8502262 0.8506582 0.8510695 0.8511107 0.8513986 [3081] 0.8514809 0.8516454 0.8522419 0.8525093 0.8526121 0.8526532 0.8531057 [3088] 0.8535582 0.8539079 0.8541958 0.8542164 0.8544220 0.8551419 0.8553887 [3095] 0.8556972 0.8558001 0.8560880 0.8564788 0.8568285 0.8568696 0.8570958 [3102] 0.8572810 0.8575072 0.8580420 0.8581654 0.8583093 0.8583505 0.8585973 [3109] 0.8590086 0.8593994 0.8594611 0.8595023 0.8596051 0.8597696 0.8602221 [3116] 0.8605512 0.8605718 0.8607363 0.8607775 0.8611065 0.8617236 0.8621555 [3123] 0.8624434 0.8626080 0.8628342 0.8632044 0.8633690 0.8634101 0.8637186 [3130] 0.8637803 0.8639860 0.8645825 0.8648087 0.8648704 0.8649321 0.8650350 [3137] 0.8651789 0.8655286 0.8657548 0.8657754 0.8659811 0.8660839 0.8662896 [3144] 0.8669066 0.8670917 0.8671329 0.8671740 0.8673180 0.8675648 0.8679967 [3151] 0.8683669 0.8683875 0.8687166 0.8688400 0.8689223 0.8695393 0.8697450 [3158] 0.8699301 0.8700535 0.8704854 0.8707733 0.8711024 0.8711230 0.8713081 [3165] 0.8714109 0.8716166 0.8721925 0.8724188 0.8724393 0.8725422 0.8726244 [3172] 0.8728712 0.8733854 0.8736940 0.8739202 0.8740847 0.8743316 0.8750103 [3179] 0.8751543 0.8753805 0.8754833 0.8758536 0.8762032 0.8764912 0.8766968 [3186] 0.8767791 0.8768408 0.8772522 0.8774578 0.8776018 0.8776635 0.8779515 [3193] 0.8784657 0.8789181 0.8789387 0.8790621 0.8792061 0.8794940 0.8799671 [3200] 0.8801316 0.8803784 0.8807281 0.8813451 0.8816331 0.8816536 0.8817770 [3207] 0.8818799 0.8820444 0.8823118 0.8825792 0.8828260 0.8829083 0.8830934 [3214] 0.8837721 0.8841012 0.8842246 0.8843069 0.8844303 0.8847799 0.8851090 [3221] 0.8853353 0.8854381 0.8856232 0.8861374 0.8863842 0.8864253 0.8864870 [3228] 0.8865693 0.8868778 0.8872069 0.8873303 0.8873715 0.8876183 0.8876800 [3235] 0.8877828 0.8881942 0.8884410 0.8885644 0.8887906 0.8891197 0.8894899 [3242] 0.8896956 0.8898396 0.8899835 0.8906211 0.8908268 0.8910325 0.8912176 [3249] 0.8914439 0.8918141 0.8920609 0.8921226 0.8922460 0.8923694 0.8924722 [3256] 0.8929453 0.8931098 0.8931304 0.8932538 0.8932744 0.8934389 0.8938091 [3263] 0.8940148 0.8940971 0.8941999 0.8943645 0.8947347 0.8948787 0.8950432 [3270] 0.8953517 0.8959070 0.8962978 0.8963184 0.8965652 0.8967297 0.8968737 [3277] 0.8972028 0.8974085 0.8975936 0.8977170 0.8979844 0.8985603 0.8987659 [3284] 0.8987865 0.8988071 0.8988893 0.8991156 0.8994652 0.8998149 0.8999589 [3291] 0.9001234 0.9006582 0.9009461 0.9009667 0.9010490 0.9013575 0.9017071 [3298] 0.9020568 0.9023447 0.9024476 0.9026944 0.9032703 0.9034554 0.9035993 [3305] 0.9036816 0.9038256 0.9040107 0.9043603 0.9043809 0.9044632 0.9045043 [3312] 0.9046483 0.9049979 0.9052448 0.9052859 0.9055738 0.9059441 0.9062731 [3319] 0.9062937 0.9064582 0.9065405 0.9066434 0.9072398 0.9075072 0.9076923 [3326] 0.9077129 0.9079186 0.9082271 0.9085561 0.9087207 0.9088852 0.9090086 [3333] 0.9092760 0.9093789 0.9095023 0.9095640 0.9096257 0.9099342 0.9102633 [3340] 0.9102838 0.9103250 0.9104072 0.9104895 0.9109009 0.9111888 0.9113945 [3347] 0.9114562 0.9117030 0.9122583 0.9125463 0.9126697 0.9128137 0.9129576 [3354] 0.9131222 0.9132250 0.9134718 0.9135130 0.9135952 0.9140066 0.9142534 [3361] 0.9142740 0.9143562 0.9144796 0.9146647 0.9149116 0.9151584 0.9153229 [3368] 0.9154258 0.9156520 0.9161662 0.9162896 0.9163513 0.9163924 0.9166392 [3375] 0.9169683 0.9173180 0.9175442 0.9176059 0.9176676 0.9180378 0.9182435 [3382] 0.9183464 0.9184286 0.9186137 0.9187988 0.9190868 0.9191074 0.9192513 [3389] 0.9192719 0.9193747 0.9199095 0.9201769 0.9202797 0.9203414 0.9206294 [3396] 0.9209379 0.9212464 0.9212670 0.9213081 0.9213698 0.9215961 0.9220280 [3403] 0.9220897 0.9221925 0.9223982 0.9227273 0.9230769 0.9232003 0.9232415 [3410] 0.9232620 0.9236117 0.9238791 0.9239613 0.9239819 0.9242081 0.9246606 [3417] 0.9250720 0.9251748 0.9252982 0.9254628 0.9257919 0.9259564 0.9259770 [3424] 0.9260592 0.9260798 0.9262443 0.9266146 0.9269025 0.9269231 0.9270259 [3431] 0.9272522 0.9274990 0.9276018 0.9277869 0.9282394 0.9285068 0.9285479 [3438] 0.9286302 0.9287742 0.9290004 0.9293295 0.9295352 0.9296174 0.9296997 [3445] 0.9300905 0.9302962 0.9303373 0.9304196 0.9306458 0.9308104 0.9309749 [3452] 0.9309955 0.9310366 0.9311189 0.9312012 0.9314685 0.9316948 0.9318593 [3459] 0.9321473 0.9324352 0.9325998 0.9327232 0.9328466 0.9332785 0.9334430 [3466] 0.9335870 0.9336898 0.9338749 0.9341012 0.9343274 0.9344097 0.9344920 [3473] 0.9345331 0.9348005 0.9349239 0.9350473 0.9350679 0.9352735 0.9355204 [3480] 0.9358083 0.9358494 0.9359317 0.9361374 0.9365076 0.9365899 0.9367750 [3487] 0.9369601 0.9374332 0.9377828 0.9379268 0.9380090 0.9380913 0.9382970 [3494] 0.9386055 0.9387289 0.9387906 0.9389757 0.9392431 0.9393871 0.9394077 [3501] 0.9394282 0.9394899 0.9396339 0.9398807 0.9399630 0.9401070 0.9405800 [3508] 0.9409502 0.9409914 0.9412176 0.9415261 0.9417318 0.9418963 0.9419375 [3515] 0.9420814 0.9423694 0.9425339 0.9426162 0.9426573 0.9427396 0.9428013 [3522] 0.9430687 0.9430893 0.9431510 0.9432127 0.9432538 0.9436446 0.9438708 [3529] 0.9438914 0.9439325 0.9441176 0.9443645 0.9446524 0.9446730 0.9447552 [3536] 0.9451049 0.9452694 0.9453517 0.9454340 0.9457014 0.9458248 0.9459276 [3543] 0.9459893 0.9460304 0.9462567 0.9463184 0.9464007 0.9464212 0.9465858 [3550] 0.9468737 0.9471822 0.9472234 0.9473056 0.9473879 0.9476759 0.9478404 [3557] 0.9478610 0.9478815 0.9480666 0.9484780 0.9486425 0.9486837 0.9487248 [3564] 0.9488893 0.9490539 0.9492596 0.9493624 0.9494035 0.9497326 0.9499383 [3571] 0.9499589 0.9500411 0.9501851 0.9503291 0.9505759 0.9506582 0.9507199 [3578] 0.9509255 0.9512752 0.9513780 0.9513986 0.9515837 0.9517894 0.9519745 [3585] 0.9520568 0.9520979 0.9521802 0.9524681 0.9526738 0.9526944 0.9527355 [3592] 0.9529000 0.9531263 0.9534554 0.9535788 0.9536405 0.9536610 0.9539284 [3599] 0.9541547 0.9542369 0.9542781 0.9544426 0.9545455 0.9548540 0.9548951 [3606] 0.9550596 0.9553270 0.9553682 0.9554504 0.9555327 0.9556767 0.9560469 [3613] 0.9560880 0.9561086 0.9563760 0.9566228 0.9567256 0.9567668 0.9568490 [3620] 0.9571575 0.9573838 0.9574866 0.9575689 0.9575895 0.9577334 0.9578363 [3627] 0.9578980 0.9579186 0.9580008 0.9581654 0.9584327 0.9584739 0.9585561 [3634] 0.9586384 0.9587618 0.9587824 0.9588030 0.9589264 0.9592760 0.9594406 [3641] 0.9594817 0.9595640 0.9597491 0.9600165 0.9601604 0.9602016 0.9604689 [3648] 0.9605718 0.9606129 0.9606746 0.9607569 0.9608186 0.9609009 0.9609420 [3655] 0.9609626 0.9610037 0.9613328 0.9614768 0.9614973 0.9616619 0.9618881 [3662] 0.9621349 0.9621555 0.9622583 0.9625463 0.9626080 0.9626491 0.9626903 [3669] 0.9628754 0.9631016 0.9633690 0.9634307 0.9634718 0.9634924 0.9636569 [3676] 0.9638626 0.9638832 0.9640477 0.9642534 0.9645619 0.9647059 0.9650144 [3683] 0.9651172 0.9652201 0.9655492 0.9657960 0.9658371 0.9658782 0.9659399 [3690] 0.9660633 0.9661662 0.9662279 0.9662485 0.9663719 0.9665570 0.9667626 [3697] 0.9668038 0.9668655 0.9669066 0.9672151 0.9672357 0.9673385 0.9676265 [3704] 0.9679350 0.9680790 0.9683052 0.9684286 0.9685315 0.9685726 0.9686137 [3711] 0.9688194 0.9689428 0.9689840 0.9690045 0.9690868 0.9692925 0.9693336 [3718] 0.9693747 0.9693953 0.9695187 0.9696216 0.9696421 0.9697038 0.9698272 [3725] 0.9698889 0.9700535 0.9700740 0.9701357 0.9703826 0.9705060 0.9705677 [3732] 0.9706911 0.9708350 0.9711230 0.9711436 0.9711641 0.9712258 0.9713904 [3739] 0.9714932 0.9715343 0.9715755 0.9716989 0.9719251 0.9719868 0.9720485 [3746] 0.9720897 0.9721719 0.9723159 0.9723365 0.9723571 0.9725216 0.9726861 [3753] 0.9727684 0.9728301 0.9729329 0.9730975 0.9731386 0.9731798 0.9734471 [3760] 0.9736734 0.9736940 0.9737351 0.9738379 0.9740025 0.9740847 0.9741670 [3767] 0.9744344 0.9745784 0.9745989 0.9746812 0.9747635 0.9750103 0.9750720 [3774] 0.9753599 0.9754422 0.9755450 0.9757507 0.9759564 0.9759770 0.9761621 [3781] 0.9763677 0.9763883 0.9764706 0.9765940 0.9767585 0.9767791 0.9768408 [3788] 0.9769642 0.9770053 0.9771288 0.9772727 0.9774784 0.9775401 0.9777869 [3795] 0.9778898 0.9779720 0.9781983 0.9783628 0.9784245 0.9784862 0.9785479 [3802] 0.9786302 0.9786508 0.9786713 0.9787947 0.9789181 0.9790004 0.9790210 [3809] 0.9791238 0.9791444 0.9792884 0.9795352 0.9795763 0.9796586 0.9798231 [3816] 0.9799260 0.9799877 0.9800082 0.9800288 0.9802139 0.9802962 0.9803167 [3823] 0.9803373 0.9804401 0.9805019 0.9806664 0.9807487 0.9808926 0.9810160 [3830] 0.9810777 0.9814068 0.9815097 0.9817565 0.9817976 0.9818387 0.9819005 [3837] 0.9819827 0.9821267 0.9821473 0.9821678 0.9822090 0.9823735 0.9824146 [3844] 0.9824558 0.9827026 0.9827232 0.9827437 0.9828466 0.9829494 0.9830317 [3851] 0.9831962 0.9834019 0.9834225 0.9835047 0.9835459 0.9835870 0.9837310 [3858] 0.9838749 0.9841012 0.9841218 0.9841423 0.9841629 0.9843686 0.9844714 [3865] 0.9845537 0.9846565 0.9846977 0.9847182 0.9848828 0.9849445 0.9849856 [3872] 0.9851090 0.9852118 0.9853353 0.9853970 0.9854175 0.9855409 0.9856438 [3879] 0.9858083 0.9858494 0.9859317 0.9860140 0.9860551 0.9861580 0.9862608 [3886] 0.9862814 0.9863431 0.9865487 0.9865899 0.9866310 0.9867750 0.9869601 [3893] 0.9870012 0.9870218 0.9871041 0.9871863 0.9873303 0.9874126 0.9874332 [3900] 0.9874743 0.9875771 0.9875977 0.9876594 0.9878445 0.9880502 0.9881119 [3907] 0.9882147 0.9883381 0.9883587 0.9884204 0.9885438 0.9885849 0.9887906 [3914] 0.9888318 0.9888729 0.9889140 0.9889757 0.9890374 0.9891608 0.9892842 [3921] 0.9894077 0.9894282 0.9894694 0.9896133 0.9896339 0.9896956 0.9898807 [3928] 0.9899218 0.9900041 0.9901070 0.9901481 0.9902921 0.9903332 0.9903538 [3935] 0.9903743 0.9904360 0.9904566 0.9905389 0.9906828 0.9908063 0.9908680 [3942] 0.9910325 0.9910942 0.9911559 0.9912587 0.9914027 0.9914644 0.9914850 [3949] 0.9915261 0.9915878 0.9916907 0.9917318 0.9919169 0.9919580 0.9920403 [3956] 0.9922049 0.9922666 0.9923900 0.9924105 0.9924517 0.9925134 0.9926162 [3963] 0.9926573 0.9927396 0.9929042 0.9929453 0.9930070 0.9930481 0.9931304 [3970] 0.9932332 0.9932538 0.9932949 0.9933155 0.9933566 0.9934595 0.9935006 [3977] 0.9935212 0.9935418 0.9936446 0.9937063 0.9937474 0.9938297 0.9938503 [3984] 0.9938914 0.9939325 0.9939737 0.9941176 0.9941382 0.9941794 0.9942205 [3991] 0.9942411 0.9943233 0.9943645 0.9944879 0.9945084 0.9945290 0.9946318 [3998] 0.9946935 0.9947141 0.9947758 0.9949609 0.9950226 0.9950638 0.9951049 [4005] 0.9952283 0.9952489 0.9953928 0.9954751 0.9955368 0.9956191 0.9956602 [4012] 0.9956808 0.9957631 0.9958248 0.9958659 0.9959070 0.9959482 0.9959893 [4019] 0.9960099 0.9961127 0.9961538 0.9961950 0.9962155 0.9962361 0.9963390 [4026] 0.9963801 0.9964418 0.9965035 0.9965241 0.9965446 0.9965858 0.9967092 [4033] 0.9967297 0.9968531 0.9968943 0.9969148 0.9969971 0.9970177 0.9970383 [4040] 0.9971205 0.9972645 0.9973468 0.9973879 0.9974085 0.9974290 0.9975113 [4047] 0.9975319 0.9976142 0.9976759 0.9976964 0.9978198 0.9978610 0.9979021 [4054] 0.9979227 0.9979638 0.9979844 0.9980666 0.9980872 0.9981489 0.9981900 [4061] 0.9982517 0.9982723 0.9983135 0.9983340 0.9983546 0.9984163 0.9984574 [4068] 0.9985397 0.9985808 0.9986014 0.9986631 0.9987042 0.9987248 0.9988071 [4075] 0.9988688 0.9989099 0.9989305 0.9989716 0.9990950 0.9991362 0.9991567 [4082] 0.9991773 0.9992184 0.9992596 0.9993007 0.9993213 0.9993418 0.9993624 [4089] 0.9994035 0.9994241 0.9994447 0.9994858 0.9995269 0.9995886 0.9996503 [4096] 0.9996915 0.9997326 0.9997532 0.9997943 0.9998355 0.9998560 0.9998972 [4103] 0.9999177 0.9999589 0.9999794 1.0000000 > round(dp_it1_SR <- dperm(it1_SR, supp_it1_SR), 7) [1] 0.0000206 0.0000206 0.0000411 0.0000206 0.0000411 0.0000206 0.0000411 [8] 0.0000411 0.0000206 0.0000411 0.0000411 0.0000617 0.0000617 0.0000411 [15] 0.0000411 0.0000206 0.0000206 0.0000411 0.0000206 0.0000206 0.0000206 [22] 0.0000411 0.0000411 0.0000411 0.0000206 0.0000206 0.0000411 0.0001234 [29] 0.0000411 0.0000206 0.0000411 0.0000617 0.0000823 0.0000206 0.0000411 [36] 0.0000617 0.0000206 0.0000411 0.0000823 0.0000411 0.0000617 0.0000206 [43] 0.0000206 0.0000411 0.0000206 0.0000617 0.0000411 0.0000617 0.0000206 [50] 0.0000823 0.0000206 0.0000411 0.0000206 0.0000411 0.0000411 0.0001234 [57] 0.0000206 0.0000617 0.0000823 0.0000206 0.0000823 0.0000206 0.0000206 [64] 0.0000411 0.0000823 0.0001440 0.0000823 0.0000206 0.0000206 0.0000823 [71] 0.0000206 0.0000411 0.0001234 0.0000206 0.0001234 0.0000411 0.0000206 [78] 0.0000206 0.0000617 0.0000617 0.0000411 0.0001028 0.0000206 0.0000206 [85] 0.0000411 0.0000411 0.0001028 0.0000206 0.0000411 0.0000411 0.0000411 [92] 0.0000411 0.0000617 0.0000823 0.0000206 0.0000411 0.0000823 0.0000617 [99] 0.0000823 0.0001440 0.0000206 0.0001234 0.0000411 0.0000411 0.0000617 [106] 0.0001851 0.0000617 0.0000206 0.0000617 0.0001028 0.0000206 0.0000206 [113] 0.0001234 0.0000411 0.0000823 0.0000206 0.0000411 0.0000411 0.0000206 [120] 0.0001440 0.0000411 0.0000411 0.0000411 0.0000206 0.0000823 0.0000411 [127] 0.0000617 0.0001028 0.0000206 0.0000206 0.0000411 0.0001028 0.0000411 [134] 0.0000206 0.0000411 0.0000206 0.0001028 0.0000823 0.0000411 0.0000617 [141] 0.0000411 0.0001645 0.0000823 0.0000411 0.0001028 0.0000617 0.0000411 [148] 0.0000206 0.0001234 0.0000617 0.0001645 0.0000823 0.0000411 0.0001851 [155] 0.0000411 0.0001028 0.0000617 0.0000411 0.0000206 0.0000617 0.0001440 [162] 0.0001028 0.0000617 0.0000617 0.0001645 0.0000617 0.0001234 0.0001440 [169] 0.0000823 0.0000206 0.0000617 0.0000206 0.0000206 0.0000411 0.0001440 [176] 0.0000411 0.0001028 0.0000823 0.0000411 0.0001851 0.0000617 0.0000206 [183] 0.0001440 0.0000411 0.0000206 0.0001234 0.0001234 0.0001234 0.0000617 [190] 0.0000617 0.0000411 0.0000411 0.0000411 0.0002057 0.0000411 0.0001234 [197] 0.0000617 0.0000206 0.0001234 0.0001028 0.0000617 0.0002057 0.0001851 [204] 0.0000617 0.0000206 0.0001028 0.0000411 0.0000206 0.0000823 0.0001440 [211] 0.0000823 0.0000823 0.0000206 0.0000411 0.0001851 0.0001440 0.0000411 [218] 0.0000411 0.0002057 0.0000617 0.0000206 0.0001028 0.0001028 0.0000411 [225] 0.0000823 0.0000823 0.0000411 0.0001645 0.0001028 0.0001234 0.0000206 [232] 0.0000617 0.0001234 0.0001028 0.0001234 0.0000411 0.0000617 0.0001645 [239] 0.0000206 0.0000411 0.0001028 0.0000823 0.0001028 0.0002057 0.0000206 [246] 0.0000206 0.0000206 0.0002262 0.0001440 0.0001440 0.0000411 0.0000411 [253] 0.0000823 0.0000206 0.0002057 0.0001645 0.0000823 0.0001028 0.0001028 [260] 0.0000206 0.0000206 0.0002468 0.0000411 0.0000411 0.0001645 0.0000411 [267] 0.0000206 0.0000206 0.0001440 0.0000823 0.0000617 0.0000411 0.0000411 [274] 0.0002468 0.0001028 0.0003291 0.0000617 0.0001234 0.0001440 0.0000823 [281] 0.0001645 0.0000617 0.0001028 0.0000206 0.0000206 0.0000823 0.0001851 [288] 0.0000206 0.0000206 0.0000617 0.0001028 0.0001645 0.0000823 0.0000411 [295] 0.0002468 0.0001440 0.0000206 0.0001028 0.0000206 0.0000823 0.0001234 [302] 0.0001234 0.0000206 0.0000206 0.0000823 0.0000617 0.0000617 0.0000617 [309] 0.0001645 0.0002262 0.0000823 0.0001028 0.0002468 0.0000617 0.0002057 [316] 0.0001440 0.0001234 0.0000411 0.0001234 0.0000617 0.0000206 0.0001645 [323] 0.0001234 0.0000823 0.0000206 0.0002057 0.0001851 0.0000206 0.0002057 [330] 0.0002057 0.0001028 0.0000823 0.0002879 0.0000617 0.0002468 0.0000823 [337] 0.0000823 0.0000206 0.0001440 0.0002674 0.0000823 0.0000823 0.0001645 [344] 0.0001028 0.0000411 0.0000206 0.0002262 0.0002674 0.0000411 0.0000411 [351] 0.0001645 0.0001028 0.0000617 0.0000823 0.0001645 0.0001645 0.0000206 [358] 0.0000206 0.0001440 0.0000823 0.0000411 0.0000617 0.0000617 0.0002262 [365] 0.0001234 0.0000411 0.0000411 0.0001028 0.0001645 0.0000617 0.0000206 [372] 0.0000206 0.0002879 0.0001440 0.0001234 0.0000617 0.0001234 0.0002468 [379] 0.0000617 0.0000206 0.0001645 0.0000617 0.0001234 0.0000617 0.0000206 [386] 0.0001028 0.0001234 0.0000206 0.0000411 0.0000411 0.0002057 0.0000823 [393] 0.0000206 0.0000411 0.0001234 0.0002057 0.0000411 0.0000411 0.0001028 [400] 0.0001234 0.0002262 0.0001440 0.0003085 0.0002879 0.0001028 0.0000206 [407] 0.0003085 0.0000411 0.0000617 0.0000411 0.0002057 0.0001851 0.0001234 [414] 0.0000206 0.0000617 0.0001028 0.0001234 0.0000617 0.0000411 0.0000411 [421] 0.0002468 0.0003291 0.0001028 0.0001028 0.0003085 0.0001440 0.0003085 [428] 0.0002057 0.0001645 0.0000206 0.0002057 0.0001645 0.0000206 0.0000411 [435] 0.0000617 0.0002674 0.0002262 0.0001851 0.0000411 0.0000411 0.0000617 [442] 0.0002879 0.0001028 0.0000206 0.0002468 0.0002262 0.0001645 0.0000206 [449] 0.0001440 0.0003291 0.0000411 0.0000206 0.0000411 0.0000823 0.0000617 [456] 0.0000823 0.0000617 0.0000411 0.0001028 0.0002674 0.0000411 0.0001440 [463] 0.0002674 0.0001851 0.0000823 0.0000411 0.0001645 0.0003497 0.0001234 [470] 0.0000206 0.0000206 0.0001234 0.0000823 0.0000823 0.0000411 0.0002674 [477] 0.0001645 0.0000823 0.0000206 0.0000617 0.0001028 0.0001440 0.0000206 [484] 0.0000823 0.0001028 0.0002262 0.0003085 0.0000823 0.0000411 0.0001028 [491] 0.0002468 0.0002674 0.0000206 0.0000411 0.0003702 0.0001440 0.0000823 [498] 0.0000823 0.0000411 0.0002674 0.0001645 0.0000411 0.0003085 0.0001028 [505] 0.0001645 0.0000411 0.0000823 0.0002262 0.0002674 0.0000206 0.0000617 [512] 0.0001234 0.0003291 0.0002262 0.0001645 0.0000411 0.0000206 0.0002057 [519] 0.0002879 0.0000823 0.0000411 0.0000823 0.0001851 0.0002057 0.0001851 [526] 0.0000206 0.0001028 0.0003497 0.0002057 0.0000617 0.0000823 0.0002468 [533] 0.0001440 0.0001440 0.0000823 0.0000206 0.0002057 0.0003291 0.0000411 [540] 0.0001028 0.0002057 0.0001645 0.0001645 0.0000411 0.0000411 0.0001645 [547] 0.0004114 0.0001851 0.0000206 0.0000206 0.0001645 0.0002879 0.0000823 [554] 0.0000823 0.0000411 0.0003085 0.0002879 0.0001645 0.0000206 0.0000823 [561] 0.0000617 0.0002262 0.0000411 0.0000617 0.0001028 0.0001234 0.0002674 [568] 0.0000823 0.0000823 0.0001645 0.0003497 0.0000823 0.0000206 0.0002879 [575] 0.0002468 0.0001851 0.0000411 0.0000206 0.0002262 0.0003908 0.0000411 [582] 0.0000617 0.0000617 0.0000206 0.0002674 0.0000617 0.0000823 0.0000411 [589] 0.0000823 0.0001645 0.0002879 0.0001440 0.0000411 0.0001645 0.0002057 [596] 0.0003085 0.0002262 0.0000411 0.0003702 0.0004731 0.0001440 0.0000823 [603] 0.0002468 0.0001440 0.0000617 0.0000206 0.0000206 0.0001440 0.0002674 [610] 0.0001851 0.0000617 0.0001234 0.0003085 0.0002057 0.0000823 0.0000823 [617] 0.0001440 0.0003497 0.0004731 0.0001851 0.0001851 0.0000823 0.0003702 [624] 0.0002057 0.0000823 0.0000411 0.0002879 0.0002468 0.0002057 0.0000206 [631] 0.0001234 0.0001234 0.0002674 0.0000411 0.0000823 0.0000823 0.0002262 [638] 0.0002262 0.0001851 0.0001028 0.0001440 0.0001645 0.0004319 0.0001234 [645] 0.0001234 0.0001645 0.0002879 0.0002879 0.0001645 0.0002262 0.0002674 [652] 0.0000823 0.0000823 0.0000411 0.0000206 0.0001645 0.0001645 0.0002262 [659] 0.0000823 0.0000411 0.0002057 0.0003908 0.0000823 0.0000823 0.0002057 [666] 0.0003291 0.0002262 0.0001440 0.0000823 0.0000411 0.0002674 0.0004525 [673] 0.0001851 0.0001028 0.0002468 0.0002262 0.0001028 0.0000206 0.0002879 [680] 0.0003702 0.0001645 0.0000206 0.0000823 0.0000206 0.0001645 0.0003291 [687] 0.0001645 0.0001234 0.0001028 0.0004114 0.0004525 0.0002262 0.0000206 [694] 0.0000823 0.0002674 0.0003497 0.0000206 0.0000411 0.0001234 0.0003497 [701] 0.0003291 0.0002057 0.0001028 0.0000617 0.0004319 0.0002262 0.0000617 [708] 0.0000411 0.0000206 0.0003085 0.0003085 0.0002879 0.0000617 0.0001028 [715] 0.0002674 0.0005348 0.0001028 0.0000206 0.0001440 0.0000206 0.0002879 [722] 0.0001851 0.0001851 0.0000823 0.0001028 0.0002057 0.0003702 0.0000617 [729] 0.0000617 0.0002262 0.0003497 0.0003291 0.0002468 0.0000411 0.0000617 [736] 0.0001234 0.0005142 0.0002262 0.0001028 0.0001645 0.0002468 0.0002468 [743] 0.0001851 0.0001234 0.0000823 0.0000206 0.0002468 0.0004114 0.0000823 [750] 0.0000411 0.0002468 0.0001028 0.0001645 0.0001440 0.0001440 0.0001234 [757] 0.0002879 0.0005553 0.0002468 0.0000617 0.0002057 0.0002879 0.0004114 [764] 0.0000823 0.0000823 0.0000411 0.0000206 0.0003291 0.0003085 0.0000617 [771] 0.0000617 0.0001234 0.0001028 0.0002674 0.0001234 0.0001645 0.0001645 [778] 0.0003291 0.0003085 0.0002057 0.0000206 0.0001851 0.0002674 0.0005965 [785] 0.0001028 0.0000823 0.0001645 0.0000206 0.0003291 0.0003702 0.0002879 [792] 0.0000411 0.0002468 0.0003497 0.0001440 0.0000411 0.0000823 0.0000206 [799] 0.0003497 0.0001851 0.0001440 0.0000823 0.0001440 0.0001851 0.0005759 [806] 0.0002468 0.0001028 0.0002879 0.0003497 0.0003497 0.0003085 0.0000823 [813] 0.0000206 0.0002879 0.0005348 0.0001645 0.0001440 0.0003497 0.0003497 [820] 0.0002262 0.0000823 0.0000206 0.0000206 0.0002057 0.0005759 0.0002674 [827] 0.0001234 0.0001851 0.0002057 0.0003291 0.0001440 0.0001645 0.0002468 [834] 0.0000206 0.0003908 0.0005553 0.0003085 0.0001645 0.0001440 0.0003702 [841] 0.0001645 0.0001028 0.0000823 0.0002057 0.0003702 0.0001645 0.0000206 [848] 0.0001234 0.0000206 0.0001645 0.0004731 0.0001028 0.0001234 0.0001234 [855] 0.0000617 0.0002468 0.0003702 0.0002262 0.0001851 0.0002057 0.0002057 [862] 0.0006376 0.0001440 0.0001440 0.0002057 0.0003702 0.0003291 0.0002262 [869] 0.0001234 0.0002468 0.0004114 0.0001028 0.0000617 0.0002468 0.0000411 [876] 0.0001234 0.0003291 0.0003085 0.0000823 0.0000617 0.0000411 0.0002468 [883] 0.0005142 0.0001851 0.0001028 0.0002262 0.0003291 0.0003497 0.0001234 [890] 0.0000823 0.0001234 0.0003291 0.0006787 0.0001851 0.0000823 0.0002468 [897] 0.0002674 0.0002674 0.0001645 0.0001028 0.0001234 0.0000206 0.0002879 [904] 0.0006170 0.0003497 0.0002468 0.0001645 0.0004731 0.0002879 0.0001440 [911] 0.0001234 0.0000206 0.0004525 0.0005142 0.0002879 0.0000617 0.0001440 [918] 0.0002057 0.0004114 0.0000617 0.0000823 0.0002057 0.0002879 0.0003497 [925] 0.0003702 0.0001028 0.0002262 0.0001440 0.0006787 0.0002468 0.0001645 [932] 0.0002262 0.0003085 0.0005142 0.0002468 0.0000823 0.0001028 0.0000206 [939] 0.0002262 0.0005759 0.0002057 0.0001028 0.0001851 0.0000206 0.0003291 [946] 0.0002879 0.0004319 0.0001234 0.0001851 0.0002057 0.0006170 0.0000823 [953] 0.0001234 0.0003291 0.0000206 0.0003702 0.0004319 0.0002468 0.0001440 [960] 0.0000411 0.0000411 0.0001851 0.0006170 0.0002057 0.0001028 0.0002057 [967] 0.0000206 0.0002262 0.0003497 0.0001440 0.0001028 0.0000617 0.0000617 [974] 0.0002262 0.0005965 0.0002057 0.0000617 0.0003085 0.0000411 0.0001645 [981] 0.0003702 0.0002262 0.0001645 0.0002879 0.0004319 0.0006170 0.0003291 [988] 0.0000411 0.0001645 0.0000206 0.0003291 0.0004525 0.0001645 0.0001028 [995] 0.0000411 0.0000617 0.0003908 0.0004114 0.0002468 0.0000411 0.0001440 [1002] 0.0001234 0.0005348 0.0002262 0.0001851 0.0002262 0.0000411 0.0003497 [1009] 0.0003908 0.0002879 0.0001028 0.0003085 0.0002468 0.0007199 0.0002057 [1016] 0.0000206 0.0002879 0.0003497 0.0004525 0.0004525 0.0000411 0.0001028 [1023] 0.0002674 0.0005965 0.0001645 0.0000823 0.0002879 0.0000411 0.0004114 [1030] 0.0004319 0.0003085 0.0001440 0.0001440 0.0000411 0.0001645 0.0006170 [1037] 0.0002879 0.0002057 0.0003497 0.0003497 0.0004319 0.0003908 0.0002057 [1044] 0.0001851 0.0002879 0.0008433 0.0002262 0.0000206 0.0003497 0.0000206 [1051] 0.0002057 0.0003085 0.0001851 0.0001851 0.0001234 0.0000617 0.0001645 [1058] 0.0006993 0.0003291 0.0001440 0.0003291 0.0002674 0.0004731 0.0002262 [1065] 0.0002057 0.0002468 0.0000206 0.0003702 0.0006376 0.0002879 0.0001234 [1072] 0.0002468 0.0002262 0.0004936 0.0002262 0.0002674 0.0001645 0.0000206 [1079] 0.0003497 0.0003497 0.0002468 0.0000206 0.0002057 0.0000617 0.0001645 [1086] 0.0005965 0.0001851 0.0001645 0.0002879 0.0000823 0.0002262 0.0005759 [1093] 0.0003702 0.0001645 0.0002468 0.0003085 0.0007816 0.0001440 0.0001440 [1100] 0.0002262 0.0000411 0.0004731 0.0003908 0.0001645 0.0000411 0.0001851 [1107] 0.0002262 0.0005142 0.0002879 0.0000823 0.0003497 0.0000411 0.0002674 [1114] 0.0004525 0.0003702 0.0001440 0.0001234 0.0000411 0.0002262 0.0008227 [1121] 0.0002468 0.0001440 0.0003497 0.0000617 0.0003908 0.0004525 0.0002674 [1128] 0.0001234 0.0001234 0.0000411 0.0003702 0.0005759 0.0003291 0.0001234 [1135] 0.0003702 0.0002674 0.0004114 0.0001645 0.0001851 0.0003085 0.0000206 [1142] 0.0003497 0.0008227 0.0003908 0.0000823 0.0002674 0.0002262 0.0005759 [1149] 0.0002879 0.0002468 0.0001440 0.0000411 0.0003291 0.0005553 0.0003497 [1156] 0.0000823 0.0002674 0.0000411 0.0002262 0.0005142 0.0002057 0.0001851 [1163] 0.0003702 0.0000411 0.0003085 0.0004525 0.0003291 0.0002057 0.0003497 [1170] 0.0002468 0.0007199 0.0002262 0.0002468 0.0003702 0.0000411 0.0004936 [1177] 0.0005553 0.0003908 0.0001028 0.0002262 0.0000411 0.0002057 0.0006787 [1184] 0.0001440 0.0001851 0.0003497 0.0000617 0.0001440 0.0004731 0.0003908 [1191] 0.0002262 0.0002674 0.0002674 0.0006376 0.0001851 0.0001440 0.0004731 [1198] 0.0000206 0.0003085 0.0005142 0.0002468 0.0001645 0.0001851 0.0000411 [1205] 0.0002468 0.0008433 0.0002674 0.0002057 0.0003702 0.0000206 0.0003085 [1212] 0.0003291 0.0001645 0.0001645 0.0001645 0.0001028 0.0002674 0.0007199 [1219] 0.0002674 0.0001234 0.0003908 0.0000411 0.0001234 0.0005142 0.0003497 [1226] 0.0002674 0.0003085 0.0004319 0.0006993 0.0004936 0.0000617 0.0003085 [1233] 0.0002468 0.0005965 0.0001645 0.0001028 0.0002468 0.0000411 0.0003908 [1240] 0.0005348 0.0002674 0.0001440 0.0001851 0.0000411 0.0001645 0.0006787 [1247] 0.0002674 0.0002262 0.0002879 0.0000411 0.0003085 0.0005965 0.0004525 [1254] 0.0001440 0.0004319 0.0002468 0.0008433 0.0003085 0.0001645 0.0004114 [1261] 0.0000411 0.0004319 0.0005348 0.0004114 0.0002057 0.0002468 0.0001645 [1268] 0.0006376 0.0001234 0.0001028 0.0003702 0.0000617 0.0003085 0.0005142 [1275] 0.0004525 0.0001440 0.0002674 0.0000823 0.0001851 0.0009667 0.0003291 [1282] 0.0002879 0.0005965 0.0003291 0.0005759 0.0002879 0.0002879 0.0001645 [1289] 0.0000411 0.0003085 0.0006376 0.0001851 0.0001234 0.0004114 0.0000411 [1296] 0.0001851 0.0003291 0.0002879 0.0001851 0.0003085 0.0001028 0.0001645 [1303] 0.0008227 0.0003291 0.0001851 0.0004525 0.0000617 0.0002674 0.0005965 [1310] 0.0002674 0.0003497 0.0002879 0.0001028 0.0003908 0.0006787 0.0003291 [1317] 0.0000823 0.0003291 0.0002879 0.0005348 0.0002674 0.0002262 0.0003497 [1324] 0.0000617 0.0003291 0.0004731 0.0003085 0.0001028 0.0003908 0.0000617 [1331] 0.0001851 0.0006993 0.0002879 0.0002057 0.0004319 0.0000823 0.0003291 [1338] 0.0006582 0.0004525 0.0001851 0.0002879 0.0002674 0.0008021 0.0001851 [1345] 0.0001440 0.0003497 0.0000411 0.0002674 0.0004731 0.0003291 0.0001234 [1352] 0.0003497 0.0001645 0.0006170 0.0003291 0.0002468 0.0005553 0.0000411 [1359] 0.0004525 0.0005965 0.0004525 0.0002674 0.0002468 0.0000411 0.0002879 [1366] 0.0010490 0.0003291 0.0000823 0.0004525 0.0000411 0.0002468 0.0004319 [1373] 0.0003702 0.0001851 0.0002057 0.0000823 0.0002262 0.0007610 0.0004114 [1380] 0.0002262 0.0005553 0.0003291 0.0005142 0.0002468 0.0002879 0.0003908 [1387] 0.0000411 0.0002879 0.0008433 0.0003497 0.0001851 0.0004319 0.0000206 [1394] 0.0002057 0.0006376 0.0003702 0.0003497 0.0003702 0.0000617 0.0003291 [1401] 0.0006787 0.0003702 0.0000617 0.0003702 0.0001028 0.0002057 0.0006582 [1408] 0.0002468 0.0003291 0.0003085 0.0001440 0.0002674 0.0006582 0.0005142 [1415] 0.0002468 0.0005348 0.0002674 0.0007610 0.0002674 0.0002674 0.0004525 [1422] 0.0000823 0.0003085 0.0006170 0.0002262 0.0001645 0.0003085 0.0000823 [1429] 0.0001851 0.0007199 0.0002057 0.0002674 0.0004114 0.0000823 0.0002057 [1436] 0.0005142 0.0003702 0.0001645 0.0003497 0.0000823 0.0002262 0.0008227 [1443] 0.0002674 0.0002468 0.0007199 0.0001028 0.0003085 0.0005965 0.0003908 [1450] 0.0001645 0.0002262 0.0000411 0.0003291 0.0006993 0.0003497 0.0001851 [1457] 0.0003908 0.0000206 0.0003702 0.0003702 0.0001851 0.0002262 0.0003085 [1464] 0.0001234 0.0002674 0.0008638 0.0003702 0.0001645 0.0006170 0.0000617 [1471] 0.0001851 0.0005965 0.0003908 0.0003702 0.0004525 0.0000206 0.0003085 [1478] 0.0008021 0.0004731 0.0001440 0.0004114 0.0003085 0.0006582 0.0002057 [1485] 0.0001645 0.0003702 0.0000617 0.0003908 0.0005965 0.0003085 0.0002057 [1492] 0.0004936 0.0000617 0.0001645 0.0007199 0.0003085 0.0004114 0.0005965 [1499] 0.0000617 0.0003908 0.0007404 0.0005965 0.0002674 0.0004114 0.0000411 [1506] 0.0002674 0.0008021 0.0002468 0.0002674 0.0004114 0.0000617 0.0003497 [1513] 0.0004731 0.0004319 0.0002468 0.0004114 0.0000206 0.0001851 0.0006376 [1520] 0.0001851 0.0002468 0.0006787 0.0001440 0.0002057 0.0006170 0.0003908 [1527] 0.0003291 0.0003702 0.0001440 0.0001440 0.0010901 0.0003085 0.0003291 [1534] 0.0005965 0.0000206 0.0003702 0.0005553 0.0003085 0.0002262 0.0002057 [1541] 0.0000617 0.0002468 0.0006993 0.0002468 0.0001851 0.0006582 0.0000823 [1548] 0.0001851 0.0003908 0.0004114 0.0003908 0.0004114 0.0001440 0.0002879 [1555] 0.0008021 0.0004114 0.0001851 0.0005142 0.0000617 0.0001851 0.0007199 [1562] 0.0002468 0.0002468 0.0003908 0.0001440 0.0002674 0.0008638 0.0003497 [1569] 0.0001440 0.0004936 0.0000206 0.0001440 0.0005965 0.0002674 0.0003291 [1576] 0.0004319 0.0000823 0.0002879 0.0006787 0.0003085 0.0001645 0.0005965 [1583] 0.0000411 0.0001851 0.0008433 0.0003291 0.0002468 0.0004731 0.0000823 [1590] 0.0003702 0.0006170 0.0004731 0.0002262 0.0003497 0.0000617 0.0001851 [1597] 0.0007610 0.0001645 0.0002262 0.0005142 0.0001440 0.0003085 0.0005759 [1604] 0.0004936 0.0002674 0.0003908 0.0000823 0.0001645 0.0008227 0.0003291 [1611] 0.0003497 0.0007816 0.0003291 0.0006376 0.0004114 0.0003085 0.0003702 [1618] 0.0000823 0.0002262 0.0009461 0.0003085 0.0001645 0.0006582 0.0000823 [1625] 0.0003085 0.0004525 0.0004114 0.0002879 0.0003497 0.0000823 0.0001440 [1632] 0.0009461 0.0003497 0.0002262 0.0006582 0.0000411 0.0003085 0.0004936 [1639] 0.0003497 0.0004114 0.0005142 0.0001851 0.0002674 0.0008844 0.0003291 [1646] 0.0002262 0.0006170 0.0000206 0.0002262 0.0006582 0.0002674 0.0004936 [1653] 0.0004319 0.0000823 0.0003085 0.0006787 0.0003291 0.0001440 0.0005759 [1660] 0.0001028 0.0000823 0.0007610 0.0003085 0.0002468 0.0006787 0.0002057 [1667] 0.0001645 0.0006993 0.0004936 0.0002468 0.0005759 0.0000617 0.0002057 [1674] 0.0006787 0.0003085 0.0003497 0.0004319 0.0001028 0.0003085 0.0005348 [1681] 0.0002674 0.0001851 0.0003702 0.0000411 0.0001851 0.0007199 0.0002057 [1688] 0.0003291 0.0005965 0.0001851 0.0002468 0.0005553 0.0004114 0.0003497 [1695] 0.0004319 0.0000823 0.0001440 0.0009461 0.0004114 0.0002468 0.0007404 [1702] 0.0000617 0.0002468 0.0006170 0.0005553 0.0002057 0.0002879 0.0000617 [1709] 0.0002468 0.0008227 0.0003497 0.0001851 0.0006582 0.0000411 0.0002468 [1716] 0.0004319 0.0002674 0.0002057 0.0004114 0.0001851 0.0001851 0.0008021 [1723] 0.0004319 0.0002468 0.0006582 0.0000617 0.0002262 0.0007404 0.0003702 [1730] 0.0004936 0.0004936 0.0000411 0.0003085 0.0011107 0.0004114 0.0001440 [1737] 0.0005348 0.0000617 0.0001234 0.0005759 0.0003085 0.0003291 0.0005142 [1744] 0.0001851 0.0002468 0.0006170 0.0005142 0.0002468 0.0007610 0.0001234 [1751] 0.0001645 0.0008433 0.0003085 0.0004114 0.0005965 0.0001234 0.0002674 [1758] 0.0008021 0.0004731 0.0002674 0.0004319 0.0001028 0.0002057 0.0008433 [1765] 0.0002879 0.0003085 0.0005348 0.0001440 0.0002057 0.0005142 0.0004525 [1772] 0.0002468 0.0004525 0.0001440 0.0001645 0.0006787 0.0001645 0.0004114 [1779] 0.0007816 0.0001851 0.0001645 0.0006170 0.0004731 0.0002879 0.0004731 [1786] 0.0001028 0.0001645 0.0009872 0.0003497 0.0002674 0.0007610 0.0001028 [1793] 0.0003702 0.0005759 0.0002674 0.0002468 0.0003497 0.0002262 0.0001851 [1800] 0.0008638 0.0004114 0.0002262 0.0005965 0.0000617 0.0001440 0.0003908 [1807] 0.0003497 0.0003702 0.0005142 0.0001234 0.0002674 0.0008227 0.0003497 [1814] 0.0002468 0.0007816 0.0001234 0.0001645 0.0007199 0.0002674 0.0002674 [1821] 0.0004936 0.0001851 0.0002674 0.0006170 0.0003908 0.0002057 0.0005142 [1828] 0.0000617 0.0001440 0.0006993 0.0002468 0.0003497 0.0006582 0.0000823 [1835] 0.0003291 0.0007610 0.0004525 0.0002674 0.0006582 0.0000617 0.0001851 [1842] 0.0007610 0.0003085 0.0004319 0.0005553 0.0001234 0.0003291 0.0005553 [1849] 0.0005553 0.0003085 0.0004936 0.0001028 0.0002057 0.0007610 0.0002262 [1856] 0.0001851 0.0006582 0.0002057 0.0002057 0.0005348 0.0003908 0.0003085 [1863] 0.0004936 0.0001645 0.0000823 0.0008638 0.0003291 0.0004114 0.0009050 [1870] 0.0000617 0.0003702 0.0006170 0.0005553 0.0003497 0.0004114 0.0001234 [1877] 0.0002262 0.0008844 0.0002262 0.0003085 0.0008021 0.0001234 0.0001645 [1884] 0.0005348 0.0003497 0.0004525 0.0004114 0.0002057 0.0001851 0.0007816 [1891] 0.0004114 0.0002468 0.0008021 0.0001234 0.0001440 0.0005553 0.0004319 [1898] 0.0004114 0.0005759 0.0002674 0.0001851 0.0010490 0.0004319 0.0002674 [1905] 0.0005759 0.0000823 0.0001851 0.0005142 0.0002057 0.0004731 0.0005142 [1912] 0.0001440 0.0002057 0.0005348 0.0001645 0.0001645 0.0007610 0.0001851 [1919] 0.0000823 0.0007404 0.0003085 0.0003908 0.0006582 0.0002262 0.0002057 [1926] 0.0008021 0.0005142 0.0003085 0.0005759 0.0000411 0.0001440 0.0008638 [1933] 0.0002879 0.0002674 0.0005142 0.0001645 0.0002468 0.0005142 0.0004114 [1940] 0.0002674 0.0004731 0.0001440 0.0001234 0.0005348 0.0002262 0.0003497 [1947] 0.0007404 0.0001851 0.0002468 0.0005553 0.0003497 0.0003702 0.0005965 [1954] 0.0001028 0.0001645 0.0010078 0.0003702 0.0003085 0.0008021 0.0001234 [1961] 0.0002879 0.0006170 0.0003497 0.0002674 0.0003908 0.0001234 0.0001440 [1968] 0.0008021 0.0002879 0.0002468 0.0007404 0.0000823 0.0002262 0.0004114 [1975] 0.0004114 0.0003702 0.0005965 0.0002057 0.0001645 0.0008844 0.0004114 [1982] 0.0003497 0.0009255 0.0000823 0.0002262 0.0007199 0.0002879 0.0005348 [1989] 0.0005553 0.0001645 0.0003291 0.0007199 0.0003702 0.0001851 0.0005553 [1996] 0.0001645 0.0001028 0.0005348 0.0002879 0.0003908 0.0006170 0.0002057 [2003] 0.0000617 0.0006787 0.0004114 0.0003291 0.0008433 0.0001234 0.0001234 [2010] 0.0007199 0.0003085 0.0004936 0.0007199 0.0002262 0.0002057 0.0006582 [2017] 0.0003291 0.0002468 0.0006376 0.0001028 0.0001645 0.0007199 0.0003085 [2024] 0.0003702 0.0006376 0.0002262 0.0002057 0.0005553 0.0003908 0.0003085 [2031] 0.0005348 0.0001234 0.0001028 0.0006787 0.0002262 0.0004319 0.0009050 [2038] 0.0002468 0.0001440 0.0006170 0.0004936 0.0003702 0.0004936 0.0001851 [2045] 0.0001645 0.0007199 0.0002879 0.0003291 0.0008638 0.0000823 0.0001440 [2052] 0.0004731 0.0001851 0.0001851 0.0004731 0.0001440 0.0000823 0.0008638 [2059] 0.0003291 0.0002879 0.0007199 0.0001645 0.0001851 0.0004936 0.0003702 [2066] 0.0004936 0.0006170 0.0001440 0.0002468 0.0009050 0.0004319 0.0002262 [2073] 0.0006787 0.0001028 0.0001234 0.0005348 0.0003085 0.0003908 0.0005553 [2080] 0.0002057 0.0002262 0.0006376 0.0003702 0.0003085 0.0007199 0.0001645 [2087] 0.0001028 0.0006376 0.0002468 0.0003291 0.0006582 0.0002057 0.0002262 [2094] 0.0007199 0.0004936 0.0003085 0.0007199 0.0001234 0.0001234 0.0008433 [2101] 0.0003291 0.0004114 0.0006787 0.0000617 0.0002057 0.0006170 0.0003908 [2108] 0.0002879 0.0005348 0.0001028 0.0001645 0.0005553 0.0001851 0.0003702 [2115] 0.0007199 0.0003291 0.0001645 0.0005553 0.0005348 0.0002879 0.0007199 [2122] 0.0002262 0.0000823 0.0009255 0.0003497 0.0004114 0.0008844 0.0001645 [2129] 0.0002057 0.0005965 0.0003702 0.0004114 0.0004114 0.0002262 0.0000823 [2136] 0.0007404 0.0002468 0.0002879 0.0008021 0.0001440 0.0001234 0.0003908 [2143] 0.0002674 0.0003497 0.0006170 0.0002879 0.0001234 0.0008021 0.0003085 [2150] 0.0003702 0.0010078 0.0001645 0.0001028 0.0005965 0.0003702 0.0003497 [2157] 0.0005553 0.0002468 0.0001851 0.0007404 0.0003497 0.0002262 0.0005348 [2164] 0.0001234 0.0001440 0.0004731 0.0002674 0.0004114 0.0005142 0.0002468 [2171] 0.0001645 0.0005142 0.0002674 0.0002879 0.0008638 0.0001440 0.0000411 [2178] 0.0005759 0.0003085 0.0005142 0.0008021 0.0002057 0.0002262 0.0006582 [2185] 0.0003908 0.0003085 0.0007404 0.0000823 0.0001851 0.0007610 0.0001645 [2192] 0.0001645 0.0005348 0.0002057 0.0001440 0.0005142 0.0004731 0.0002057 [2199] 0.0005142 0.0001851 0.0000823 0.0005759 0.0002674 0.0004319 0.0010490 [2206] 0.0001851 0.0002674 0.0005759 0.0004114 0.0004319 0.0005553 0.0001440 [2213] 0.0001234 0.0008021 0.0002468 0.0004114 0.0007816 0.0001851 0.0002057 [2220] 0.0004114 0.0004525 0.0003497 0.0005348 0.0001645 0.0001234 0.0008021 [2227] 0.0003085 0.0002262 0.0008844 0.0002262 0.0001234 0.0004114 0.0003497 [2234] 0.0005553 0.0006170 0.0003702 0.0000617 0.0009050 0.0004114 0.0003291 [2241] 0.0008638 0.0000823 0.0001645 0.0004936 0.0003085 0.0003908 0.0005348 [2248] 0.0002057 0.0002057 0.0006582 0.0001851 0.0002262 0.0007610 0.0002057 [2255] 0.0001028 0.0004936 0.0003085 0.0005553 0.0005553 0.0003291 0.0001234 [2262] 0.0005553 0.0004319 0.0003085 0.0007610 0.0001851 0.0000617 0.0006582 [2269] 0.0002674 0.0004525 0.0007610 0.0003291 0.0000823 0.0006582 0.0003497 [2276] 0.0002468 0.0006993 0.0001440 0.0000617 0.0005142 0.0002057 0.0003908 [2283] 0.0006170 0.0002674 0.0001851 0.0004936 0.0002674 0.0002674 0.0007199 [2290] 0.0001645 0.0001234 0.0007816 0.0002468 0.0003497 0.0008227 0.0002674 [2297] 0.0001234 0.0005142 0.0003702 0.0003497 0.0003908 0.0001440 0.0000617 [2304] 0.0005965 0.0002262 0.0004114 0.0008638 0.0001851 0.0002262 0.0003497 [2311] 0.0002468 0.0002674 0.0005759 0.0003702 0.0001028 0.0007610 0.0002674 [2318] 0.0003497 0.0009872 0.0001645 0.0001028 0.0004731 0.0002879 0.0004731 [2325] 0.0006170 0.0001645 0.0001851 0.0007816 0.0004114 0.0001645 0.0006787 [2332] 0.0001645 0.0001440 0.0004525 0.0002468 0.0004525 0.0005142 0.0002057 [2339] 0.0001440 0.0005348 0.0003085 0.0002879 0.0008433 0.0002057 0.0001028 [2346] 0.0004319 0.0002674 0.0004731 0.0008021 0.0002674 0.0001234 0.0005965 [2353] 0.0004114 0.0003085 0.0008433 0.0001645 0.0001234 0.0007610 0.0002468 [2360] 0.0005142 0.0006170 0.0002468 0.0001851 0.0005142 0.0003291 0.0003085 [2367] 0.0005759 0.0001234 0.0000617 0.0005348 0.0001440 0.0004114 0.0011107 [2374] 0.0003085 0.0000411 0.0004936 0.0004936 0.0003702 0.0007404 0.0002262 [2381] 0.0000617 0.0006582 0.0002468 0.0004319 0.0008021 0.0001851 0.0001851 [2388] 0.0004114 0.0002057 0.0002674 0.0004319 0.0002468 0.0000411 0.0006582 [2395] 0.0001851 0.0003497 0.0008227 0.0002468 0.0000617 0.0002879 0.0002057 [2402] 0.0005553 0.0006170 0.0002468 0.0000617 0.0007404 0.0002468 0.0004114 [2409] 0.0009461 0.0001440 0.0000823 0.0004319 0.0003497 0.0004114 0.0005553 [2416] 0.0002468 0.0001851 0.0005965 0.0003291 0.0002057 0.0007199 0.0001851 [2423] 0.0000411 0.0003702 0.0001851 0.0002674 0.0005348 0.0003085 0.0001028 [2430] 0.0004319 0.0003497 0.0003085 0.0006787 0.0002057 0.0000617 0.0005759 [2437] 0.0002468 0.0004936 0.0006993 0.0001645 0.0002057 0.0006787 0.0002468 [2444] 0.0003085 0.0007610 0.0000823 0.0001028 0.0005759 0.0001440 0.0003291 [2451] 0.0006787 0.0003085 0.0000823 0.0004319 0.0004936 0.0002674 0.0006582 [2458] 0.0002262 0.0000206 0.0006170 0.0002262 0.0003291 0.0008844 0.0002674 [2465] 0.0001851 0.0005142 0.0004114 0.0003497 0.0004936 0.0003085 0.0000411 [2472] 0.0006582 0.0002262 0.0003497 0.0009461 0.0001440 0.0000823 0.0003497 [2479] 0.0002879 0.0004114 0.0004525 0.0003085 0.0000823 0.0006582 0.0001645 [2486] 0.0003085 0.0009461 0.0002262 0.0000823 0.0003702 0.0003085 0.0004114 [2493] 0.0006376 0.0003291 0.0007816 0.0003497 0.0003291 0.0008227 0.0001645 [2500] 0.0000823 0.0003908 0.0002674 0.0004936 0.0005759 0.0003085 0.0001440 [2507] 0.0005142 0.0002262 0.0001645 0.0007610 0.0001851 0.0000617 0.0003497 [2514] 0.0002262 0.0004731 0.0006170 0.0003702 0.0000823 0.0004731 0.0002468 [2521] 0.0003291 0.0008433 0.0001851 0.0000411 0.0005965 0.0001645 0.0003085 [2528] 0.0006787 0.0002879 0.0000823 0.0004319 0.0003291 0.0002674 0.0005965 [2535] 0.0001440 0.0000206 0.0004936 0.0001440 0.0003497 0.0008638 0.0002674 [2542] 0.0001440 0.0003908 0.0002468 0.0002468 0.0007199 0.0001851 0.0000617 [2549] 0.0005142 0.0001851 0.0004114 0.0008021 0.0002879 0.0001440 0.0004114 [2556] 0.0003908 0.0004114 0.0003908 0.0001851 0.0000823 0.0006582 0.0001851 [2563] 0.0002468 0.0006993 0.0002468 0.0000617 0.0002057 0.0002262 0.0003085 [2570] 0.0005553 0.0003702 0.0000206 0.0005965 0.0003291 0.0003085 0.0010901 [2577] 0.0001440 0.0001440 0.0003702 0.0003291 0.0003908 0.0006170 0.0002057 [2584] 0.0001440 0.0006787 0.0002468 0.0001851 0.0006376 0.0001851 0.0000206 [2591] 0.0004114 0.0002468 0.0004319 0.0004731 0.0003497 0.0000617 0.0004114 [2598] 0.0002674 0.0002468 0.0008021 0.0002674 0.0000411 0.0004114 0.0002674 [2605] 0.0005965 0.0007404 0.0003908 0.0000617 0.0005965 0.0004114 0.0003085 [2612] 0.0007199 0.0001645 0.0000617 0.0004936 0.0002057 0.0003085 0.0005965 [2619] 0.0003908 0.0000617 0.0003702 0.0001645 0.0002057 0.0006582 0.0003085 [2626] 0.0004114 0.0001440 0.0004731 0.0008021 0.0003085 0.0000206 0.0004525 [2633] 0.0003702 0.0003908 0.0005965 0.0001851 0.0000617 0.0006170 0.0001645 [2640] 0.0003702 0.0008638 0.0002674 0.0001234 0.0003085 0.0002262 0.0001851 [2647] 0.0003702 0.0003702 0.0000206 0.0003908 0.0001851 0.0003497 0.0006993 [2654] 0.0003291 0.0000411 0.0002262 0.0001645 0.0003908 0.0005965 0.0003085 [2661] 0.0001028 0.0007199 0.0002468 0.0002674 0.0008227 0.0002262 0.0000823 [2668] 0.0003497 0.0001645 0.0003702 0.0005142 0.0002057 0.0000823 0.0004114 [2675] 0.0002674 0.0002057 0.0007199 0.0001851 0.0000823 0.0003085 0.0001645 [2682] 0.0002262 0.0006170 0.0003085 0.0000823 0.0004525 0.0002674 0.0002674 [2689] 0.0007610 0.0002674 0.0005348 0.0002468 0.0005142 0.0006582 0.0002674 [2696] 0.0001440 0.0003085 0.0003291 0.0002468 0.0006582 0.0002057 0.0001028 [2703] 0.0003702 0.0000617 0.0003702 0.0006787 0.0003291 0.0000617 0.0003702 [2710] 0.0003497 0.0003702 0.0006376 0.0002057 0.0000206 0.0004319 0.0001851 [2717] 0.0003497 0.0008433 0.0002879 0.0000411 0.0003908 0.0002879 0.0002468 [2724] 0.0005142 0.0003291 0.0005553 0.0002262 0.0004114 0.0007610 0.0002262 [2731] 0.0000823 0.0002057 0.0001851 0.0003702 0.0004319 0.0002468 0.0000411 [2738] 0.0004525 0.0000823 0.0003291 0.0010490 0.0002879 0.0000411 0.0002468 [2745] 0.0002674 0.0004525 0.0005965 0.0004525 0.0000411 0.0005553 0.0002468 [2752] 0.0003291 0.0006170 0.0001645 0.0003497 0.0001234 0.0003291 0.0004731 [2759] 0.0002674 0.0000411 0.0003497 0.0001440 0.0001851 0.0008021 0.0002674 [2766] 0.0002879 0.0001851 0.0004525 0.0006582 0.0003291 0.0000823 0.0004319 [2773] 0.0002057 0.0002879 0.0006993 0.0001851 0.0000617 0.0003908 0.0001028 [2780] 0.0003085 0.0004731 0.0003291 0.0000617 0.0003497 0.0002262 0.0002674 [2787] 0.0005348 0.0002879 0.0003291 0.0000823 0.0003291 0.0006787 0.0003908 [2794] 0.0001028 0.0002879 0.0003497 0.0002674 0.0005965 0.0002674 0.0000617 [2801] 0.0004525 0.0001851 0.0003291 0.0008227 0.0001645 0.0001028 0.0003085 [2808] 0.0001851 0.0002879 0.0003291 0.0001851 0.0000411 0.0004114 0.0001234 [2815] 0.0001851 0.0006376 0.0003085 0.0000411 0.0001645 0.0002879 0.0002879 [2822] 0.0005759 0.0003291 0.0005965 0.0002879 0.0003291 0.0009667 0.0001851 [2829] 0.0000823 0.0002674 0.0001440 0.0004525 0.0005142 0.0003085 0.0000617 [2836] 0.0003702 0.0001028 0.0001234 0.0006376 0.0001645 0.0002468 0.0002057 [2843] 0.0004114 0.0005348 0.0004319 0.0000411 0.0004114 0.0001645 0.0003085 [2850] 0.0008433 0.0002468 0.0004319 0.0001440 0.0004525 0.0005965 0.0003085 [2857] 0.0000411 0.0002879 0.0002262 0.0002674 0.0006787 0.0001645 0.0000411 [2864] 0.0001851 0.0001440 0.0002674 0.0005348 0.0003908 0.0000411 0.0002468 [2871] 0.0001028 0.0001645 0.0005965 0.0002468 0.0003085 0.0000617 0.0004936 [2878] 0.0006993 0.0004319 0.0003085 0.0002674 0.0003497 0.0005142 0.0001234 [2885] 0.0000411 0.0003908 0.0001234 0.0002674 0.0007199 0.0002674 0.0001028 [2892] 0.0001645 0.0001645 0.0001645 0.0003291 0.0003085 0.0000206 0.0003702 [2899] 0.0002057 0.0002674 0.0008433 0.0002468 0.0000411 0.0001851 0.0001645 [2906] 0.0002468 0.0005142 0.0003085 0.0000206 0.0004731 0.0001440 0.0001851 [2913] 0.0006376 0.0002674 0.0002674 0.0002262 0.0003908 0.0004731 0.0001440 [2920] 0.0000617 0.0003497 0.0001851 0.0001440 0.0006787 0.0002057 0.0000411 [2927] 0.0002262 0.0001028 0.0003908 0.0005553 0.0004936 0.0000411 0.0003702 [2934] 0.0002468 0.0002262 0.0007199 0.0002468 0.0003497 0.0002057 0.0003291 [2941] 0.0004525 0.0003085 0.0000411 0.0003702 0.0001851 0.0002057 0.0005142 [2948] 0.0002262 0.0000411 0.0002674 0.0000823 0.0003497 0.0005553 0.0003291 [2955] 0.0000411 0.0001440 0.0002468 0.0002879 0.0005759 0.0002262 0.0002674 [2962] 0.0000823 0.0003908 0.0008227 0.0003497 0.0000206 0.0003085 0.0001851 [2969] 0.0001645 0.0004114 0.0002674 0.0003702 0.0001234 0.0003291 0.0005759 [2976] 0.0003702 0.0000411 0.0001234 0.0001234 0.0002674 0.0004525 0.0003908 [2983] 0.0000617 0.0003497 0.0001440 0.0002468 0.0008227 0.0002262 0.0000411 [2990] 0.0001234 0.0001440 0.0003702 0.0004525 0.0002674 0.0000411 0.0003497 [2997] 0.0000823 0.0002879 0.0005142 0.0002262 0.0001851 0.0000411 0.0001645 [3004] 0.0003908 0.0004731 0.0000411 0.0002262 0.0001440 0.0001440 0.0007816 [3011] 0.0003085 0.0002468 0.0001645 0.0003702 0.0005759 0.0002262 0.0000823 [3018] 0.0002879 0.0001645 0.0001851 0.0005965 0.0001645 0.0000617 0.0002057 [3025] 0.0000206 0.0002468 0.0003497 0.0003497 0.0000206 0.0001645 0.0002674 [3032] 0.0002262 0.0004936 0.0002262 0.0002468 0.0001234 0.0002879 0.0006376 [3039] 0.0003702 0.0000206 0.0002468 0.0002057 0.0002262 0.0004731 0.0002674 [3046] 0.0003291 0.0001440 0.0003291 0.0006993 0.0001645 0.0000617 0.0001234 [3053] 0.0001851 0.0001851 0.0003085 0.0002057 0.0000206 0.0003497 0.0000206 [3060] 0.0002262 0.0008433 0.0002879 0.0001851 0.0002057 0.0003908 0.0004319 [3067] 0.0003497 0.0003497 0.0002057 0.0002879 0.0006170 0.0001645 0.0000411 [3074] 0.0001440 0.0001440 0.0003085 0.0004319 0.0004114 0.0000411 0.0002879 [3081] 0.0000823 0.0001645 0.0005965 0.0002674 0.0001028 0.0000411 0.0004525 [3088] 0.0004525 0.0003497 0.0002879 0.0000206 0.0002057 0.0007199 0.0002468 [3095] 0.0003085 0.0001028 0.0002879 0.0003908 0.0003497 0.0000411 0.0002262 [3102] 0.0001851 0.0002262 0.0005348 0.0001234 0.0001440 0.0000411 0.0002468 [3109] 0.0004114 0.0003908 0.0000617 0.0000411 0.0001028 0.0001645 0.0004525 [3116] 0.0003291 0.0000206 0.0001645 0.0000411 0.0003291 0.0006170 0.0004319 [3123] 0.0002879 0.0001645 0.0002262 0.0003702 0.0001645 0.0000411 0.0003085 [3130] 0.0000617 0.0002057 0.0005965 0.0002262 0.0000617 0.0000617 0.0001028 [3137] 0.0001440 0.0003497 0.0002262 0.0000206 0.0002057 0.0001028 0.0002057 [3144] 0.0006170 0.0001851 0.0000411 0.0000411 0.0001440 0.0002468 0.0004319 [3151] 0.0003702 0.0000206 0.0003291 0.0001234 0.0000823 0.0006170 0.0002057 [3158] 0.0001851 0.0001234 0.0004319 0.0002879 0.0003291 0.0000206 0.0001851 [3165] 0.0001028 0.0002057 0.0005759 0.0002262 0.0000206 0.0001028 0.0000823 [3172] 0.0002468 0.0005142 0.0003085 0.0002262 0.0001645 0.0002468 0.0006787 [3179] 0.0001440 0.0002262 0.0001028 0.0003702 0.0003497 0.0002879 0.0002057 [3186] 0.0000823 0.0000617 0.0004114 0.0002057 0.0001440 0.0000617 0.0002879 [3193] 0.0005142 0.0004525 0.0000206 0.0001234 0.0001440 0.0002879 0.0004731 [3200] 0.0001645 0.0002468 0.0003497 0.0006170 0.0002879 0.0000206 0.0001234 [3207] 0.0001028 0.0001645 0.0002674 0.0002674 0.0002468 0.0000823 0.0001851 [3214] 0.0006787 0.0003291 0.0001234 0.0000823 0.0001234 0.0003497 0.0003291 [3221] 0.0002262 0.0001028 0.0001851 0.0005142 0.0002468 0.0000411 0.0000617 [3228] 0.0000823 0.0003085 0.0003291 0.0001234 0.0000411 0.0002468 0.0000617 [3235] 0.0001028 0.0004114 0.0002468 0.0001234 0.0002262 0.0003291 0.0003702 [3242] 0.0002057 0.0001440 0.0001440 0.0006376 0.0002057 0.0002057 0.0001851 [3249] 0.0002262 0.0003702 0.0002468 0.0000617 0.0001234 0.0001234 0.0001028 [3256] 0.0004731 0.0001645 0.0000206 0.0001234 0.0000206 0.0001645 0.0003702 [3263] 0.0002057 0.0000823 0.0001028 0.0001645 0.0003702 0.0001440 0.0001645 [3270] 0.0003085 0.0005553 0.0003908 0.0000206 0.0002468 0.0001645 0.0001440 [3277] 0.0003291 0.0002057 0.0001851 0.0001234 0.0002674 0.0005759 0.0002057 [3284] 0.0000206 0.0000206 0.0000823 0.0002262 0.0003497 0.0003497 0.0001440 [3291] 0.0001645 0.0005348 0.0002879 0.0000206 0.0000823 0.0003085 0.0003497 [3298] 0.0003497 0.0002879 0.0001028 0.0002468 0.0005759 0.0001851 0.0001440 [3305] 0.0000823 0.0001440 0.0001851 0.0003497 0.0000206 0.0000823 0.0000411 [3312] 0.0001440 0.0003497 0.0002468 0.0000411 0.0002879 0.0003702 0.0003291 [3319] 0.0000206 0.0001645 0.0000823 0.0001028 0.0005965 0.0002674 0.0001851 [3326] 0.0000206 0.0002057 0.0003085 0.0003291 0.0001645 0.0001645 0.0001234 [3333] 0.0002674 0.0001028 0.0001234 0.0000617 0.0000617 0.0003085 0.0003291 [3340] 0.0000206 0.0000411 0.0000823 0.0000823 0.0004114 0.0002879 0.0002057 [3347] 0.0000617 0.0002468 0.0005553 0.0002879 0.0001234 0.0001440 0.0001440 [3354] 0.0001645 0.0001028 0.0002468 0.0000411 0.0000823 0.0004114 0.0002468 [3361] 0.0000206 0.0000823 0.0001234 0.0001851 0.0002468 0.0002468 0.0001645 [3368] 0.0001028 0.0002262 0.0005142 0.0001234 0.0000617 0.0000411 0.0002468 [3375] 0.0003291 0.0003497 0.0002262 0.0000617 0.0000617 0.0003702 0.0002057 [3382] 0.0001028 0.0000823 0.0001851 0.0001851 0.0002879 0.0000206 0.0001440 [3389] 0.0000206 0.0001028 0.0005348 0.0002674 0.0001028 0.0000617 0.0002879 [3396] 0.0003085 0.0003085 0.0000206 0.0000411 0.0000617 0.0002262 0.0004319 [3403] 0.0000617 0.0001028 0.0002057 0.0003291 0.0003497 0.0001234 0.0000411 [3410] 0.0000206 0.0003497 0.0002674 0.0000823 0.0000206 0.0002262 0.0004525 [3417] 0.0004114 0.0001028 0.0001234 0.0001645 0.0003291 0.0001645 0.0000206 [3424] 0.0000823 0.0000206 0.0001645 0.0003702 0.0002879 0.0000206 0.0001028 [3431] 0.0002262 0.0002468 0.0001028 0.0001851 0.0004525 0.0002674 0.0000411 [3438] 0.0000823 0.0001440 0.0002262 0.0003291 0.0002057 0.0000823 0.0000823 [3445] 0.0003908 0.0002057 0.0000411 0.0000823 0.0002262 0.0001645 0.0001645 [3452] 0.0000206 0.0000411 0.0000823 0.0000823 0.0002674 0.0002262 0.0001645 [3459] 0.0002879 0.0002879 0.0001645 0.0001234 0.0001234 0.0004319 0.0001645 [3466] 0.0001440 0.0001028 0.0001851 0.0002262 0.0002262 0.0000823 0.0000823 [3473] 0.0000411 0.0002674 0.0001234 0.0001234 0.0000206 0.0002057 0.0002468 [3480] 0.0002879 0.0000411 0.0000823 0.0002057 0.0003702 0.0000823 0.0001851 [3487] 0.0001851 0.0004731 0.0003497 0.0001440 0.0000823 0.0000823 0.0002057 [3494] 0.0003085 0.0001234 0.0000617 0.0001851 0.0002674 0.0001440 0.0000206 [3501] 0.0000206 0.0000617 0.0001440 0.0002468 0.0000823 0.0001440 0.0004731 [3508] 0.0003702 0.0000411 0.0002262 0.0003085 0.0002057 0.0001645 0.0000411 [3515] 0.0001440 0.0002879 0.0001645 0.0000823 0.0000411 0.0000823 0.0000617 [3522] 0.0002674 0.0000206 0.0000617 0.0000617 0.0000411 0.0003908 0.0002262 [3529] 0.0000206 0.0000411 0.0001851 0.0002468 0.0002879 0.0000206 0.0000823 [3536] 0.0003497 0.0001645 0.0000823 0.0000823 0.0002674 0.0001234 0.0001028 [3543] 0.0000617 0.0000411 0.0002262 0.0000617 0.0000823 0.0000206 0.0001645 [3550] 0.0002879 0.0003085 0.0000411 0.0000823 0.0000823 0.0002879 0.0001645 [3557] 0.0000206 0.0000206 0.0001851 0.0004114 0.0001645 0.0000411 0.0000411 [3564] 0.0001645 0.0001645 0.0002057 0.0001028 0.0000411 0.0003291 0.0002057 [3571] 0.0000206 0.0000823 0.0001440 0.0001440 0.0002468 0.0000823 0.0000617 [3578] 0.0002057 0.0003497 0.0001028 0.0000206 0.0001851 0.0002057 0.0001851 [3585] 0.0000823 0.0000411 0.0000823 0.0002879 0.0002057 0.0000206 0.0000411 [3592] 0.0001645 0.0002262 0.0003291 0.0001234 0.0000617 0.0000206 0.0002674 [3599] 0.0002262 0.0000823 0.0000411 0.0001645 0.0001028 0.0003085 0.0000411 [3606] 0.0001645 0.0002674 0.0000411 0.0000823 0.0000823 0.0001440 0.0003702 [3613] 0.0000411 0.0000206 0.0002674 0.0002468 0.0001028 0.0000411 0.0000823 [3620] 0.0003085 0.0002262 0.0001028 0.0000823 0.0000206 0.0001440 0.0001028 [3627] 0.0000617 0.0000206 0.0000823 0.0001645 0.0002674 0.0000411 0.0000823 [3634] 0.0000823 0.0001234 0.0000206 0.0000206 0.0001234 0.0003497 0.0001645 [3641] 0.0000411 0.0000823 0.0001851 0.0002674 0.0001440 0.0000411 0.0002674 [3648] 0.0001028 0.0000411 0.0000617 0.0000823 0.0000617 0.0000823 0.0000411 [3655] 0.0000206 0.0000411 0.0003291 0.0001440 0.0000206 0.0001645 0.0002262 [3662] 0.0002468 0.0000206 0.0001028 0.0002879 0.0000617 0.0000411 0.0000411 [3669] 0.0001851 0.0002262 0.0002674 0.0000617 0.0000411 0.0000206 0.0001645 [3676] 0.0002057 0.0000206 0.0001645 0.0002057 0.0003085 0.0001440 0.0003085 [3683] 0.0001028 0.0001028 0.0003291 0.0002468 0.0000411 0.0000411 0.0000617 [3690] 0.0001234 0.0001028 0.0000617 0.0000206 0.0001234 0.0001851 0.0002057 [3697] 0.0000411 0.0000617 0.0000411 0.0003085 0.0000206 0.0001028 0.0002879 [3704] 0.0003085 0.0001440 0.0002262 0.0001234 0.0001028 0.0000411 0.0000411 [3711] 0.0002057 0.0001234 0.0000411 0.0000206 0.0000823 0.0002057 0.0000411 [3718] 0.0000411 0.0000206 0.0001234 0.0001028 0.0000206 0.0000617 0.0001234 [3725] 0.0000617 0.0001645 0.0000206 0.0000617 0.0002468 0.0001234 0.0000617 [3732] 0.0001234 0.0001440 0.0002879 0.0000206 0.0000206 0.0000617 0.0001645 [3739] 0.0001028 0.0000411 0.0000411 0.0001234 0.0002262 0.0000617 0.0000617 [3746] 0.0000411 0.0000823 0.0001440 0.0000206 0.0000206 0.0001645 0.0001645 [3753] 0.0000823 0.0000617 0.0001028 0.0001645 0.0000411 0.0000411 0.0002674 [3760] 0.0002262 0.0000206 0.0000411 0.0001028 0.0001645 0.0000823 0.0000823 [3767] 0.0002674 0.0001440 0.0000206 0.0000823 0.0000823 0.0002468 0.0000617 [3774] 0.0002879 0.0000823 0.0001028 0.0002057 0.0002057 0.0000206 0.0001851 [3781] 0.0002057 0.0000206 0.0000823 0.0001234 0.0001645 0.0000206 0.0000617 [3788] 0.0001234 0.0000411 0.0001234 0.0001440 0.0002057 0.0000617 0.0002468 [3795] 0.0001028 0.0000823 0.0002262 0.0001645 0.0000617 0.0000617 0.0000617 [3802] 0.0000823 0.0000206 0.0000206 0.0001234 0.0001234 0.0000823 0.0000206 [3809] 0.0001028 0.0000206 0.0001440 0.0002468 0.0000411 0.0000823 0.0001645 [3816] 0.0001028 0.0000617 0.0000206 0.0000206 0.0001851 0.0000823 0.0000206 [3823] 0.0000206 0.0001028 0.0000617 0.0001645 0.0000823 0.0001440 0.0001234 [3830] 0.0000617 0.0003291 0.0001028 0.0002468 0.0000411 0.0000411 0.0000617 [3837] 0.0000823 0.0001440 0.0000206 0.0000206 0.0000411 0.0001645 0.0000411 [3844] 0.0000411 0.0002468 0.0000206 0.0000206 0.0001028 0.0001028 0.0000823 [3851] 0.0001645 0.0002057 0.0000206 0.0000823 0.0000411 0.0000411 0.0001440 [3858] 0.0001440 0.0002262 0.0000206 0.0000206 0.0000206 0.0002057 0.0001028 [3865] 0.0000823 0.0001028 0.0000411 0.0000206 0.0001645 0.0000617 0.0000411 [3872] 0.0001234 0.0001028 0.0001234 0.0000617 0.0000206 0.0001234 0.0001028 [3879] 0.0001645 0.0000411 0.0000823 0.0000823 0.0000411 0.0001028 0.0001028 [3886] 0.0000206 0.0000617 0.0002057 0.0000411 0.0000411 0.0001440 0.0001851 [3893] 0.0000411 0.0000206 0.0000823 0.0000823 0.0001440 0.0000823 0.0000206 [3900] 0.0000411 0.0001028 0.0000206 0.0000617 0.0001851 0.0002057 0.0000617 [3907] 0.0001028 0.0001234 0.0000206 0.0000617 0.0001234 0.0000411 0.0002057 [3914] 0.0000411 0.0000411 0.0000411 0.0000617 0.0000617 0.0001234 0.0001234 [3921] 0.0001234 0.0000206 0.0000411 0.0001440 0.0000206 0.0000617 0.0001851 [3928] 0.0000411 0.0000823 0.0001028 0.0000411 0.0001440 0.0000411 0.0000206 [3935] 0.0000206 0.0000617 0.0000206 0.0000823 0.0001440 0.0001234 0.0000617 [3942] 0.0001645 0.0000617 0.0000617 0.0001028 0.0001440 0.0000617 0.0000206 [3949] 0.0000411 0.0000617 0.0001028 0.0000411 0.0001851 0.0000411 0.0000823 [3956] 0.0001645 0.0000617 0.0001234 0.0000206 0.0000411 0.0000617 0.0001028 [3963] 0.0000411 0.0000823 0.0001645 0.0000411 0.0000617 0.0000411 0.0000823 [3970] 0.0001028 0.0000206 0.0000411 0.0000206 0.0000411 0.0001028 0.0000411 [3977] 0.0000206 0.0000206 0.0001028 0.0000617 0.0000411 0.0000823 0.0000206 [3984] 0.0000411 0.0000411 0.0000411 0.0001440 0.0000206 0.0000411 0.0000411 [3991] 0.0000206 0.0000823 0.0000411 0.0001234 0.0000206 0.0000206 0.0001028 [3998] 0.0000617 0.0000206 0.0000617 0.0001851 0.0000617 0.0000411 0.0000411 [4005] 0.0001234 0.0000206 0.0001440 0.0000823 0.0000617 0.0000823 0.0000411 [4012] 0.0000206 0.0000823 0.0000617 0.0000411 0.0000411 0.0000411 0.0000411 [4019] 0.0000206 0.0001028 0.0000411 0.0000411 0.0000206 0.0000206 0.0001028 [4026] 0.0000411 0.0000617 0.0000617 0.0000206 0.0000206 0.0000411 0.0001234 [4033] 0.0000206 0.0001234 0.0000411 0.0000206 0.0000823 0.0000206 0.0000206 [4040] 0.0000823 0.0001440 0.0000823 0.0000411 0.0000206 0.0000206 0.0000823 [4047] 0.0000206 0.0000823 0.0000617 0.0000206 0.0001234 0.0000411 0.0000411 [4054] 0.0000206 0.0000411 0.0000206 0.0000823 0.0000206 0.0000617 0.0000411 [4061] 0.0000617 0.0000206 0.0000411 0.0000206 0.0000206 0.0000617 0.0000411 [4068] 0.0000823 0.0000411 0.0000206 0.0000617 0.0000411 0.0000206 0.0000823 [4075] 0.0000617 0.0000411 0.0000206 0.0000411 0.0001234 0.0000411 0.0000206 [4082] 0.0000206 0.0000411 0.0000411 0.0000411 0.0000206 0.0000206 0.0000206 [4089] 0.0000411 0.0000206 0.0000206 0.0000411 0.0000411 0.0000617 0.0000617 [4096] 0.0000411 0.0000411 0.0000206 0.0000411 0.0000411 0.0000206 0.0000411 [4103] 0.0000206 0.0000411 0.0000206 0.0000206 > round(qp_it1_SR <- qperm(it1_SR, seq(0, 1, 0.01)), 7) [1] -3.2641751 -2.2408882 -2.0193392 -1.8687838 -1.7525012 -1.6582511 [7] -1.5731812 -1.4942314 -1.4281340 -1.3669326 -1.3100153 -1.2555461 [13] -1.2016889 -1.1563999 -1.1086628 -1.0652098 -1.0229809 -0.9813640 [19] -0.9434191 -0.9066983 -0.8693655 -0.8320326 -0.7965358 -0.7647111 [25] -0.7292143 -0.6980016 -0.6674009 -0.6355762 -0.6019155 -0.5743749 [31] -0.5443862 -0.5143975 -0.4844088 -0.4550322 -0.4287156 -0.4017870 [37] -0.3724103 -0.3436457 -0.3173291 -0.2928486 -0.2640839 -0.2377673 [43] -0.2090027 -0.1839101 -0.1582055 -0.1306649 -0.1037363 -0.0786438 [49] -0.0529392 -0.0253986 -0.0003060 0.0253986 0.0529392 0.0786438 [55] 0.1037363 0.1306649 0.1582055 0.1839101 0.2090027 0.2377673 [61] 0.2640839 0.2928486 0.3173291 0.3436457 0.3724103 0.3999510 [67] 0.4287156 0.4550322 0.4844088 0.5143975 0.5443862 0.5743749 [73] 0.6019155 0.6355762 0.6674009 0.6980016 0.7292143 0.7647111 [79] 0.7965358 0.8320326 0.8693655 0.9066983 0.9434191 0.9813640 [85] 1.0229809 1.0652098 1.1086628 1.1563999 1.2016889 1.2555461 [91] 1.3100153 1.3669326 1.4281340 1.4942314 1.5731812 1.6582511 [97] 1.7525012 1.8687838 2.0193392 2.2408882 3.2641751 > round(rp_it1_SR <- rperm(it1_SR, 5), 7) [1] 0.9923802 0.6722970 0.4593163 0.7224822 -0.5945713 > stopifnot(all(rp_it1_SR %in% supp_it1_SR)) > > ### split-up without block > it1_vdW <- independence_test(y ~ x, data = dta1, + distribution = exact(algorithm = "split-up")) > round(pp_it1_vdW <- pperm(it1_vdW, supp_it1_SR), 7) [1] 0.0000206 0.0000411 0.0000823 0.0001028 0.0001440 0.0001645 0.0002057 [8] 0.0002468 0.0002674 0.0003085 0.0003497 0.0004114 0.0004731 0.0005142 [15] 0.0005553 0.0005759 0.0005965 0.0006376 0.0006582 0.0006787 0.0006993 [22] 0.0007404 0.0007816 0.0008227 0.0008433 0.0008638 0.0009050 0.0010284 [29] 0.0010695 0.0010901 0.0011312 0.0011929 0.0012752 0.0012958 0.0013369 [36] 0.0013986 0.0014192 0.0014603 0.0015426 0.0015837 0.0016454 0.0016660 [43] 0.0016865 0.0017277 0.0017483 0.0018100 0.0018511 0.0019128 0.0019334 [50] 0.0020156 0.0020362 0.0020773 0.0020979 0.0021390 0.0021802 0.0023036 [57] 0.0023241 0.0023858 0.0024681 0.0024887 0.0025710 0.0025915 0.0026121 [64] 0.0026532 0.0027355 0.0028795 0.0029617 0.0029823 0.0030029 0.0030852 [71] 0.0031057 0.0031469 0.0032703 0.0032908 0.0034142 0.0034554 0.0034759 [78] 0.0034965 0.0035582 0.0036199 0.0036610 0.0037639 0.0037845 0.0038050 [85] 0.0038462 0.0038873 0.0039901 0.0040107 0.0040518 0.0040930 0.0041341 [92] 0.0041752 0.0042369 0.0043192 0.0043398 0.0043809 0.0044632 0.0045249 [99] 0.0046072 0.0047511 0.0047717 0.0048951 0.0049362 0.0049774 0.0050391 [106] 0.0052242 0.0052859 0.0053065 0.0053682 0.0054710 0.0054916 0.0055121 [113] 0.0056355 0.0056767 0.0057589 0.0057795 0.0058206 0.0058618 0.0058824 [120] 0.0060263 0.0060675 0.0061086 0.0061497 0.0061703 0.0062526 0.0062937 [127] 0.0063554 0.0064582 0.0064788 0.0064994 0.0065405 0.0066434 0.0066845 [134] 0.0067051 0.0067462 0.0067668 0.0068696 0.0069519 0.0069930 0.0070547 [141] 0.0070958 0.0072604 0.0073427 0.0073838 0.0074866 0.0075483 0.0075895 [148] 0.0076100 0.0077334 0.0077951 0.0079597 0.0080420 0.0080831 0.0082682 [155] 0.0083093 0.0084122 0.0084739 0.0085150 0.0085356 0.0085973 0.0087413 [162] 0.0088441 0.0089058 0.0089675 0.0091320 0.0091937 0.0093172 0.0094611 [169] 0.0095434 0.0095640 0.0096257 0.0096462 0.0096668 0.0097079 0.0098519 [176] 0.0098930 0.0099959 0.0100782 0.0101193 0.0103044 0.0103661 0.0103867 [183] 0.0105306 0.0105718 0.0105923 0.0107158 0.0108392 0.0109626 0.0110243 [190] 0.0110860 0.0111271 0.0111682 0.0112094 0.0114151 0.0114562 0.0115796 [197] 0.0116413 0.0116619 0.0117853 0.0118881 0.0119498 0.0121555 0.0123406 [204] 0.0124023 0.0124229 0.0125257 0.0125668 0.0125874 0.0126697 0.0128137 [211] 0.0128959 0.0129782 0.0129988 0.0130399 0.0132250 0.0133690 0.0134101 [218] 0.0134513 0.0136569 0.0137186 0.0137392 0.0138420 0.0139449 0.0139860 [225] 0.0140683 0.0141506 0.0141917 0.0143562 0.0144591 0.0145825 0.0146030 [232] 0.0146647 0.0147882 0.0148910 0.0150144 0.0150555 0.0151172 0.0152818 [239] 0.0153023 0.0153435 0.0154463 0.0155286 0.0156314 0.0158371 0.0158577 [246] 0.0158782 0.0158988 0.0161251 0.0162690 0.0164130 0.0164541 0.0164953 [253] 0.0165775 0.0165981 0.0168038 0.0169683 0.0170506 0.0171534 0.0172563 [260] 0.0172768 0.0172974 0.0175442 0.0175854 0.0176265 0.0177910 0.0178322 [267] 0.0178527 0.0178733 0.0180173 0.0180995 0.0181613 0.0182024 0.0182435 [274] 0.0184903 0.0185932 0.0189223 0.0189840 0.0191074 0.0192513 0.0193336 [281] 0.0194981 0.0195599 0.0196627 0.0196833 0.0197038 0.0197861 0.0199712 [288] 0.0199918 0.0200123 0.0200740 0.0201769 0.0203414 0.0204237 0.0204648 [295] 0.0207116 0.0208556 0.0208762 0.0209790 0.0209996 0.0210819 0.0212053 [302] 0.0213287 0.0213492 0.0213698 0.0214521 0.0215138 0.0215755 0.0216372 [309] 0.0218017 0.0220280 0.0221102 0.0222131 0.0224599 0.0225216 0.0227273 [316] 0.0228712 0.0229947 0.0230358 0.0231592 0.0232209 0.0232415 0.0234060 [323] 0.0235294 0.0236117 0.0236323 0.0238379 0.0240230 0.0240436 0.0242493 [330] 0.0244550 0.0245578 0.0246401 0.0249280 0.0249897 0.0252365 0.0253188 [337] 0.0254011 0.0254216 0.0255656 0.0258330 0.0259153 0.0259975 0.0261621 [344] 0.0262649 0.0263060 0.0263266 0.0265529 0.0268202 0.0268614 0.0269025 [351] 0.0270671 0.0271699 0.0272316 0.0273139 0.0274784 0.0276429 0.0276635 [358] 0.0276841 0.0278281 0.0279103 0.0279515 0.0280132 0.0280749 0.0283011 [365] 0.0284245 0.0284657 0.0285068 0.0286096 0.0287742 0.0288359 0.0288564 [372] 0.0288770 0.0291650 0.0293089 0.0294323 0.0294940 0.0296174 0.0298643 [379] 0.0299260 0.0299465 0.0301111 0.0301728 0.0302962 0.0303579 0.0303784 [386] 0.0304813 0.0306047 0.0306253 0.0306664 0.0307075 0.0309132 0.0309955 [393] 0.0310160 0.0310572 0.0311806 0.0313863 0.0314274 0.0314685 0.0315714 [400] 0.0316948 0.0319210 0.0320650 0.0323735 0.0326615 0.0327643 0.0327849 [407] 0.0330934 0.0331345 0.0331962 0.0332374 0.0334430 0.0336281 0.0337515 [414] 0.0337721 0.0338338 0.0339367 0.0340601 0.0341218 0.0341629 0.0342040 [421] 0.0344508 0.0347799 0.0348828 0.0349856 0.0352941 0.0354381 0.0357466 [428] 0.0359523 0.0361168 0.0361374 0.0363431 0.0365076 0.0365282 0.0365693 [435] 0.0366310 0.0368984 0.0371246 0.0373097 0.0373509 0.0373920 0.0374537 [442] 0.0377417 0.0378445 0.0378651 0.0381119 0.0383381 0.0385027 0.0385232 [449] 0.0386672 0.0389963 0.0390374 0.0390580 0.0390991 0.0391814 0.0392431 [456] 0.0393254 0.0393871 0.0394282 0.0395311 0.0397984 0.0398396 0.0399835 [463] 0.0402509 0.0404360 0.0405183 0.0405594 0.0407240 0.0410736 0.0411970 [470] 0.0412176 0.0412382 0.0413616 0.0414439 0.0415261 0.0415673 0.0418346 [477] 0.0419992 0.0420814 0.0421020 0.0421637 0.0422666 0.0424105 0.0424311 [484] 0.0425134 0.0426162 0.0428425 0.0431510 0.0432332 0.0432744 0.0433772 [491] 0.0436240 0.0438914 0.0439120 0.0439531 0.0443233 0.0444673 0.0445496 [498] 0.0446318 0.0446730 0.0449404 0.0451049 0.0451460 0.0454545 0.0455574 [505] 0.0457219 0.0457631 0.0458453 0.0460716 0.0463390 0.0463595 0.0464212 [512] 0.0465446 0.0468737 0.0471000 0.0472645 0.0473056 0.0473262 0.0475319 [519] 0.0478198 0.0479021 0.0479432 0.0480255 0.0482106 0.0484163 0.0486014 [526] 0.0486220 0.0487248 0.0490745 0.0492801 0.0493418 0.0494241 0.0496709 [533] 0.0498149 0.0499589 0.0500411 0.0500617 0.0502674 0.0505965 0.0506376 [540] 0.0507404 0.0509461 0.0511107 0.0512752 0.0513163 0.0513575 0.0515220 [547] 0.0519334 0.0521185 0.0521390 0.0521596 0.0523241 0.0526121 0.0526944 [554] 0.0527766 0.0528178 0.0531263 0.0534142 0.0535788 0.0535993 0.0536816 [561] 0.0537433 0.0539696 0.0540107 0.0540724 0.0541752 0.0542986 0.0545660 [568] 0.0546483 0.0547306 0.0548951 0.0552448 0.0553270 0.0553476 0.0556355 [575] 0.0558824 0.0560675 0.0561086 0.0561292 0.0563554 0.0567462 0.0567873 [582] 0.0568490 0.0569107 0.0569313 0.0571987 0.0572604 0.0573427 0.0573838 [589] 0.0574661 0.0576306 0.0579186 0.0580625 0.0581037 0.0582682 0.0584739 [596] 0.0587824 0.0590086 0.0590498 0.0594200 0.0598930 0.0600370 0.0601193 [603] 0.0603661 0.0605101 0.0605718 0.0605923 0.0606129 0.0607569 0.0610243 [610] 0.0612094 0.0612711 0.0613945 0.0617030 0.0619087 0.0619910 0.0620732 [617] 0.0622172 0.0625668 0.0630399 0.0632250 0.0634101 0.0634924 0.0638626 [624] 0.0640683 0.0641506 0.0641917 0.0644796 0.0647265 0.0649321 0.0649527 [631] 0.0650761 0.0651995 0.0654669 0.0655080 0.0655903 0.0656726 0.0658988 [638] 0.0661251 0.0663102 0.0664130 0.0665570 0.0667215 0.0671534 0.0672768 [645] 0.0674002 0.0675648 0.0678527 0.0681407 0.0683052 0.0685315 0.0687988 [652] 0.0688811 0.0689634 0.0690045 0.0690251 0.0691896 0.0693542 0.0695804 [659] 0.0696627 0.0697038 0.0699095 0.0703003 0.0703826 0.0704648 0.0706705 [666] 0.0709996 0.0712258 0.0713698 0.0714521 0.0714932 0.0717606 0.0722131 [673] 0.0723982 0.0725010 0.0727478 0.0729741 0.0730769 0.0730975 0.0733854 [680] 0.0737557 0.0739202 0.0739408 0.0740230 0.0740436 0.0742081 0.0745372 [687] 0.0747018 0.0748252 0.0749280 0.0753394 0.0757919 0.0760181 0.0760387 [694] 0.0761209 0.0763883 0.0767380 0.0767585 0.0767997 0.0769231 0.0772727 [701] 0.0776018 0.0778075 0.0779103 0.0779720 0.0784039 0.0786302 0.0786919 [708] 0.0787330 0.0787536 0.0790621 0.0793706 0.0796586 0.0797203 0.0798231 [715] 0.0800905 0.0806253 0.0807281 0.0807487 0.0808926 0.0809132 0.0812012 [722] 0.0813863 0.0815714 0.0816536 0.0817565 0.0819622 0.0823324 0.0823941 [729] 0.0824558 0.0826820 0.0830317 0.0833608 0.0836076 0.0836487 0.0837104 [736] 0.0838338 0.0843480 0.0845742 0.0846771 0.0848416 0.0850884 0.0853353 [743] 0.0855204 0.0856438 0.0857260 0.0857466 0.0859934 0.0864048 0.0864870 [750] 0.0865282 0.0867750 0.0868778 0.0870424 0.0871863 0.0873303 0.0874537 [757] 0.0877417 0.0882970 0.0885438 0.0886055 0.0888112 0.0890991 0.0895105 [764] 0.0895928 0.0896750 0.0897162 0.0897367 0.0900658 0.0903743 0.0904360 [771] 0.0904977 0.0906211 0.0907240 0.0909914 0.0911148 0.0912793 0.0914439 [778] 0.0917729 0.0920814 0.0922871 0.0923077 0.0924928 0.0927602 0.0933566 [785] 0.0934595 0.0935418 0.0937063 0.0937269 0.0940559 0.0944262 0.0947141 [792] 0.0947552 0.0950021 0.0953517 0.0954957 0.0955368 0.0956191 0.0956397 [799] 0.0959893 0.0961744 0.0963184 0.0964007 0.0965446 0.0967297 0.0973056 [806] 0.0975524 0.0976553 0.0979432 0.0982929 0.0986425 0.0989510 0.0990333 [813] 0.0990539 0.0993418 0.0998766 0.1000411 0.1001851 0.1005348 0.1008844 [820] 0.1011107 0.1011929 0.1012135 0.1012341 0.1014397 0.1020156 0.1022830 [827] 0.1024064 0.1025915 0.1027972 0.1031263 0.1032703 0.1034348 0.1036816 [834] 0.1037022 0.1040930 0.1046483 0.1049568 0.1051213 0.1052653 0.1056355 [841] 0.1058001 0.1059029 0.1059852 0.1061909 0.1065611 0.1067256 0.1067462 [848] 0.1068696 0.1068902 0.1070547 0.1075278 0.1076306 0.1077540 0.1078774 [855] 0.1079391 0.1081859 0.1085561 0.1087824 0.1089675 0.1091732 0.1093789 [862] 0.1100165 0.1101604 0.1103044 0.1105101 0.1108803 0.1112094 0.1114356 [869] 0.1115590 0.1118058 0.1122172 0.1123200 0.1123817 0.1126285 0.1126697 [876] 0.1127931 0.1131222 0.1134307 0.1135130 0.1135747 0.1136158 0.1138626 [883] 0.1143768 0.1145619 0.1146647 0.1148910 0.1152201 0.1155697 0.1156931 [890] 0.1157754 0.1158988 0.1162279 0.1169066 0.1170917 0.1171740 0.1174208 [897] 0.1176882 0.1179556 0.1181201 0.1182230 0.1183464 0.1183669 0.1186549 [904] 0.1192719 0.1196216 0.1198684 0.1200329 0.1205060 0.1207939 0.1209379 [911] 0.1210613 0.1210819 0.1215343 0.1220485 0.1223365 0.1223982 0.1225422 [918] 0.1227478 0.1231592 0.1232209 0.1233032 0.1235088 0.1237968 0.1241464 [925] 0.1245167 0.1246195 0.1248457 0.1249897 0.1256684 0.1259153 0.1260798 [932] 0.1263060 0.1266146 0.1271288 0.1273756 0.1274578 0.1275607 0.1275812 [939] 0.1278075 0.1283834 0.1285891 0.1286919 0.1288770 0.1288976 0.1292267 [946] 0.1295146 0.1299465 0.1300699 0.1302550 0.1304607 0.1310777 0.1311600 [953] 0.1312834 0.1316125 0.1316331 0.1320033 0.1324352 0.1326820 0.1328260 [960] 0.1328671 0.1329083 0.1330934 0.1337104 0.1339161 0.1340189 0.1342246 [967] 0.1342452 0.1344714 0.1348211 0.1349650 0.1350679 0.1351296 0.1351913 [974] 0.1354175 0.1360140 0.1362197 0.1362814 0.1365899 0.1366310 0.1367956 [981] 0.1371658 0.1373920 0.1375566 0.1378445 0.1382764 0.1388935 0.1392225 [988] 0.1392637 0.1394282 0.1394488 0.1397779 0.1402304 0.1403949 0.1404977 [995] 0.1405389 0.1406006 0.1409914 0.1414027 0.1416495 0.1416907 0.1418346 [1002] 0.1419580 0.1424928 0.1427190 0.1429042 0.1431304 0.1431715 0.1435212 [1009] 0.1439120 0.1441999 0.1443028 0.1446113 0.1448581 0.1455780 0.1457836 [1016] 0.1458042 0.1460921 0.1464418 0.1468943 0.1473468 0.1473879 0.1474907 [1023] 0.1477581 0.1483546 0.1485191 0.1486014 0.1488893 0.1489305 0.1493418 [1030] 0.1497738 0.1500823 0.1502262 0.1503702 0.1504114 0.1505759 0.1511929 [1037] 0.1514809 0.1516865 0.1520362 0.1523858 0.1528178 0.1532086 0.1534142 [1044] 0.1535993 0.1538873 0.1547306 0.1549568 0.1549774 0.1553270 0.1553476 [1051] 0.1555533 0.1558618 0.1560469 0.1562320 0.1563554 0.1564171 0.1565817 [1058] 0.1572810 0.1576100 0.1577540 0.1580831 0.1583505 0.1588235 0.1590498 [1065] 0.1592555 0.1595023 0.1595228 0.1598930 0.1605306 0.1608186 0.1609420 [1072] 0.1611888 0.1614151 0.1619087 0.1621349 0.1624023 0.1625668 0.1625874 [1079] 0.1629371 0.1632867 0.1635335 0.1635541 0.1637598 0.1638215 0.1639860 [1086] 0.1645825 0.1647676 0.1649321 0.1652201 0.1653023 0.1655286 0.1661045 [1093] 0.1664747 0.1666392 0.1668861 0.1671946 0.1679761 0.1681201 0.1682641 [1100] 0.1684903 0.1685315 0.1690045 0.1693953 0.1695599 0.1696010 0.1697861 [1107] 0.1700123 0.1705265 0.1708145 0.1708968 0.1712464 0.1712875 0.1715549 [1114] 0.1720074 0.1723776 0.1725216 0.1726450 0.1726861 0.1729124 0.1737351 [1121] 0.1739819 0.1741259 0.1744755 0.1745372 0.1749280 0.1753805 0.1756479 [1128] 0.1757713 0.1758947 0.1759358 0.1763060 0.1768819 0.1772110 0.1773344 [1135] 0.1777046 0.1779720 0.1783834 0.1785479 0.1787330 0.1790415 0.1790621 [1142] 0.1794118 0.1802345 0.1806253 0.1807075 0.1809749 0.1812012 0.1817770 [1149] 0.1820650 0.1823118 0.1824558 0.1824969 0.1828260 0.1833813 0.1837310 [1156] 0.1838132 0.1840806 0.1841218 0.1843480 0.1848622 0.1850679 0.1852530 [1163] 0.1856232 0.1856643 0.1859729 0.1864253 0.1867544 0.1869601 0.1873097 [1170] 0.1875566 0.1882764 0.1885027 0.1887495 0.1891197 0.1891608 0.1896545 [1177] 0.1902098 0.1906006 0.1907034 0.1909297 0.1909708 0.1911765 0.1918552 [1184] 0.1919992 0.1921843 0.1925339 0.1925956 0.1927396 0.1932127 0.1936035 [1191] 0.1938297 0.1940971 0.1943645 0.1950021 0.1951872 0.1953311 0.1958042 [1198] 0.1958248 0.1961333 0.1966475 0.1968943 0.1970588 0.1972439 0.1972851 [1205] 0.1975319 0.1983752 0.1986425 0.1988482 0.1992184 0.1992390 0.1995475 [1212] 0.1998766 0.2000411 0.2002057 0.2003702 0.2004731 0.2007404 0.2014603 [1219] 0.2017277 0.2018511 0.2022419 0.2022830 0.2024064 0.2029206 0.2032703 [1226] 0.2035376 0.2038462 0.2042781 0.2049774 0.2054710 0.2055327 0.2058412 [1233] 0.2060880 0.2066845 0.2068490 0.2069519 0.2071987 0.2072398 0.2076306 [1240] 0.2081654 0.2084327 0.2085767 0.2087618 0.2088030 0.2089675 0.2096462 [1247] 0.2099136 0.2101399 0.2104278 0.2104689 0.2107775 0.2113739 0.2118264 [1254] 0.2119704 0.2124023 0.2126491 0.2134924 0.2138009 0.2139654 0.2143768 [1261] 0.2144179 0.2148499 0.2153846 0.2157960 0.2160016 0.2162485 0.2164130 [1268] 0.2170506 0.2171740 0.2172768 0.2176471 0.2177088 0.2180173 0.2185315 [1275] 0.2189840 0.2191279 0.2193953 0.2194776 0.2196627 0.2206294 0.2209585 [1282] 0.2212464 0.2218429 0.2221719 0.2227478 0.2230358 0.2233237 0.2234883 [1289] 0.2235294 0.2238379 0.2244755 0.2246606 0.2247840 0.2251954 0.2252365 [1296] 0.2254216 0.2257507 0.2260387 0.2262238 0.2265323 0.2266351 0.2267997 [1303] 0.2276224 0.2279515 0.2281366 0.2285891 0.2286508 0.2289181 0.2295146 [1310] 0.2297820 0.2301316 0.2304196 0.2305224 0.2309132 0.2315919 0.2319210 [1317] 0.2320033 0.2323324 0.2326203 0.2331551 0.2334225 0.2336487 0.2339984 [1324] 0.2340601 0.2343891 0.2348622 0.2351707 0.2352735 0.2356643 0.2357260 [1331] 0.2359111 0.2366104 0.2368984 0.2371041 0.2375360 0.2376183 0.2379473 [1338] 0.2386055 0.2390580 0.2392431 0.2395311 0.2397984 0.2406006 0.2407857 [1345] 0.2409297 0.2412793 0.2413204 0.2415878 0.2420609 0.2423900 0.2425134 [1352] 0.2428630 0.2430276 0.2436446 0.2439737 0.2442205 0.2447758 0.2448169 [1359] 0.2452694 0.2458659 0.2463184 0.2465858 0.2468326 0.2468737 0.2471617 [1366] 0.2482106 0.2485397 0.2486220 0.2490745 0.2491156 0.2493624 0.2497943 [1373] 0.2501645 0.2503497 0.2505553 0.2506376 0.2508638 0.2516248 0.2520362 [1380] 0.2522624 0.2528178 0.2531469 0.2536610 0.2539079 0.2541958 0.2545866 [1387] 0.2546277 0.2549157 0.2557589 0.2561086 0.2562937 0.2567256 0.2567462 [1394] 0.2569519 0.2575895 0.2579597 0.2583093 0.2586796 0.2587413 0.2590703 [1401] 0.2597491 0.2601193 0.2601810 0.2605512 0.2606541 0.2608597 0.2615179 [1408] 0.2617647 0.2620938 0.2624023 0.2625463 0.2628137 0.2634718 0.2639860 [1415] 0.2642328 0.2647676 0.2650350 0.2657960 0.2660633 0.2663307 0.2667832 [1422] 0.2668655 0.2671740 0.2677910 0.2680173 0.2681818 0.2684903 0.2685726 [1429] 0.2687577 0.2694776 0.2696833 0.2699506 0.2703620 0.2704443 0.2706499 [1436] 0.2711641 0.2715343 0.2716989 0.2720485 0.2721308 0.2723571 0.2731798 [1443] 0.2734471 0.2736940 0.2744138 0.2745167 0.2748252 0.2754216 0.2758124 [1450] 0.2759770 0.2762032 0.2762443 0.2765734 0.2772727 0.2776224 0.2778075 [1457] 0.2781983 0.2782188 0.2785891 0.2789593 0.2791444 0.2793706 0.2796791 [1464] 0.2798026 0.2800699 0.2809338 0.2813040 0.2814685 0.2820856 0.2821473 [1471] 0.2823324 0.2829288 0.2833196 0.2836898 0.2841423 0.2841629 0.2844714 [1478] 0.2852735 0.2857466 0.2858906 0.2863019 0.2866104 0.2872686 0.2874743 [1485] 0.2876388 0.2880090 0.2880708 0.2884615 0.2890580 0.2893665 0.2895722 [1492] 0.2900658 0.2901275 0.2902921 0.2910119 0.2913204 0.2917318 0.2923283 [1499] 0.2923900 0.2927807 0.2935212 0.2941176 0.2943850 0.2947964 0.2948375 [1506] 0.2951049 0.2959070 0.2961538 0.2964212 0.2968326 0.2968943 0.2972439 [1513] 0.2977170 0.2981489 0.2983957 0.2988071 0.2988276 0.2990128 0.2996503 [1520] 0.2998355 0.3000823 0.3007610 0.3009050 0.3011107 0.3017277 0.3021185 [1527] 0.3024476 0.3028178 0.3029617 0.3031057 0.3041958 0.3045043 0.3048334 [1534] 0.3054299 0.3054504 0.3058206 0.3063760 0.3066845 0.3069107 0.3071164 [1541] 0.3071781 0.3074249 0.3081242 0.3083710 0.3085561 0.3092143 0.3092966 [1548] 0.3094817 0.3098725 0.3102838 0.3106746 0.3110860 0.3112299 0.3115179 [1555] 0.3123200 0.3127314 0.3129165 0.3134307 0.3134924 0.3136775 0.3143974 [1562] 0.3146442 0.3148910 0.3152818 0.3154258 0.3156931 0.3165570 0.3169066 [1569] 0.3170506 0.3175442 0.3175648 0.3177088 0.3183052 0.3185726 0.3189017 [1576] 0.3193336 0.3194159 0.3197038 0.3203826 0.3206911 0.3208556 0.3214521 [1583] 0.3214932 0.3216783 0.3225216 0.3228507 0.3230975 0.3235705 0.3236528 [1590] 0.3240230 0.3246401 0.3251131 0.3253394 0.3256890 0.3257507 0.3259358 [1597] 0.3266968 0.3268614 0.3270876 0.3276018 0.3277458 0.3280543 0.3286302 [1604] 0.3291238 0.3293912 0.3297820 0.3298643 0.3300288 0.3308515 0.3311806 [1611] 0.3315302 0.3323118 0.3326409 0.3332785 0.3336898 0.3339984 0.3343686 [1618] 0.3344508 0.3346771 0.3356232 0.3359317 0.3360963 0.3367544 0.3368367 [1625] 0.3371452 0.3375977 0.3380090 0.3382970 0.3386466 0.3387289 0.3388729 [1632] 0.3398190 0.3401687 0.3403949 0.3410531 0.3410942 0.3414027 0.3418963 [1639] 0.3422460 0.3426573 0.3431715 0.3433566 0.3436240 0.3445084 0.3448375 [1646] 0.3450638 0.3456808 0.3457014 0.3459276 0.3465858 0.3468531 0.3473468 [1653] 0.3477787 0.3478610 0.3481695 0.3488482 0.3491773 0.3493213 0.3498972 [1660] 0.3500000 0.3500823 0.3508433 0.3511518 0.3513986 0.3520773 0.3522830 [1667] 0.3524476 0.3531469 0.3536405 0.3538873 0.3544632 0.3545249 0.3547306 [1674] 0.3554093 0.3557178 0.3560675 0.3564994 0.3566022 0.3569107 0.3574455 [1681] 0.3577129 0.3578980 0.3582682 0.3583093 0.3584944 0.3592143 0.3594200 [1688] 0.3597491 0.3603455 0.3605306 0.3607775 0.3613328 0.3617441 0.3620938 [1695] 0.3625257 0.3626080 0.3627520 0.3636981 0.3641094 0.3643562 0.3650967 [1702] 0.3651584 0.3654052 0.3660222 0.3665775 0.3667832 0.3670712 0.3671329 [1709] 0.3673797 0.3682024 0.3685520 0.3687371 0.3693953 0.3694364 0.3696833 [1716] 0.3701152 0.3703826 0.3705882 0.3709996 0.3711847 0.3713698 0.3721719 [1723] 0.3726039 0.3728507 0.3735088 0.3735705 0.3737968 0.3745372 0.3749074 [1730] 0.3754011 0.3758947 0.3759358 0.3762443 0.3773550 0.3777664 0.3779103 [1737] 0.3784451 0.3785068 0.3786302 0.3792061 0.3795146 0.3798437 0.3803579 [1744] 0.3805430 0.3807898 0.3814068 0.3819210 0.3821678 0.3829288 0.3830522 [1751] 0.3832168 0.3840601 0.3843686 0.3847799 0.3853764 0.3854998 0.3857672 [1758] 0.3865693 0.3870424 0.3873097 0.3877417 0.3878445 0.3880502 0.3888935 [1765] 0.3891814 0.3894899 0.3900247 0.3901687 0.3903743 0.3908885 0.3913410 [1772] 0.3915878 0.3920403 0.3921843 0.3923488 0.3930276 0.3931921 0.3936035 [1779] 0.3943850 0.3945701 0.3947347 0.3953517 0.3958248 0.3961127 0.3965858 [1786] 0.3966886 0.3968531 0.3978404 0.3981900 0.3984574 0.3992184 0.3993213 [1793] 0.3996915 0.4002674 0.4005348 0.4007816 0.4011312 0.4013575 0.4015426 [1800] 0.4024064 0.4028178 0.4030440 0.4036405 0.4037022 0.4038462 0.4042369 [1807] 0.4045866 0.4049568 0.4054710 0.4055944 0.4058618 0.4066845 0.4070341 [1814] 0.4072810 0.4080625 0.4081859 0.4083505 0.4090703 0.4093377 0.4096051 [1821] 0.4100987 0.4102838 0.4105512 0.4111682 0.4115590 0.4117647 0.4122789 [1828] 0.4123406 0.4124846 0.4131839 0.4134307 0.4137803 0.4144385 0.4145208 [1835] 0.4148499 0.4156109 0.4160633 0.4163307 0.4169889 0.4170506 0.4172357 [1842] 0.4179967 0.4183052 0.4187371 0.4192925 0.4194159 0.4197450 0.4203003 [1849] 0.4208556 0.4211641 0.4216578 0.4217606 0.4219663 0.4227273 0.4229535 [1856] 0.4231386 0.4237968 0.4240025 0.4242081 0.4247429 0.4251337 0.4254422 [1863] 0.4259358 0.4261004 0.4261826 0.4270465 0.4273756 0.4277869 0.4286919 [1870] 0.4287536 0.4291238 0.4297408 0.4302962 0.4306458 0.4310572 0.4311806 [1877] 0.4314068 0.4322912 0.4325175 0.4328260 0.4336281 0.4337515 0.4339161 [1884] 0.4344508 0.4348005 0.4352530 0.4356643 0.4358700 0.4360551 0.4368367 [1891] 0.4372480 0.4374949 0.4382970 0.4384204 0.4385644 0.4391197 0.4395516 [1898] 0.4399630 0.4405389 0.4408063 0.4409914 0.4420403 0.4424722 0.4427396 [1905] 0.4433155 0.4433978 0.4435829 0.4440971 0.4443028 0.4447758 0.4452900 [1912] 0.4454340 0.4456397 0.4461744 0.4463390 0.4465035 0.4472645 0.4474496 [1919] 0.4475319 0.4482723 0.4485808 0.4489716 0.4496298 0.4498560 0.4500617 [1926] 0.4508638 0.4513780 0.4516865 0.4522624 0.4523036 0.4524476 0.4533114 [1933] 0.4535993 0.4538667 0.4543809 0.4545455 0.4547923 0.4553065 0.4557178 [1940] 0.4559852 0.4564582 0.4566022 0.4567256 0.4572604 0.4574866 0.4578363 [1947] 0.4585767 0.4587618 0.4590086 0.4595640 0.4599136 0.4602838 0.4608803 [1954] 0.4609831 0.4611477 0.4621555 0.4625257 0.4628342 0.4636364 0.4637598 [1961] 0.4640477 0.4646647 0.4650144 0.4652818 0.4656726 0.4657960 0.4659399 [1968] 0.4667421 0.4670300 0.4672768 0.4680173 0.4680995 0.4683258 0.4687371 [1975] 0.4691485 0.4695187 0.4701152 0.4703209 0.4704854 0.4713698 0.4717812 [1982] 0.4721308 0.4730564 0.4731386 0.4733649 0.4740847 0.4743727 0.4749074 [1989] 0.4754628 0.4756273 0.4759564 0.4766763 0.4770465 0.4772316 0.4777869 [1996] 0.4779515 0.4780543 0.4785891 0.4788770 0.4792678 0.4798848 0.4800905 [2003] 0.4801522 0.4808309 0.4812423 0.4815714 0.4824146 0.4825381 0.4826615 [2010] 0.4833813 0.4836898 0.4841835 0.4849033 0.4851296 0.4853353 0.4859934 [2017] 0.4863225 0.4865693 0.4872069 0.4873097 0.4874743 0.4881942 0.4885027 [2024] 0.4888729 0.4895105 0.4897367 0.4899424 0.4904977 0.4908885 0.4911970 [2031] 0.4917318 0.4918552 0.4919580 0.4926368 0.4928630 0.4932949 0.4941999 [2038] 0.4944467 0.4945907 0.4952077 0.4957014 0.4960716 0.4965652 0.4967503 [2045] 0.4969148 0.4976347 0.4979227 0.4982517 0.4991156 0.4991979 0.4993418 [2052] 0.4998149 0.5000000 0.5001851 0.5006582 0.5008021 0.5008844 0.5017483 [2059] 0.5020773 0.5023653 0.5030852 0.5032497 0.5034348 0.5039284 0.5042986 [2066] 0.5047923 0.5054093 0.5055533 0.5058001 0.5067051 0.5071370 0.5073632 [2073] 0.5080420 0.5081448 0.5082682 0.5088030 0.5091115 0.5095023 0.5100576 [2080] 0.5102633 0.5104895 0.5111271 0.5114973 0.5118058 0.5125257 0.5126903 [2087] 0.5127931 0.5134307 0.5136775 0.5140066 0.5146647 0.5148704 0.5150967 [2094] 0.5158165 0.5163102 0.5166187 0.5173385 0.5174619 0.5175854 0.5184286 [2101] 0.5187577 0.5191691 0.5198478 0.5199095 0.5201152 0.5207322 0.5211230 [2108] 0.5214109 0.5219457 0.5220485 0.5222131 0.5227684 0.5229535 0.5233237 [2115] 0.5240436 0.5243727 0.5245372 0.5250926 0.5256273 0.5259153 0.5266351 [2122] 0.5268614 0.5269436 0.5278692 0.5282188 0.5286302 0.5295146 0.5296791 [2129] 0.5298848 0.5304813 0.5308515 0.5312629 0.5316742 0.5319005 0.5319827 [2136] 0.5327232 0.5329700 0.5332579 0.5340601 0.5342040 0.5343274 0.5347182 [2143] 0.5349856 0.5353353 0.5359523 0.5362402 0.5363636 0.5371658 0.5374743 [2150] 0.5378445 0.5388523 0.5390169 0.5391197 0.5397162 0.5400864 0.5404360 [2157] 0.5409914 0.5412382 0.5414233 0.5421637 0.5425134 0.5427396 0.5432744 [2164] 0.5433978 0.5435418 0.5440148 0.5442822 0.5446935 0.5452077 0.5454545 [2171] 0.5456191 0.5461333 0.5464007 0.5466886 0.5475524 0.5476964 0.5477376 [2178] 0.5483135 0.5486220 0.5491362 0.5499383 0.5501440 0.5503702 0.5510284 [2185] 0.5514192 0.5517277 0.5524681 0.5525504 0.5527355 0.5534965 0.5536610 [2192] 0.5538256 0.5543603 0.5545660 0.5547100 0.5552242 0.5556972 0.5559029 [2199] 0.5564171 0.5566022 0.5566845 0.5572604 0.5575278 0.5579597 0.5590086 [2206] 0.5591937 0.5594611 0.5600370 0.5604484 0.5608803 0.5614356 0.5615796 [2213] 0.5617030 0.5625051 0.5627520 0.5631633 0.5639449 0.5641300 0.5643357 [2220] 0.5647470 0.5651995 0.5655492 0.5660839 0.5662485 0.5663719 0.5671740 [2227] 0.5674825 0.5677088 0.5685932 0.5688194 0.5689428 0.5693542 0.5697038 [2234] 0.5702592 0.5708762 0.5712464 0.5713081 0.5722131 0.5726244 0.5729535 [2241] 0.5738174 0.5738996 0.5740642 0.5745578 0.5748663 0.5752571 0.5757919 [2248] 0.5759975 0.5762032 0.5768614 0.5770465 0.5772727 0.5780337 0.5782394 [2255] 0.5783422 0.5788359 0.5791444 0.5796997 0.5802550 0.5805841 0.5807075 [2262] 0.5812629 0.5816948 0.5820033 0.5827643 0.5829494 0.5830111 0.5836693 [2269] 0.5839367 0.5843891 0.5851501 0.5854792 0.5855615 0.5862197 0.5865693 [2276] 0.5868161 0.5875154 0.5876594 0.5877211 0.5882353 0.5884410 0.5888318 [2283] 0.5894488 0.5897162 0.5899013 0.5903949 0.5906623 0.5909297 0.5916495 [2290] 0.5918141 0.5919375 0.5927190 0.5929659 0.5933155 0.5941382 0.5944056 [2297] 0.5945290 0.5950432 0.5954134 0.5957631 0.5961538 0.5962978 0.5963595 [2304] 0.5969560 0.5971822 0.5975936 0.5984574 0.5986425 0.5988688 0.5992184 [2311] 0.5994652 0.5997326 0.6003085 0.6006787 0.6007816 0.6015426 0.6018100 [2318] 0.6021596 0.6031469 0.6033114 0.6034142 0.6038873 0.6041752 0.6046483 [2325] 0.6052653 0.6054299 0.6056150 0.6063965 0.6068079 0.6069724 0.6076512 [2332] 0.6078157 0.6079597 0.6084122 0.6086590 0.6091115 0.6096257 0.6098313 [2339] 0.6099753 0.6105101 0.6108186 0.6111065 0.6119498 0.6121555 0.6122583 [2346] 0.6126903 0.6129576 0.6134307 0.6142328 0.6145002 0.6146236 0.6152201 [2353] 0.6156314 0.6159399 0.6167832 0.6169478 0.6170712 0.6178322 0.6180790 [2360] 0.6185932 0.6192102 0.6194570 0.6196421 0.6201563 0.6204854 0.6207939 [2367] 0.6213698 0.6214932 0.6215549 0.6220897 0.6222336 0.6226450 0.6237557 [2374] 0.6240642 0.6241053 0.6245989 0.6250926 0.6254628 0.6262032 0.6264295 [2381] 0.6264912 0.6271493 0.6273961 0.6278281 0.6286302 0.6288153 0.6290004 [2388] 0.6294118 0.6296174 0.6298848 0.6303167 0.6305636 0.6306047 0.6312629 [2395] 0.6314480 0.6317976 0.6326203 0.6328671 0.6329288 0.6332168 0.6334225 [2402] 0.6339778 0.6345948 0.6348416 0.6349033 0.6356438 0.6358906 0.6363019 [2409] 0.6372480 0.6373920 0.6374743 0.6379062 0.6382559 0.6386672 0.6392225 [2416] 0.6394694 0.6396545 0.6402509 0.6405800 0.6407857 0.6415056 0.6416907 [2423] 0.6417318 0.6421020 0.6422871 0.6425545 0.6430893 0.6433978 0.6435006 [2430] 0.6439325 0.6442822 0.6445907 0.6452694 0.6454751 0.6455368 0.6461127 [2437] 0.6463595 0.6468531 0.6475524 0.6477170 0.6479227 0.6486014 0.6488482 [2444] 0.6491567 0.6499177 0.6500000 0.6501028 0.6506787 0.6508227 0.6511518 [2451] 0.6518305 0.6521390 0.6522213 0.6526532 0.6531469 0.6534142 0.6540724 [2458] 0.6542986 0.6543192 0.6549362 0.6551625 0.6554916 0.6563760 0.6566434 [2465] 0.6568285 0.6573427 0.6577540 0.6581037 0.6585973 0.6589058 0.6589469 [2472] 0.6596051 0.6598313 0.6601810 0.6611271 0.6612711 0.6613534 0.6617030 [2479] 0.6619910 0.6624023 0.6628548 0.6631633 0.6632456 0.6639037 0.6640683 [2486] 0.6643768 0.6653229 0.6655492 0.6656314 0.6660016 0.6663102 0.6667215 [2493] 0.6673591 0.6676882 0.6684698 0.6688194 0.6691485 0.6699712 0.6701357 [2500] 0.6702180 0.6706088 0.6708762 0.6713698 0.6719457 0.6722542 0.6723982 [2507] 0.6729124 0.6731386 0.6733032 0.6740642 0.6742493 0.6743110 0.6746606 [2514] 0.6748869 0.6753599 0.6759770 0.6763472 0.6764295 0.6769025 0.6771493 [2521] 0.6774784 0.6783217 0.6785068 0.6785479 0.6791444 0.6793089 0.6796174 [2528] 0.6802962 0.6805841 0.6806664 0.6810983 0.6814274 0.6816948 0.6822912 [2535] 0.6824352 0.6824558 0.6829494 0.6830934 0.6834430 0.6843069 0.6845742 [2542] 0.6847182 0.6851090 0.6853558 0.6856026 0.6863225 0.6865076 0.6865693 [2549] 0.6870835 0.6872686 0.6876800 0.6884821 0.6887701 0.6889140 0.6893254 [2556] 0.6897162 0.6901275 0.6905183 0.6907034 0.6907857 0.6914439 0.6916290 [2563] 0.6918758 0.6925751 0.6928219 0.6928836 0.6930893 0.6933155 0.6936240 [2570] 0.6941794 0.6945496 0.6945701 0.6951666 0.6954957 0.6958042 0.6968943 [2577] 0.6970383 0.6971822 0.6975524 0.6978815 0.6982723 0.6988893 0.6990950 [2584] 0.6992390 0.6999177 0.7001645 0.7003497 0.7009872 0.7011724 0.7011929 [2591] 0.7016043 0.7018511 0.7022830 0.7027561 0.7031057 0.7031674 0.7035788 [2598] 0.7038462 0.7040930 0.7048951 0.7051625 0.7052036 0.7056150 0.7058824 [2605] 0.7064788 0.7072193 0.7076100 0.7076717 0.7082682 0.7086796 0.7089881 [2612] 0.7097079 0.7098725 0.7099342 0.7104278 0.7106335 0.7109420 0.7115385 [2619] 0.7119292 0.7119910 0.7123612 0.7125257 0.7127314 0.7133896 0.7136981 [2626] 0.7141094 0.7142534 0.7147265 0.7155286 0.7158371 0.7158577 0.7163102 [2633] 0.7166804 0.7170712 0.7176676 0.7178527 0.7179144 0.7185315 0.7186960 [2640] 0.7190662 0.7199301 0.7201974 0.7203209 0.7206294 0.7208556 0.7210407 [2647] 0.7214109 0.7217812 0.7218017 0.7221925 0.7223776 0.7227273 0.7234266 [2654] 0.7237557 0.7237968 0.7240230 0.7241876 0.7245784 0.7251748 0.7254833 [2661] 0.7255862 0.7263060 0.7265529 0.7268202 0.7276429 0.7278692 0.7279515 [2668] 0.7283011 0.7284657 0.7288359 0.7293501 0.7295557 0.7296380 0.7300494 [2675] 0.7303167 0.7305224 0.7312423 0.7314274 0.7315097 0.7318182 0.7319827 [2682] 0.7322090 0.7328260 0.7331345 0.7332168 0.7336693 0.7339367 0.7342040 [2689] 0.7349650 0.7352324 0.7357672 0.7360140 0.7365282 0.7371863 0.7374537 [2696] 0.7375977 0.7379062 0.7382353 0.7384821 0.7391403 0.7393459 0.7394488 [2703] 0.7398190 0.7398807 0.7402509 0.7409297 0.7412587 0.7413204 0.7416907 [2710] 0.7420403 0.7424105 0.7430481 0.7432538 0.7432744 0.7437063 0.7438914 [2717] 0.7442411 0.7450843 0.7453723 0.7454134 0.7458042 0.7460921 0.7463390 [2724] 0.7468531 0.7471822 0.7477376 0.7479638 0.7483752 0.7491362 0.7493624 [2731] 0.7494447 0.7496503 0.7498355 0.7502057 0.7506376 0.7508844 0.7509255 [2738] 0.7513780 0.7514603 0.7517894 0.7528383 0.7531263 0.7531674 0.7534142 [2745] 0.7536816 0.7541341 0.7547306 0.7551831 0.7552242 0.7557795 0.7560263 [2752] 0.7563554 0.7569724 0.7571370 0.7574866 0.7576100 0.7579391 0.7584122 [2759] 0.7586796 0.7587207 0.7590703 0.7592143 0.7593994 0.7602016 0.7604689 [2766] 0.7607569 0.7609420 0.7613945 0.7620527 0.7623817 0.7624640 0.7628959 [2773] 0.7631016 0.7633896 0.7640889 0.7642740 0.7643357 0.7647265 0.7648293 [2780] 0.7651378 0.7656109 0.7659399 0.7660016 0.7663513 0.7665775 0.7668449 [2787] 0.7673797 0.7676676 0.7679967 0.7680790 0.7684081 0.7690868 0.7694776 [2794] 0.7695804 0.7698684 0.7702180 0.7704854 0.7710819 0.7713492 0.7714109 [2801] 0.7718634 0.7720485 0.7723776 0.7732003 0.7733649 0.7734677 0.7737762 [2808] 0.7739613 0.7742493 0.7745784 0.7747635 0.7748046 0.7752160 0.7753394 [2815] 0.7755245 0.7761621 0.7764706 0.7765117 0.7766763 0.7769642 0.7772522 [2822] 0.7778281 0.7781571 0.7787536 0.7790415 0.7793706 0.7803373 0.7805224 [2829] 0.7806047 0.7808721 0.7810160 0.7814685 0.7819827 0.7822912 0.7823529 [2836] 0.7827232 0.7828260 0.7829494 0.7835870 0.7837515 0.7839984 0.7842040 [2843] 0.7846154 0.7851501 0.7855821 0.7856232 0.7860346 0.7861991 0.7865076 [2850] 0.7873509 0.7875977 0.7880296 0.7881736 0.7886261 0.7892225 0.7895311 [2857] 0.7895722 0.7898601 0.7900864 0.7903538 0.7910325 0.7911970 0.7912382 [2864] 0.7914233 0.7915673 0.7918346 0.7923694 0.7927602 0.7928013 0.7930481 [2871] 0.7931510 0.7933155 0.7939120 0.7941588 0.7944673 0.7945290 0.7950226 [2878] 0.7957219 0.7961538 0.7964624 0.7967297 0.7970794 0.7975936 0.7977170 [2885] 0.7977581 0.7981489 0.7982723 0.7985397 0.7992596 0.7995269 0.7996298 [2892] 0.7997943 0.7999589 0.8001234 0.8004525 0.8007610 0.8007816 0.8011518 [2899] 0.8013575 0.8016248 0.8024681 0.8027149 0.8027561 0.8029412 0.8031057 [2906] 0.8033525 0.8038667 0.8041752 0.8041958 0.8046689 0.8048128 0.8049979 [2913] 0.8056355 0.8059029 0.8061703 0.8063965 0.8067873 0.8072604 0.8074044 [2920] 0.8074661 0.8078157 0.8080008 0.8081448 0.8088235 0.8090292 0.8090703 [2927] 0.8092966 0.8093994 0.8097902 0.8103455 0.8108392 0.8108803 0.8112505 [2934] 0.8114973 0.8117236 0.8124434 0.8126903 0.8130399 0.8132456 0.8135747 [2941] 0.8140271 0.8143357 0.8143768 0.8147470 0.8149321 0.8151378 0.8156520 [2948] 0.8158782 0.8159194 0.8161868 0.8162690 0.8166187 0.8171740 0.8175031 [2955] 0.8175442 0.8176882 0.8179350 0.8182230 0.8187988 0.8190251 0.8192925 [2962] 0.8193747 0.8197655 0.8205882 0.8209379 0.8209585 0.8212670 0.8214521 [2969] 0.8216166 0.8220280 0.8222954 0.8226656 0.8227890 0.8231181 0.8236940 [2976] 0.8240642 0.8241053 0.8242287 0.8243521 0.8246195 0.8250720 0.8254628 [2983] 0.8255245 0.8258741 0.8260181 0.8262649 0.8270876 0.8273139 0.8273550 [2990] 0.8274784 0.8276224 0.8279926 0.8284451 0.8287125 0.8287536 0.8291032 [2997] 0.8291855 0.8294735 0.8299877 0.8302139 0.8303990 0.8304401 0.8306047 [3004] 0.8309955 0.8314685 0.8315097 0.8317359 0.8318799 0.8320239 0.8328054 [3011] 0.8331139 0.8333608 0.8335253 0.8338955 0.8344714 0.8346977 0.8347799 [3018] 0.8350679 0.8352324 0.8354175 0.8360140 0.8361785 0.8362402 0.8364459 [3025] 0.8364665 0.8367133 0.8370629 0.8374126 0.8374332 0.8375977 0.8378651 [3032] 0.8380913 0.8385849 0.8388112 0.8390580 0.8391814 0.8394694 0.8401070 [3039] 0.8404772 0.8404977 0.8407445 0.8409502 0.8411765 0.8416495 0.8419169 [3046] 0.8422460 0.8423900 0.8427190 0.8434183 0.8435829 0.8436446 0.8437680 [3053] 0.8439531 0.8441382 0.8444467 0.8446524 0.8446730 0.8450226 0.8450432 [3060] 0.8452694 0.8461127 0.8464007 0.8465858 0.8467914 0.8471822 0.8476142 [3067] 0.8479638 0.8483135 0.8485191 0.8488071 0.8494241 0.8495886 0.8496298 [3074] 0.8497738 0.8499177 0.8502262 0.8506582 0.8510695 0.8511107 0.8513986 [3081] 0.8514809 0.8516454 0.8522419 0.8525093 0.8526121 0.8526532 0.8531057 [3088] 0.8535582 0.8539079 0.8541958 0.8542164 0.8544220 0.8551419 0.8553887 [3095] 0.8556972 0.8558001 0.8560880 0.8564788 0.8568285 0.8568696 0.8570958 [3102] 0.8572810 0.8575072 0.8580420 0.8581654 0.8583093 0.8583505 0.8585973 [3109] 0.8590086 0.8593994 0.8594611 0.8595023 0.8596051 0.8597696 0.8602221 [3116] 0.8605512 0.8605718 0.8607363 0.8607775 0.8611065 0.8617236 0.8621555 [3123] 0.8624434 0.8626080 0.8628342 0.8632044 0.8633690 0.8634101 0.8637186 [3130] 0.8637803 0.8639860 0.8645825 0.8648087 0.8648704 0.8649321 0.8650350 [3137] 0.8651789 0.8655286 0.8657548 0.8657754 0.8659811 0.8660839 0.8662896 [3144] 0.8669066 0.8670917 0.8671329 0.8671740 0.8673180 0.8675648 0.8679967 [3151] 0.8683669 0.8683875 0.8687166 0.8688400 0.8689223 0.8695393 0.8697450 [3158] 0.8699301 0.8700535 0.8704854 0.8707733 0.8711024 0.8711230 0.8713081 [3165] 0.8714109 0.8716166 0.8721925 0.8724188 0.8724393 0.8725422 0.8726244 [3172] 0.8728712 0.8733854 0.8736940 0.8739202 0.8740847 0.8743316 0.8750103 [3179] 0.8751543 0.8753805 0.8754833 0.8758536 0.8762032 0.8764912 0.8766968 [3186] 0.8767791 0.8768408 0.8772522 0.8774578 0.8776018 0.8776635 0.8779515 [3193] 0.8784657 0.8789181 0.8789387 0.8790621 0.8792061 0.8794940 0.8799671 [3200] 0.8801316 0.8803784 0.8807281 0.8813451 0.8816331 0.8816536 0.8817770 [3207] 0.8818799 0.8820444 0.8823118 0.8825792 0.8828260 0.8829083 0.8830934 [3214] 0.8837721 0.8841012 0.8842246 0.8843069 0.8844303 0.8847799 0.8851090 [3221] 0.8853353 0.8854381 0.8856232 0.8861374 0.8863842 0.8864253 0.8864870 [3228] 0.8865693 0.8868778 0.8872069 0.8873303 0.8873715 0.8876183 0.8876800 [3235] 0.8877828 0.8881942 0.8884410 0.8885644 0.8887906 0.8891197 0.8894899 [3242] 0.8896956 0.8898396 0.8899835 0.8906211 0.8908268 0.8910325 0.8912176 [3249] 0.8914439 0.8918141 0.8920609 0.8921226 0.8922460 0.8923694 0.8924722 [3256] 0.8929453 0.8931098 0.8931304 0.8932538 0.8932744 0.8934389 0.8938091 [3263] 0.8940148 0.8940971 0.8941999 0.8943645 0.8947347 0.8948787 0.8950432 [3270] 0.8953517 0.8959070 0.8962978 0.8963184 0.8965652 0.8967297 0.8968737 [3277] 0.8972028 0.8974085 0.8975936 0.8977170 0.8979844 0.8985603 0.8987659 [3284] 0.8987865 0.8988071 0.8988893 0.8991156 0.8994652 0.8998149 0.8999589 [3291] 0.9001234 0.9006582 0.9009461 0.9009667 0.9010490 0.9013575 0.9017071 [3298] 0.9020568 0.9023447 0.9024476 0.9026944 0.9032703 0.9034554 0.9035993 [3305] 0.9036816 0.9038256 0.9040107 0.9043603 0.9043809 0.9044632 0.9045043 [3312] 0.9046483 0.9049979 0.9052448 0.9052859 0.9055738 0.9059441 0.9062731 [3319] 0.9062937 0.9064582 0.9065405 0.9066434 0.9072398 0.9075072 0.9076923 [3326] 0.9077129 0.9079186 0.9082271 0.9085561 0.9087207 0.9088852 0.9090086 [3333] 0.9092760 0.9093789 0.9095023 0.9095640 0.9096257 0.9099342 0.9102633 [3340] 0.9102838 0.9103250 0.9104072 0.9104895 0.9109009 0.9111888 0.9113945 [3347] 0.9114562 0.9117030 0.9122583 0.9125463 0.9126697 0.9128137 0.9129576 [3354] 0.9131222 0.9132250 0.9134718 0.9135130 0.9135952 0.9140066 0.9142534 [3361] 0.9142740 0.9143562 0.9144796 0.9146647 0.9149116 0.9151584 0.9153229 [3368] 0.9154258 0.9156520 0.9161662 0.9162896 0.9163513 0.9163924 0.9166392 [3375] 0.9169683 0.9173180 0.9175442 0.9176059 0.9176676 0.9180378 0.9182435 [3382] 0.9183464 0.9184286 0.9186137 0.9187988 0.9190868 0.9191074 0.9192513 [3389] 0.9192719 0.9193747 0.9199095 0.9201769 0.9202797 0.9203414 0.9206294 [3396] 0.9209379 0.9212464 0.9212670 0.9213081 0.9213698 0.9215961 0.9220280 [3403] 0.9220897 0.9221925 0.9223982 0.9227273 0.9230769 0.9232003 0.9232415 [3410] 0.9232620 0.9236117 0.9238791 0.9239613 0.9239819 0.9242081 0.9246606 [3417] 0.9250720 0.9251748 0.9252982 0.9254628 0.9257919 0.9259564 0.9259770 [3424] 0.9260592 0.9260798 0.9262443 0.9266146 0.9269025 0.9269231 0.9270259 [3431] 0.9272522 0.9274990 0.9276018 0.9277869 0.9282394 0.9285068 0.9285479 [3438] 0.9286302 0.9287742 0.9290004 0.9293295 0.9295352 0.9296174 0.9296997 [3445] 0.9300905 0.9302962 0.9303373 0.9304196 0.9306458 0.9308104 0.9309749 [3452] 0.9309955 0.9310366 0.9311189 0.9312012 0.9314685 0.9316948 0.9318593 [3459] 0.9321473 0.9324352 0.9325998 0.9327232 0.9328466 0.9332785 0.9334430 [3466] 0.9335870 0.9336898 0.9338749 0.9341012 0.9343274 0.9344097 0.9344920 [3473] 0.9345331 0.9348005 0.9349239 0.9350473 0.9350679 0.9352735 0.9355204 [3480] 0.9358083 0.9358494 0.9359317 0.9361374 0.9365076 0.9365899 0.9367750 [3487] 0.9369601 0.9374332 0.9377828 0.9379268 0.9380090 0.9380913 0.9382970 [3494] 0.9386055 0.9387289 0.9387906 0.9389757 0.9392431 0.9393871 0.9394077 [3501] 0.9394282 0.9394899 0.9396339 0.9398807 0.9399630 0.9401070 0.9405800 [3508] 0.9409502 0.9409914 0.9412176 0.9415261 0.9417318 0.9418963 0.9419375 [3515] 0.9420814 0.9423694 0.9425339 0.9426162 0.9426573 0.9427396 0.9428013 [3522] 0.9430687 0.9430893 0.9431510 0.9432127 0.9432538 0.9436446 0.9438708 [3529] 0.9438914 0.9439325 0.9441176 0.9443645 0.9446524 0.9446730 0.9447552 [3536] 0.9451049 0.9452694 0.9453517 0.9454340 0.9457014 0.9458248 0.9459276 [3543] 0.9459893 0.9460304 0.9462567 0.9463184 0.9464007 0.9464212 0.9465858 [3550] 0.9468737 0.9471822 0.9472234 0.9473056 0.9473879 0.9476759 0.9478404 [3557] 0.9478610 0.9478815 0.9480666 0.9484780 0.9486425 0.9486837 0.9487248 [3564] 0.9488893 0.9490539 0.9492596 0.9493624 0.9494035 0.9497326 0.9499383 [3571] 0.9499589 0.9500411 0.9501851 0.9503291 0.9505759 0.9506582 0.9507199 [3578] 0.9509255 0.9512752 0.9513780 0.9513986 0.9515837 0.9517894 0.9519745 [3585] 0.9520568 0.9520979 0.9521802 0.9524681 0.9526738 0.9526944 0.9527355 [3592] 0.9529000 0.9531263 0.9534554 0.9535788 0.9536405 0.9536610 0.9539284 [3599] 0.9541547 0.9542369 0.9542781 0.9544426 0.9545455 0.9548540 0.9548951 [3606] 0.9550596 0.9553270 0.9553682 0.9554504 0.9555327 0.9556767 0.9560469 [3613] 0.9560880 0.9561086 0.9563760 0.9566228 0.9567256 0.9567668 0.9568490 [3620] 0.9571575 0.9573838 0.9574866 0.9575689 0.9575895 0.9577334 0.9578363 [3627] 0.9578980 0.9579186 0.9580008 0.9581654 0.9584327 0.9584739 0.9585561 [3634] 0.9586384 0.9587618 0.9587824 0.9588030 0.9589264 0.9592760 0.9594406 [3641] 0.9594817 0.9595640 0.9597491 0.9600165 0.9601604 0.9602016 0.9604689 [3648] 0.9605718 0.9606129 0.9606746 0.9607569 0.9608186 0.9609009 0.9609420 [3655] 0.9609626 0.9610037 0.9613328 0.9614768 0.9614973 0.9616619 0.9618881 [3662] 0.9621349 0.9621555 0.9622583 0.9625463 0.9626080 0.9626491 0.9626903 [3669] 0.9628754 0.9631016 0.9633690 0.9634307 0.9634718 0.9634924 0.9636569 [3676] 0.9638626 0.9638832 0.9640477 0.9642534 0.9645619 0.9647059 0.9650144 [3683] 0.9651172 0.9652201 0.9655492 0.9657960 0.9658371 0.9658782 0.9659399 [3690] 0.9660633 0.9661662 0.9662279 0.9662485 0.9663719 0.9665570 0.9667626 [3697] 0.9668038 0.9668655 0.9669066 0.9672151 0.9672357 0.9673385 0.9676265 [3704] 0.9679350 0.9680790 0.9683052 0.9684286 0.9685315 0.9685726 0.9686137 [3711] 0.9688194 0.9689428 0.9689840 0.9690045 0.9690868 0.9692925 0.9693336 [3718] 0.9693747 0.9693953 0.9695187 0.9696216 0.9696421 0.9697038 0.9698272 [3725] 0.9698889 0.9700535 0.9700740 0.9701357 0.9703826 0.9705060 0.9705677 [3732] 0.9706911 0.9708350 0.9711230 0.9711436 0.9711641 0.9712258 0.9713904 [3739] 0.9714932 0.9715343 0.9715755 0.9716989 0.9719251 0.9719868 0.9720485 [3746] 0.9720897 0.9721719 0.9723159 0.9723365 0.9723571 0.9725216 0.9726861 [3753] 0.9727684 0.9728301 0.9729329 0.9730975 0.9731386 0.9731798 0.9734471 [3760] 0.9736734 0.9736940 0.9737351 0.9738379 0.9740025 0.9740847 0.9741670 [3767] 0.9744344 0.9745784 0.9745989 0.9746812 0.9747635 0.9750103 0.9750720 [3774] 0.9753599 0.9754422 0.9755450 0.9757507 0.9759564 0.9759770 0.9761621 [3781] 0.9763677 0.9763883 0.9764706 0.9765940 0.9767585 0.9767791 0.9768408 [3788] 0.9769642 0.9770053 0.9771288 0.9772727 0.9774784 0.9775401 0.9777869 [3795] 0.9778898 0.9779720 0.9781983 0.9783628 0.9784245 0.9784862 0.9785479 [3802] 0.9786302 0.9786508 0.9786713 0.9787947 0.9789181 0.9790004 0.9790210 [3809] 0.9791238 0.9791444 0.9792884 0.9795352 0.9795763 0.9796586 0.9798231 [3816] 0.9799260 0.9799877 0.9800082 0.9800288 0.9802139 0.9802962 0.9803167 [3823] 0.9803373 0.9804401 0.9805019 0.9806664 0.9807487 0.9808926 0.9810160 [3830] 0.9810777 0.9814068 0.9815097 0.9817565 0.9817976 0.9818387 0.9819005 [3837] 0.9819827 0.9821267 0.9821473 0.9821678 0.9822090 0.9823735 0.9824146 [3844] 0.9824558 0.9827026 0.9827232 0.9827437 0.9828466 0.9829494 0.9830317 [3851] 0.9831962 0.9834019 0.9834225 0.9835047 0.9835459 0.9835870 0.9837310 [3858] 0.9838749 0.9841012 0.9841218 0.9841423 0.9841629 0.9843686 0.9844714 [3865] 0.9845537 0.9846565 0.9846977 0.9847182 0.9848828 0.9849445 0.9849856 [3872] 0.9851090 0.9852118 0.9853353 0.9853970 0.9854175 0.9855409 0.9856438 [3879] 0.9858083 0.9858494 0.9859317 0.9860140 0.9860551 0.9861580 0.9862608 [3886] 0.9862814 0.9863431 0.9865487 0.9865899 0.9866310 0.9867750 0.9869601 [3893] 0.9870012 0.9870218 0.9871041 0.9871863 0.9873303 0.9874126 0.9874332 [3900] 0.9874743 0.9875771 0.9875977 0.9876594 0.9878445 0.9880502 0.9881119 [3907] 0.9882147 0.9883381 0.9883587 0.9884204 0.9885438 0.9885849 0.9887906 [3914] 0.9888318 0.9888729 0.9889140 0.9889757 0.9890374 0.9891608 0.9892842 [3921] 0.9894077 0.9894282 0.9894694 0.9896133 0.9896339 0.9896956 0.9898807 [3928] 0.9899218 0.9900041 0.9901070 0.9901481 0.9902921 0.9903332 0.9903538 [3935] 0.9903743 0.9904360 0.9904566 0.9905389 0.9906828 0.9908063 0.9908680 [3942] 0.9910325 0.9910942 0.9911559 0.9912587 0.9914027 0.9914644 0.9914850 [3949] 0.9915261 0.9915878 0.9916907 0.9917318 0.9919169 0.9919580 0.9920403 [3956] 0.9922049 0.9922666 0.9923900 0.9924105 0.9924517 0.9925134 0.9926162 [3963] 0.9926573 0.9927396 0.9929042 0.9929453 0.9930070 0.9930481 0.9931304 [3970] 0.9932332 0.9932538 0.9932949 0.9933155 0.9933566 0.9934595 0.9935006 [3977] 0.9935212 0.9935418 0.9936446 0.9937063 0.9937474 0.9938297 0.9938503 [3984] 0.9938914 0.9939325 0.9939737 0.9941176 0.9941382 0.9941794 0.9942205 [3991] 0.9942411 0.9943233 0.9943645 0.9944879 0.9945084 0.9945290 0.9946318 [3998] 0.9946935 0.9947141 0.9947758 0.9949609 0.9950226 0.9950638 0.9951049 [4005] 0.9952283 0.9952489 0.9953928 0.9954751 0.9955368 0.9956191 0.9956602 [4012] 0.9956808 0.9957631 0.9958248 0.9958659 0.9959070 0.9959482 0.9959893 [4019] 0.9960099 0.9961127 0.9961538 0.9961950 0.9962155 0.9962361 0.9963390 [4026] 0.9963801 0.9964418 0.9965035 0.9965241 0.9965446 0.9965858 0.9967092 [4033] 0.9967297 0.9968531 0.9968943 0.9969148 0.9969971 0.9970177 0.9970383 [4040] 0.9971205 0.9972645 0.9973468 0.9973879 0.9974085 0.9974290 0.9975113 [4047] 0.9975319 0.9976142 0.9976759 0.9976964 0.9978198 0.9978610 0.9979021 [4054] 0.9979227 0.9979638 0.9979844 0.9980666 0.9980872 0.9981489 0.9981900 [4061] 0.9982517 0.9982723 0.9983135 0.9983340 0.9983546 0.9984163 0.9984574 [4068] 0.9985397 0.9985808 0.9986014 0.9986631 0.9987042 0.9987248 0.9988071 [4075] 0.9988688 0.9989099 0.9989305 0.9989716 0.9990950 0.9991362 0.9991567 [4082] 0.9991773 0.9992184 0.9992596 0.9993007 0.9993213 0.9993418 0.9993624 [4089] 0.9994035 0.9994241 0.9994447 0.9994858 0.9995269 0.9995886 0.9996503 [4096] 0.9996915 0.9997326 0.9997532 0.9997943 0.9998355 0.9998560 0.9998972 [4103] 0.9999177 0.9999589 0.9999794 1.0000000 > round(qp_it1_vdW <- qperm(it1_vdW, seq(0, 1, 0.01)), 7) [1] -10.0000000 -2.2408882 -2.0193392 -1.8687838 -1.7525012 -1.6582511 [7] -1.5731812 -1.4942314 -1.4281340 -1.3669326 -1.3100153 -1.2555461 [13] -1.2016889 -1.1563999 -1.1086628 -1.0652098 -1.0229809 -0.9813640 [19] -0.9434191 -0.9066983 -0.8693655 -0.8320326 -0.7965358 -0.7647111 [25] -0.7292143 -0.6980016 -0.6674009 -0.6355762 -0.6019155 -0.5743749 [31] -0.5443862 -0.5143975 -0.4844088 -0.4550322 -0.4287156 -0.3999509 [37] -0.3724103 -0.3436457 -0.3173291 -0.2928486 -0.2640839 -0.2377673 [43] -0.2090027 -0.1839101 -0.1582055 -0.1306649 -0.1037363 -0.0786438 [49] -0.0529392 -0.0253986 -0.0003060 0.0253986 0.0529392 0.0786438 [55] 0.1037363 0.1306649 0.1582055 0.1839101 0.2090027 0.2377673 [61] 0.2640839 0.2928486 0.3173291 0.3436457 0.3724103 0.3999510 [67] 0.4287156 0.4550322 0.4844088 0.5143975 0.5443862 0.5743749 [73] 0.6019155 0.6355762 0.6674009 0.6980016 0.7292143 0.7647111 [79] 0.7965358 0.8320326 0.8693655 0.9066983 0.9434191 0.9813640 [85] 1.0229809 1.0652098 1.1086628 1.1563999 1.2016889 1.2555461 [91] 1.3100153 1.3669326 1.4281340 1.4942314 1.5731812 1.6582511 [97] 1.7525012 1.8687838 2.0193392 2.2408881 10.0000000 > round(rp_it1_vdW <- rperm(it1_vdW, 5), 7) [1] 0.4464640 -0.5639706 -0.1643257 -0.5388781 -1.0413413 > > ### should be equal > stopifnot(isequal(pp_it1_SR, pp_it1_vdW)) > ## Doesn't pass under Solaris or Linux w/o long doubles > ## stopifnot(isequal(qp_it1_SR[-c(1, 101)], qp_it1_vdW[-c(1, 101)])) > ## > stopifnot(isequal(pvalue(it1_SR), pvalue(it1_vdW))) > > ### shift with block > it2_SR <- independence_test(y ~ x | b, data = dta1, + distribution = exact(algorithm = "shift")) > supp_it2_SR <- support(it2_SR) > stopifnot(!is.unsorted(supp_it2_SR)) # failed in < 1.1-0 > stopifnot(all(supp_it2_SR == unique(supp_it2_SR))) # failed in < 1.1-0 > round(pp_it2_SR <- pperm(it2_SR, supp_it2_SR), 7) [1] 0.0019531 0.0039063 0.0058594 0.0078125 0.0097656 0.0117188 0.0136719 [8] 0.0156250 0.0175781 0.0195312 0.0214844 0.0234375 0.0253906 0.0273438 [15] 0.0292969 0.0312500 0.0332031 0.0351562 0.0371094 0.0390625 0.0410156 [22] 0.0429688 0.0449219 0.0468750 0.0488281 0.0507812 0.0527344 0.0546875 [29] 0.0566406 0.0585938 0.0605469 0.0625000 0.0644531 0.0664062 0.0683594 [36] 0.0703125 0.0722656 0.0742188 0.0761719 0.0781250 0.0800781 0.0820312 [43] 0.0839844 0.0859375 0.0878906 0.0898438 0.0917969 0.0937500 0.0957031 [50] 0.0996094 0.1015625 0.1035156 0.1054688 0.1074219 0.1093750 0.1113281 [57] 0.1132812 0.1152344 0.1171875 0.1191406 0.1210938 0.1250000 0.1269531 [64] 0.1289062 0.1308594 0.1328125 0.1347656 0.1367188 0.1386719 0.1406250 [71] 0.1425781 0.1445312 0.1464844 0.1503906 0.1523438 0.1542969 0.1562500 [78] 0.1582031 0.1601562 0.1621094 0.1640625 0.1660156 0.1679688 0.1699219 [85] 0.1718750 0.1757812 0.1777344 0.1796875 0.1816406 0.1835938 0.1855469 [92] 0.1875000 0.1894531 0.1914062 0.1933594 0.1953125 0.1972656 0.1992188 [99] 0.2011719 0.2031250 0.2050781 0.2070312 0.2089844 0.2128906 0.2167969 [106] 0.2187500 0.2207031 0.2226562 0.2246094 0.2285156 0.2304688 0.2343750 [113] 0.2363281 0.2382812 0.2421875 0.2441406 0.2460938 0.2480469 0.2500000 [120] 0.2519531 0.2539062 0.2558594 0.2597656 0.2617188 0.2636719 0.2675781 [127] 0.2695312 0.2714844 0.2734375 0.2773438 0.2792969 0.2812500 0.2832031 [134] 0.2851562 0.2871094 0.2910156 0.2929688 0.2949219 0.2968750 0.2988281 [141] 0.3027344 0.3066406 0.3085938 0.3125000 0.3144531 0.3164062 0.3183594 [148] 0.3203125 0.3222656 0.3242188 0.3261719 0.3281250 0.3300781 0.3320312 [155] 0.3339844 0.3359375 0.3378906 0.3398438 0.3417969 0.3437500 0.3457031 [162] 0.3476562 0.3515625 0.3535156 0.3554688 0.3574219 0.3593750 0.3613281 [169] 0.3632812 0.3652344 0.3691406 0.3710938 0.3730469 0.3750000 0.3769531 [176] 0.3789062 0.3808594 0.3828125 0.3847656 0.3867188 0.3886719 0.3906250 [183] 0.3925781 0.3945312 0.3964844 0.4003906 0.4023438 0.4042969 0.4062500 [190] 0.4082031 0.4101562 0.4121094 0.4140625 0.4160156 0.4179688 0.4199219 [197] 0.4238281 0.4277344 0.4316406 0.4335938 0.4375000 0.4394531 0.4433594 [204] 0.4472656 0.4492188 0.4511719 0.4550781 0.4570312 0.4589844 0.4628906 [211] 0.4648438 0.4667969 0.4707031 0.4726562 0.4746094 0.4765625 0.4804688 [218] 0.4824219 0.4863281 0.4882812 0.4921875 0.4941406 0.4980469 0.5000000 [225] 0.5019531 0.5058594 0.5078125 0.5117188 0.5136719 0.5175781 0.5195312 [232] 0.5234375 0.5253906 0.5273438 0.5292969 0.5332031 0.5351562 0.5371094 [239] 0.5410156 0.5429688 0.5449219 0.5488281 0.5507812 0.5527344 0.5566406 [246] 0.5605469 0.5625000 0.5664062 0.5683594 0.5722656 0.5761719 0.5800781 [253] 0.5820312 0.5839844 0.5859375 0.5878906 0.5898438 0.5917969 0.5937500 [260] 0.5957031 0.5976562 0.5996094 0.6035156 0.6054688 0.6074219 0.6093750 [267] 0.6113281 0.6132812 0.6152344 0.6171875 0.6191406 0.6210938 0.6230469 [274] 0.6250000 0.6269531 0.6289062 0.6308594 0.6347656 0.6367188 0.6386719 [281] 0.6406250 0.6425781 0.6445312 0.6464844 0.6484375 0.6523438 0.6542969 [288] 0.6562500 0.6582031 0.6601562 0.6621094 0.6640625 0.6660156 0.6679688 [295] 0.6699219 0.6718750 0.6738281 0.6757812 0.6777344 0.6796875 0.6816406 [302] 0.6835938 0.6855469 0.6875000 0.6914062 0.6933594 0.6972656 0.7011719 [309] 0.7031250 0.7050781 0.7070312 0.7089844 0.7128906 0.7148438 0.7167969 [316] 0.7187500 0.7207031 0.7226562 0.7265625 0.7285156 0.7304688 0.7324219 [323] 0.7363281 0.7382812 0.7402344 0.7441406 0.7460938 0.7480469 0.7500000 [330] 0.7519531 0.7539062 0.7558594 0.7578125 0.7617188 0.7636719 0.7656250 [337] 0.7695312 0.7714844 0.7753906 0.7773438 0.7792969 0.7812500 0.7832031 [344] 0.7871094 0.7910156 0.7929688 0.7949219 0.7968750 0.7988281 0.8007812 [351] 0.8027344 0.8046875 0.8066406 0.8085938 0.8105469 0.8125000 0.8144531 [358] 0.8164062 0.8183594 0.8203125 0.8222656 0.8242188 0.8281250 0.8300781 [365] 0.8320312 0.8339844 0.8359375 0.8378906 0.8398438 0.8417969 0.8437500 [372] 0.8457031 0.8476562 0.8496094 0.8535156 0.8554688 0.8574219 0.8593750 [379] 0.8613281 0.8632812 0.8652344 0.8671875 0.8691406 0.8710938 0.8730469 [386] 0.8750000 0.8789062 0.8808594 0.8828125 0.8847656 0.8867188 0.8886719 [393] 0.8906250 0.8925781 0.8945312 0.8964844 0.8984375 0.9003906 0.9042969 [400] 0.9062500 0.9082031 0.9101562 0.9121094 0.9140625 0.9160156 0.9179688 [407] 0.9199219 0.9218750 0.9238281 0.9257812 0.9277344 0.9296875 0.9316406 [414] 0.9335938 0.9355469 0.9375000 0.9394531 0.9414062 0.9433594 0.9453125 [421] 0.9472656 0.9492188 0.9511719 0.9531250 0.9550781 0.9570312 0.9589844 [428] 0.9609375 0.9628906 0.9648438 0.9667969 0.9687500 0.9707031 0.9726562 [435] 0.9746094 0.9765625 0.9785156 0.9804688 0.9824219 0.9843750 0.9863281 [442] 0.9882812 0.9902344 0.9921875 0.9941406 0.9960938 0.9980469 1.0000000 > round(dp_it2_SR <- dperm(it2_SR, supp_it2_SR), 7) # failed in < 1.1-0 [1] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [8] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [15] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [22] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [29] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [36] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [43] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [50] 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [57] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 [64] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [71] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [78] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [85] 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [92] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [99] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0039063 [106] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0039063 [113] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [120] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0039063 [127] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [134] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [141] 0.0039063 0.0039063 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [148] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [155] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [162] 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [169] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [176] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [183] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [190] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [197] 0.0039063 0.0039063 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 [204] 0.0039063 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0039063 [211] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0039063 [218] 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 [225] 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 [232] 0.0039063 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [239] 0.0039063 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0039063 [246] 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 0.0039063 0.0039063 [253] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [260] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [267] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [274] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [281] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 [288] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [295] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [302] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0039063 0.0039063 [309] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [316] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [323] 0.0039063 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [330] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [337] 0.0039063 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [344] 0.0039063 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [351] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [358] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 [365] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [372] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [379] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [386] 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [393] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 [400] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [407] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [414] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [421] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [428] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [435] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [442] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 > round(qp_it2_SR <- qperm(it2_SR, seq(0, 1, 0.01)), 7) [1] -2.4511747 -2.2738725 -1.8978112 -1.7995609 -1.7510004 -1.6979227 [7] -1.6414570 -1.5736982 -1.4122064 -1.2992751 -1.2744302 -1.2315163 [13] -1.1987662 -1.1750506 -1.1332660 -1.1197142 -1.0880935 -1.0406623 [19] -1.0090415 -0.9638690 -0.8904636 -0.8114117 -0.7459115 -0.7244545 [25] -0.7097735 -0.6646009 -0.6442733 -0.6228163 -0.6081353 -0.5855490 [31] -0.5663507 -0.5437644 -0.5313420 -0.5064971 -0.4782642 -0.4534193 [37] -0.4308331 -0.4082468 -0.3427466 -0.3258069 -0.2467550 -0.2106169 [43] -0.1564099 -0.1338236 -0.1112374 -0.0886511 -0.0660648 -0.0547717 [49] -0.0434786 -0.0208923 -0.0016940 0.0208923 0.0434786 0.0547717 [55] 0.0660648 0.0886511 0.1112374 0.1338236 0.1564099 0.2106169 [61] 0.2467550 0.3258069 0.3427466 0.4082468 0.4308331 0.4534193 [67] 0.4782642 0.5064971 0.5313420 0.5437644 0.5663507 0.5855490 [73] 0.6081353 0.6228163 0.6442733 0.6566957 0.7097735 0.7244545 [79] 0.7459115 0.8114117 0.8904636 0.9638690 1.0090415 1.0406623 [85] 1.0880935 1.1197142 1.1332660 1.1750506 1.1987662 1.2315163 [91] 1.2744302 1.2992751 1.4122064 1.5736982 1.6414570 1.6979227 [97] 1.7510004 1.7995609 1.8978112 2.2738725 2.4511747 > round(rp_it2_SR <- rperm(it2_SR, 5), 7) [1] -0.0660648 1.1411712 0.0242802 0.4895574 -0.4556780 > stopifnot(all(rp_it2_SR %in% supp_it2_SR)) > > ### paired shift with block > st3_SR <- symmetry_test(y ~ x | b, data = dta2, + distribution = exact(algorithm = "shift"), + paired = TRUE) > supp_st3_SR <- support(st3_SR) > stopifnot(!is.unsorted(supp_st3_SR)) > stopifnot(all(supp_st3_SR == unique(supp_st3_SR))) > round(pp_st3_SR <- pperm(st3_SR, supp_st3_SR), 7) [1] 0.0019531 0.0039063 0.0058594 0.0078125 0.0097656 0.0117188 0.0136719 [8] 0.0156250 0.0175781 0.0195312 0.0214844 0.0234375 0.0253906 0.0273438 [15] 0.0292969 0.0312500 0.0332031 0.0351562 0.0371094 0.0390625 0.0410156 [22] 0.0429688 0.0449219 0.0468750 0.0488281 0.0507812 0.0527344 0.0546875 [29] 0.0566406 0.0585938 0.0605469 0.0625000 0.0644531 0.0664062 0.0683594 [36] 0.0703125 0.0722656 0.0742188 0.0761719 0.0781250 0.0800781 0.0820312 [43] 0.0839844 0.0859375 0.0878906 0.0898438 0.0917969 0.0937500 0.0957031 [50] 0.0996094 0.1015625 0.1035156 0.1054688 0.1074219 0.1093750 0.1113281 [57] 0.1132812 0.1152344 0.1171875 0.1191406 0.1210938 0.1250000 0.1269531 [64] 0.1289062 0.1308594 0.1328125 0.1347656 0.1367188 0.1386719 0.1406250 [71] 0.1425781 0.1445312 0.1464844 0.1503906 0.1523438 0.1542969 0.1562500 [78] 0.1582031 0.1601562 0.1621094 0.1640625 0.1660156 0.1679688 0.1699219 [85] 0.1718750 0.1757812 0.1777344 0.1796875 0.1816406 0.1835938 0.1855469 [92] 0.1875000 0.1894531 0.1914062 0.1933594 0.1953125 0.1972656 0.1992188 [99] 0.2011719 0.2031250 0.2050781 0.2070312 0.2089844 0.2128906 0.2167969 [106] 0.2187500 0.2207031 0.2226562 0.2246094 0.2285156 0.2304688 0.2343750 [113] 0.2363281 0.2382812 0.2421875 0.2441406 0.2460938 0.2480469 0.2500000 [120] 0.2519531 0.2539062 0.2558594 0.2597656 0.2617188 0.2636719 0.2675781 [127] 0.2695312 0.2714844 0.2734375 0.2773438 0.2792969 0.2812500 0.2832031 [134] 0.2851562 0.2871094 0.2910156 0.2929688 0.2949219 0.2968750 0.2988281 [141] 0.3027344 0.3066406 0.3085938 0.3125000 0.3144531 0.3164062 0.3183594 [148] 0.3203125 0.3222656 0.3242188 0.3261719 0.3281250 0.3300781 0.3320312 [155] 0.3339844 0.3359375 0.3378906 0.3398438 0.3417969 0.3437500 0.3457031 [162] 0.3476562 0.3515625 0.3535156 0.3554688 0.3574219 0.3593750 0.3613281 [169] 0.3632812 0.3652344 0.3691406 0.3710938 0.3730469 0.3750000 0.3769531 [176] 0.3789062 0.3808594 0.3828125 0.3847656 0.3867188 0.3886719 0.3906250 [183] 0.3925781 0.3945312 0.3964844 0.4003906 0.4023438 0.4042969 0.4062500 [190] 0.4082031 0.4101562 0.4121094 0.4140625 0.4160156 0.4179688 0.4199219 [197] 0.4238281 0.4277344 0.4316406 0.4335938 0.4375000 0.4394531 0.4433594 [204] 0.4472656 0.4492188 0.4511719 0.4550781 0.4570312 0.4589844 0.4628906 [211] 0.4648438 0.4667969 0.4707031 0.4726562 0.4746094 0.4765625 0.4804688 [218] 0.4824219 0.4863281 0.4882812 0.4921875 0.4941406 0.4980469 0.5000000 [225] 0.5019531 0.5058594 0.5078125 0.5117188 0.5136719 0.5175781 0.5195312 [232] 0.5234375 0.5253906 0.5273438 0.5292969 0.5332031 0.5351562 0.5371094 [239] 0.5410156 0.5429688 0.5449219 0.5488281 0.5507812 0.5527344 0.5566406 [246] 0.5605469 0.5625000 0.5664062 0.5683594 0.5722656 0.5761719 0.5800781 [253] 0.5820312 0.5839844 0.5859375 0.5878906 0.5898438 0.5917969 0.5937500 [260] 0.5957031 0.5976562 0.5996094 0.6035156 0.6054688 0.6074219 0.6093750 [267] 0.6113281 0.6132812 0.6152344 0.6171875 0.6191406 0.6210938 0.6230469 [274] 0.6250000 0.6269531 0.6289062 0.6308594 0.6347656 0.6367188 0.6386719 [281] 0.6406250 0.6425781 0.6445312 0.6464844 0.6484375 0.6523438 0.6542969 [288] 0.6562500 0.6582031 0.6601562 0.6621094 0.6640625 0.6660156 0.6679688 [295] 0.6699219 0.6718750 0.6738281 0.6757812 0.6777344 0.6796875 0.6816406 [302] 0.6835938 0.6855469 0.6875000 0.6914062 0.6933594 0.6972656 0.7011719 [309] 0.7031250 0.7050781 0.7070312 0.7089844 0.7128906 0.7148438 0.7167969 [316] 0.7187500 0.7207031 0.7226562 0.7265625 0.7285156 0.7304688 0.7324219 [323] 0.7363281 0.7382812 0.7402344 0.7441406 0.7460938 0.7480469 0.7500000 [330] 0.7519531 0.7539062 0.7558594 0.7578125 0.7617188 0.7636719 0.7656250 [337] 0.7695312 0.7714844 0.7753906 0.7773438 0.7792969 0.7812500 0.7832031 [344] 0.7871094 0.7910156 0.7929688 0.7949219 0.7968750 0.7988281 0.8007812 [351] 0.8027344 0.8046875 0.8066406 0.8085938 0.8105469 0.8125000 0.8144531 [358] 0.8164062 0.8183594 0.8203125 0.8222656 0.8242188 0.8281250 0.8300781 [365] 0.8320312 0.8339844 0.8359375 0.8378906 0.8398438 0.8417969 0.8437500 [372] 0.8457031 0.8476562 0.8496094 0.8535156 0.8554688 0.8574219 0.8593750 [379] 0.8613281 0.8632812 0.8652344 0.8671875 0.8691406 0.8710938 0.8730469 [386] 0.8750000 0.8789062 0.8808594 0.8828125 0.8847656 0.8867188 0.8886719 [393] 0.8906250 0.8925781 0.8945312 0.8964844 0.8984375 0.9003906 0.9042969 [400] 0.9062500 0.9082031 0.9101562 0.9121094 0.9140625 0.9160156 0.9179688 [407] 0.9199219 0.9218750 0.9238281 0.9257812 0.9277344 0.9296875 0.9316406 [414] 0.9335938 0.9355469 0.9375000 0.9394531 0.9414062 0.9433594 0.9453125 [421] 0.9472656 0.9492188 0.9511719 0.9531250 0.9550781 0.9570312 0.9589844 [428] 0.9609375 0.9628906 0.9648438 0.9667969 0.9687500 0.9707031 0.9726562 [435] 0.9746094 0.9765625 0.9785156 0.9804688 0.9824219 0.9843750 0.9863281 [442] 0.9882812 0.9902344 0.9921875 0.9941406 0.9960938 0.9980469 1.0000000 > round(dp_st3_SR <- dperm(st3_SR, supp_st3_SR), 7) [1] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [8] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [15] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [22] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [29] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [36] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [43] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [50] 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [57] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 [64] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [71] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [78] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [85] 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [92] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [99] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0039063 [106] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0039063 [113] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [120] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0039063 [127] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [134] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [141] 0.0039063 0.0039063 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [148] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [155] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [162] 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [169] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [176] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [183] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [190] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [197] 0.0039063 0.0039063 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 [204] 0.0039063 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0039063 [211] 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0039063 [218] 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 [225] 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 0.0019531 [232] 0.0039063 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [239] 0.0039063 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0039063 [246] 0.0039063 0.0019531 0.0039063 0.0019531 0.0039063 0.0039063 0.0039063 [253] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [260] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [267] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [274] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [281] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 [288] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [295] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [302] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0039063 0.0039063 [309] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [316] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [323] 0.0039063 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [330] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 [337] 0.0039063 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 [344] 0.0039063 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [351] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [358] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 [365] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [372] 0.0019531 0.0019531 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 [379] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [386] 0.0019531 0.0039063 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [393] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039063 [400] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [407] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [414] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [421] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [428] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [435] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [442] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 > round(qp_st3_SR <- qperm(st3_SR, seq(0, 1, 0.01)), 7) [1] -2.4511747 -2.2738725 -1.8978112 -1.7995609 -1.7510004 -1.6979227 [7] -1.6414570 -1.5736982 -1.4122064 -1.2992751 -1.2744302 -1.2315163 [13] -1.1987662 -1.1750506 -1.1332660 -1.1197142 -1.0880935 -1.0406623 [19] -1.0090415 -0.9638690 -0.8904636 -0.8114117 -0.7459115 -0.7244545 [25] -0.7097735 -0.6646009 -0.6442733 -0.6228163 -0.6081353 -0.5855490 [31] -0.5663507 -0.5437644 -0.5313420 -0.5064971 -0.4782642 -0.4534193 [37] -0.4308331 -0.4082468 -0.3427466 -0.3258069 -0.2467550 -0.2106169 [43] -0.1564099 -0.1338236 -0.1112374 -0.0886511 -0.0660648 -0.0547717 [49] -0.0434786 -0.0208923 -0.0016940 0.0208923 0.0434786 0.0547717 [55] 0.0660648 0.0886511 0.1112374 0.1338236 0.1564099 0.2106169 [61] 0.2467550 0.3258069 0.3427466 0.4082468 0.4308331 0.4534193 [67] 0.4782642 0.5064971 0.5313420 0.5437644 0.5663507 0.5855490 [73] 0.6081353 0.6228163 0.6442733 0.6566957 0.7097735 0.7244545 [79] 0.7459115 0.8114117 0.8904636 0.9638690 1.0090415 1.0406623 [85] 1.0880935 1.1197142 1.1332660 1.1750506 1.1987662 1.2315163 [91] 1.2744302 1.2992751 1.4122064 1.5736982 1.6414570 1.6979227 [97] 1.7510004 1.7995609 1.8978112 2.2738725 2.4511747 > round(rp_st3_SR <- rperm(st3_SR, 5), 7) [1] 0.7244545 -0.3404880 0.8001185 -1.2653957 -0.7459115 > stopifnot(all(rp_st3_SR %in% supp_st3_SR)) > > ### should be equal > stopifnot(isequal(pp_it2_SR, pp_st3_SR)) # failed in < 1.1-0 > stopifnot(isequal(qp_it2_SR, qp_st3_SR)) # failed in < 1.1-0 > stopifnot(isequal(pvalue(it2_SR), pvalue(st3_SR))) > stopifnot(isequal(midpvalue(it2_SR), midpvalue(st3_SR))) > stopifnot(isequal(pvalue_interval(it2_SR), pvalue_interval(st3_SR))) > > > ### exact test based on quadratic forms > > ### shift with block > itq1 <- independence_test(y ~ x | b, data = dta1, + distribution = exact(algorithm = "shift"), + teststat = "quad") > its1 <- independence_test(y ~ x | b, data = dta1, + distribution = exact(algorithm = "shift"), + teststat = "scalar") > stopifnot(isequal(statistic(itq1), statistic(its1)^2)) > stopifnot(isequal(pvalue(itq1), pvalue(its1))) > stopifnot(isequal(midpvalue(itq1), midpvalue(its1))) > stopifnot(isequal(pvalue_interval(itq1), pvalue_interval(its1))) > stopifnot(isequal(support(itq1), support(its1)[support(its1) >= 0]^2)) > > ### paired shift with block > sts2 <- symmetry_test(y ~ x | b, data = dta2, + distribution = exact(algorithm = "shift"), + paired = TRUE, teststat = "scalar") > stq2 <- symmetry_test(y ~ x | b, data = dta2, + distribution = exact(algorithm = "shift"), + paired = TRUE, teststat = "quad") > stopifnot(isequal(statistic(stq2), statistic(sts2)^2)) > stopifnot(isequal(pvalue(stq2), pvalue(sts2))) > stopifnot(isequal(midpvalue(stq2), midpvalue(sts2))) > stopifnot(isequal(pvalue_interval(stq2), pvalue_interval(sts2))) > stopifnot(isequal(support(stq2), support(sts2)[support(sts2) >= 0]^2)) > > ### should be equal > stopifnot(isequal(statistic(itq1), statistic(stq2))) > stopifnot(isequal(pvalue(itq1), pvalue(stq2))) > stopifnot(isequal(midpvalue(itq1), midpvalue(stq2))) > stopifnot(isequal(pvalue_interval(itq1), pvalue_interval(stq2))) > stopifnot(isequal(support(itq1), support(stq2))) > > ### dperm gave an error here (fixed in r869) > tab <- as.table(matrix(c(3, 0, 0, 3), ncol = 2)) > itq <- independence_test(tab, distribution = exact(algorithm = "shift"), + teststat = "quad") > stopifnot(is.numeric(dperm(itq, statistic(itq)))) > > > ### check vectorization > dta <- data.frame(y1 = sample(1:20), y2 = sample(1:20), x = gl(2, 10)) > > ### univariate, asymptotic and scalar > it_uas <- independence_test(y1 ~ x, data = dta, + distribution = "asymptotic", teststat = "scalar") > (dp_uas <- dperm(it_uas, 0:1)) [1] 0.3989423 0.2419707 > stopifnot(isequal(dp_uas, c(dperm(it_uas, 0), dperm(it_uas, 1)))) > (pp_uas <- pperm(it_uas, 0:1)) [1] 0.5000000 0.8413447 > stopifnot(isequal(pp_uas, c(pperm(it_uas, 0), pperm(it_uas, 1)))) > (qp_uas <- qperm(it_uas, c(0.5, 0.75))) [1] 0.0000000 0.6744898 > stopifnot(isequal(qp_uas, c(qperm(it_uas, 0.5), qperm(it_uas, 0.75)))) > (pv_uas <- pvalue(it_uas@distribution, 0:1)) [1] 1.0000000 0.3173105 > stopifnot(isequal(pv_uas, c(pvalue(it_uas@distribution, 0), + pvalue(it_uas@distribution, 1)))) > > ### univariate, asymptotic and quad > it_uaq <- independence_test(y1 ~ x, data = dta, + distribution = "asymptotic", teststat = "quad") > (dp_uaq <- dperm(it_uaq, 0:1)) [1] Inf 0.2419707 > stopifnot(isequal(dp_uaq, c(dperm(it_uaq, 0), dperm(it_uaq, 1)))) > (pp_uaq <- pperm(it_uaq, 0:1)) [1] 0.0000000 0.6826895 > stopifnot(isequal(pp_uaq, c(pperm(it_uaq, 0), pperm(it_uaq, 1)))) > (qp_uaq <- qperm(it_uaq, c(0.5, 0.75))) [1] 0.4549364 1.3233037 > stopifnot(isequal(qp_uaq, c(qperm(it_uaq, 0.5), qperm(it_uaq, 0.75)))) > (pv_uaq <- pvalue(it_uaq@distribution, 0:1)) [1] 1.0000000 0.3173105 > stopifnot(isequal(pv_uaq, c(pvalue(it_uaq@distribution, 0), + pvalue(it_uaq@distribution, 1)))) > > ### multivariate, asymptotic and max > it_mam <- independence_test(y1 + y2 ~ x, data = dta, + distribution = "asymptotic", teststat = "max") > (dp_mam <- dperm(it_mam, 0:1)) [1] NA > ## stopifnot(isequal(dp_mam, c(dperm(it_mam, 0), dperm(it_mam, 1)))) > (pp_mam <- pperm(it_mam, 0:1)) # failed in < 1.1-0 [1] 0.0000000 0.4673673 > stopifnot(isequal(pp_mam, c(pperm(it_mam, 0), pperm(it_mam, 1)))) > (qp_mam <- qperm(it_mam, c(0.5, 0.75))) # failed in < 1.1-0 [1] 1.049971 1.496775 > stopifnot(isequal(qp_mam, c(qperm(it_mam, 0.5), qperm(it_mam, 0.75)))) > (pv_mam <- pvalue(it_mam@distribution, 0:1)) [1] 1.0000000 0.5326327 > stopifnot(isequal(pv_mam, c(pvalue(it_mam@distribution, 0), + pvalue(it_mam@distribution, 1)))) > > ### multivariate, asymptotic and quad > it_maq <- independence_test(y1 + y2 ~ x, data = dta, + distribution = "asymptotic", teststat = "quad") > (dp_maq <- dperm(it_maq, 0:1)) [1] 0.5000000 0.3032653 > stopifnot(isequal(dp_maq, c(dperm(it_maq, 0), dperm(it_maq, 1)))) > (pp_maq <- pperm(it_maq, 0:1)) [1] 0.0000000 0.3934693 > stopifnot(isequal(pp_maq, c(pperm(it_maq, 0), pperm(it_maq, 1)))) > (qp_maq <- qperm(it_maq, c(0.5, 0.75))) [1] 1.386294 2.772589 > stopifnot(isequal(qp_maq, c(qperm(it_maq, 0.5), qperm(it_maq, 0.75)))) > (pv_maq <- pvalue(it_maq@distribution, 0:1)) [1] 1.0000000 0.6065307 > stopifnot(isequal(pv_maq, c(pvalue(it_maq@distribution, 0), + pvalue(it_maq@distribution, 1)))) > > ### univariate, approximate and scalar > it_ums <- independence_test(y1 ~ x, data = dta, + distribution = "approximate", teststat = "scalar") > (dp_ums <- dperm(it_ums, 0:1)) [1] 0.0334 0.0000 > stopifnot(isequal(dp_ums, c(dperm(it_ums, 0), dperm(it_ums, 1)))) > (pp_ums <- pperm(it_ums, 0:1)) [1] 0.5210 0.8487 > stopifnot(isequal(pp_ums, c(pperm(it_ums, 0), pperm(it_ums, 1)))) > (qp_ums <- qperm(it_ums, c(0.5, 0.75))) [1] 0.0000000 0.6803361 > stopifnot(isequal(qp_ums, c(qperm(it_ums, 0.5), qperm(it_ums, 0.75)))) > (pv_ums <- pvalue(it_ums@distribution, 0:1)) [1] 1.0000 0.3117 > stopifnot(isequal(pv_ums, c(pvalue(it_ums@distribution, 0), + pvalue(it_ums@distribution, 1)))) > (mp_ums <- midpvalue(it_ums@distribution, 0:1)) [1] 0.9666 0.3117 > stopifnot(isequal(mp_ums, c(midpvalue(it_ums@distribution, 0), + midpvalue(it_ums@distribution, 1)))) > (pi_ums <- pvalue_interval(it_ums@distribution, 0:1)) [,1] [,2] p_0 0.9332 0.3117 p_1 1.0000 0.3117 > stopifnot(isequal(pi_ums, cbind(pvalue_interval(it_ums@distribution, 0), + pvalue_interval(it_ums@distribution, 1)))) > > ### univariate, approximate and quad > it_umq <- independence_test(y1 ~ x, data = dta, + distribution = "approximate", teststat = "quad") > (dp_umq <- dperm(it_umq, 0:1)) [1] 0.0328 0.0000 > stopifnot(isequal(dp_umq, c(dperm(it_umq, 0), dperm(it_umq, 1)))) > (pp_umq <- pperm(it_umq, 0:1)) [1] 0.0328 0.6853 > stopifnot(isequal(pp_umq, c(pperm(it_umq, 0), pperm(it_umq, 1)))) > (qp_umq <- qperm(it_umq, c(0.5, 0.75))) [1] 0.4628571 1.2857143 > stopifnot(isequal(qp_umq, c(qperm(it_umq, 0.5), qperm(it_umq, 0.75)))) > (pv_umq <- pvalue(it_umq@distribution, 0:1)) [1] 1.0000 0.3147 > stopifnot(isequal(pv_umq, c(pvalue(it_umq@distribution, 0), + pvalue(it_umq@distribution, 1)))) > (mp_umq <- midpvalue(it_umq@distribution, 0:1)) [1] 0.9836 0.3147 > stopifnot(isequal(mp_umq, c(midpvalue(it_umq@distribution, 0), + midpvalue(it_umq@distribution, 1)))) > (pi_umq <- pvalue_interval(it_umq@distribution, 0:1)) [,1] [,2] p_0 0.9672 0.3147 p_1 1.0000 0.3147 > stopifnot(isequal(pi_umq, cbind(pvalue_interval(it_umq@distribution, 0), + pvalue_interval(it_umq@distribution, 1)))) > > ### multivariate, approximate and max > it_mmm <- independence_test(y1 + y2 ~ x, data = dta, + distribution = "approximate", teststat = "max") > (dp_mmm <- dperm(it_mmm, 0:1)) [1] 0.0017 0.0000 > stopifnot(isequal(dp_mmm, c(dperm(it_mmm, 0), dperm(it_mmm, 1)))) > (pp_mmm <- pperm(it_mmm, 0:1)) [1] 0.0017 0.4639 > stopifnot(isequal(pp_mmm, c(pperm(it_mmm, 0), pperm(it_mmm, 1)))) > (qp_mmm <- qperm(it_mmm, c(0.5, 0.75))) [1] 1.058301 1.511858 > stopifnot(isequal(qp_mmm, c(qperm(it_mmm, 0.5), qperm(it_mmm, 0.75)))) > (pv_mmm <- pvalue(it_mmm@distribution, 0:1)) [1] 1.0000 0.5361 > stopifnot(isequal(pv_mmm, c(pvalue(it_mmm@distribution, 0), + pvalue(it_mmm@distribution, 1)))) > (mp_mmm <- midpvalue(it_mmm@distribution, 0:1)) [1] 0.9983 0.5361 > stopifnot(isequal(mp_mmm, c(midpvalue(it_mmm@distribution, 0), + midpvalue(it_mmm@distribution, 1)))) > (pi_mmm <- pvalue_interval(it_mmm@distribution, 0:1)) [,1] [,2] p_0 0.9966 0.5361 p_1 1.0000 0.5361 > stopifnot(isequal(pi_mmm, cbind(pvalue_interval(it_mmm@distribution, 0), + pvalue_interval(it_mmm@distribution, 1)))) > > ### multivariate, approximate and quad > it_mmq <- independence_test(y1 + y2 ~ x, data = dta, + distribution = "approximate", teststat = "quad") > (dp_mmq <- dperm(it_mmq, 0:1)) [1] 7e-04 0e+00 > stopifnot(isequal(dp_mmq, c(dperm(it_mmq, 0), dperm(it_mmq, 1)))) > (pp_mmq <- pperm(it_mmq, 0:1)) [1] 0.0007 0.3821 > stopifnot(isequal(pp_mmq, c(pperm(it_mmq, 0), pperm(it_mmq, 1)))) > (qp_mmq <- qperm(it_mmq, c(0.5, 0.75))) [1] 1.465562 2.820424 > stopifnot(isequal(qp_mmq, c(qperm(it_mmq, 0.5), qperm(it_mmq, 0.75)))) > (pv_mmq <- pvalue(it_mmq@distribution, 0:1)) [1] 1.0000 0.6179 > stopifnot(isequal(pv_mmq, c(pvalue(it_mmq@distribution, 0), + pvalue(it_mmq@distribution, 1)))) > (mp_mmq <- midpvalue(it_mmq@distribution, 0:1)) [1] 0.99965 0.61790 > stopifnot(isequal(mp_mmq, c(midpvalue(it_mmq@distribution, 0), + midpvalue(it_mmq@distribution, 1)))) > (pi_mmq <- pvalue_interval(it_mmq@distribution, 0:1)) [,1] [,2] p_0 0.9993 0.6179 p_1 1.0000 0.6179 > stopifnot(isequal(pi_mmq, cbind(pvalue_interval(it_mmq@distribution, 0), + pvalue_interval(it_mmq@distribution, 1)))) > > ### univariate, exact and scalar > it_ues <- independence_test(y1 ~ x, data = dta, + distribution = "exact", teststat = "scalar") > (dp_ues <- dperm(it_ues, 0:1)) [1] 0.02948754 0.00000000 > stopifnot(isequal(dp_ues, c(dperm(it_ues, 0), dperm(it_ues, 1)))) > (pp_ues <- pperm(it_ues, 0:1)) [1] 0.5147438 0.8425004 > stopifnot(isequal(pp_ues, c(pperm(it_ues, 0), pperm(it_ues, 1)))) > (qp_ues <- qperm(it_ues, c(0.5, 0.75))) [1] 0.0000000 0.6803361 > stopifnot(isequal(qp_ues, c(qperm(it_ues, 0.5), qperm(it_ues, 0.75)))) > (pv_ues <- pvalue(it_ues@distribution, 0:1)) [1] 1.0000000 0.3149992 > stopifnot(isequal(pv_ues, c(pvalue(it_ues@distribution, 0), + pvalue(it_ues@distribution, 1)))) > (mp_ues <- midpvalue(it_ues@distribution, 0:1)) [1] 0.9705125 0.3149992 > stopifnot(isequal(mp_ues, c(midpvalue(it_ues@distribution, 0), + midpvalue(it_ues@distribution, 1)))) > (pi_ues <- pvalue_interval(it_ues@distribution, 0:1)) [,1] [,2] p_0 0.9410249 0.3149992 p_1 1.0000000 0.3149992 > stopifnot(isequal(pi_ues, cbind(pvalue_interval(it_ues@distribution, 0), + pvalue_interval(it_ues@distribution, 1)))) > > ### univariate, exact and quad > it_ueq <- independence_test(y1 ~ x, data = dta, + distribution = "exact", teststat = "quad") > (dp_ueq <- dperm(it_ueq, 0:1)) [1] 0.02948754 0.00000000 > stopifnot(isequal(dp_ueq, c(dperm(it_ueq, 0), dperm(it_ueq, 1)))) > (pp_ueq <- pperm(it_ueq, 0:1)) [1] 0.02948754 0.68500076 > stopifnot(isequal(pp_ueq, c(pperm(it_ueq, 0), pperm(it_ueq, 1)))) > (qp_ueq <- qperm(it_ueq, c(0.5, 0.75))) [1] 0.4628571 1.2857143 > stopifnot(isequal(qp_ueq, c(qperm(it_ueq, 0.5), qperm(it_ueq, 0.75)))) > (pv_ueq <- pvalue(it_ueq@distribution, 0:1)) [1] 1.0000000 0.3149992 > stopifnot(isequal(pv_ueq, c(pvalue(it_ueq@distribution, 0), + pvalue(it_ueq@distribution, 1)))) > (mp_ueq <- midpvalue(it_ueq@distribution, 0:1)) [1] 0.9852562 0.3149992 > stopifnot(isequal(mp_ueq, c(midpvalue(it_ueq@distribution, 0), + midpvalue(it_ueq@distribution, 1)))) > (pi_ueq <- pvalue_interval(it_ueq@distribution, 0:1)) [,1] [,2] p_0 0.9705125 0.3149992 p_1 1.0000000 0.3149992 > stopifnot(isequal(pi_ueq, cbind(pvalue_interval(it_ueq@distribution, 0), + pvalue_interval(it_ueq@distribution, 1)))) > > proc.time() user system elapsed 4.64 0.56 5.18 coin/tests/regtest_Ksample.R0000644000176200001440000002323713763400162015631 0ustar liggesusers### Regression tests for the K sample problem, i.e., ### testing the independence of a numeric variable ### 'y' and a factor 'x' (possibly blocked) suppressWarnings(RNGversion("3.5.2")) set.seed(290875) library("coin") isequal <- coin:::isequal options(useFancyQuotes = FALSE) ### generate data dat <- data.frame(x = gl(4, 25), y = rnorm(100), block = gl(5, 20))[sample(1:100, 50), ] ### Kruskal-Wallis Test ### asymptotic distribution ptwo <- kruskal.test(y ~ x, data = dat)$p.value stopifnot(isequal(pvalue(kruskal_test(y ~ x, data = dat)), ptwo)) stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo))), ptwo)) ### approximated distribution rtwo <- pvalue(kruskal_test(y ~ x, data = dat, distribution = "approx")) / ptwo stopifnot(all(rtwo > 0.9 & rtwo < 1.1)) ### add block examples ### sanity checks try(kruskal_test(x ~ y, data = dat)) try(kruskal_test(x ~ y | y, data = dat)) ### Fligner-Killeen Test ### asymptotic distribution ptwo <- fligner.test(y ~ x, data = dat)$p.value stopifnot(isequal(pvalue(fligner_test(y ~ x, data = dat)), ptwo)) dat$yy <- dat$y - tapply(dat$y, dat$x, median)[dat$x] stopifnot(isequal(pvalue(oneway_test(yy ~ x, data = dat, distribution = "asympt", ytrafo = function(data) trafo(data, numeric_trafo = fligner_trafo))), ptwo)) ### approximated distribution rtwo <- pvalue(fligner_test(y ~ x, data = dat, distribution = "approx")) / ptwo stopifnot(all(rtwo > 0.9 & rtwo < 1.1)) ### add block examples ### sanity checks try(fligner_test(x ~ y, data = dat)) try(fligner_test(x ~ y | y, data = dat)) ### One-way Test oneway_test(y ~ x, data = dat) oneway_test(y ~ ordered(x), data = dat) oneway_test(y ~ ordered(x), data = dat, alternative = "less") oneway_test(y ~ ordered(x), data = dat, alternative = "greater") oneway_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))) oneway_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less") oneway_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater") ### Normal Scores Test normal_test(y ~ x, data = dat) normal_test(y ~ ordered(x), data = dat) normal_test(y ~ ordered(x), data = dat, alternative = "less") normal_test(y ~ ordered(x), data = dat, alternative = "greater") normal_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))) normal_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less") normal_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater") ### Median Test median_test(y ~ x, data = dat) median_test(y ~ ordered(x), data = dat) median_test(y ~ ordered(x), data = dat, alternative = "less") median_test(y ~ ordered(x), data = dat, alternative = "greater") median_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))) median_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less") median_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater") ### Savage Test savage_test(y ~ x, data = dat) savage_test(y ~ ordered(x), data = dat) savage_test(y ~ ordered(x), data = dat, alternative = "less") savage_test(y ~ ordered(x), data = dat, alternative = "greater") savage_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))) savage_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less") savage_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater") ### Taha Test taha_test(y ~ x, data = dat) try(taha_test(y ~ ordered(x), data = dat)) try(taha_test(y ~ ordered(x), data = dat, alternative = "less")) try(taha_test(y ~ ordered(x), data = dat, alternative = "greater")) try(taha_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))) try(taha_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less")) try(taha_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater")) ### Klotz Test klotz_test(y ~ x, data = dat) try(klotz_test(y ~ ordered(x), data = dat)) try(klotz_test(y ~ ordered(x), data = dat, alternative = "less")) try(klotz_test(y ~ ordered(x), data = dat, alternative = "greater")) try(klotz_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))) try(klotz_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less")) try(klotz_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater")) ### Mood Test mood_test(y ~ x, data = dat) try(mood_test(y ~ ordered(x), data = dat)) try(mood_test(y ~ ordered(x), data = dat, alternative = "less")) try(mood_test(y ~ ordered(x), data = dat, alternative = "greater")) try(mood_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))) try(mood_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less")) try(mood_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater")) ### Ansari-Bradley Test ansari_test(y ~ x, data = dat) try(ansari_test(y ~ ordered(x), data = dat)) try(ansari_test(y ~ ordered(x), data = dat, alternative = "less")) try(ansari_test(y ~ ordered(x), data = dat, alternative = "greater")) try(ansari_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))) try(ansari_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less")) try(ansari_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater")) ### Conover-Iman Test conover_test(y ~ x, data = dat) try(conover_test(y ~ ordered(x), data = dat)) try(conover_test(y ~ ordered(x), data = dat, alternative = "less")) try(conover_test(y ~ ordered(x), data = dat, alternative = "greater")) try(conover_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))) try(conover_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less")) try(conover_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater")) ### Logrank Test logrank_test(Surv(y) ~ x, data = dat) logrank_test(Surv(y) ~ ordered(x), data = dat) logrank_test(Surv(y) ~ ordered(x), data = dat, alternative = "less") logrank_test(Surv(y) ~ ordered(x), data = dat, alternative = "greater") logrank_test(Surv(y) ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))) logrank_test(Surv(y) ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "less") logrank_test(Surv(y) ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)), alternative = "greater") ### Weighted logrank tests ### Lee & Wang (2003, p. 130, Table 5.11) leukemia <- data.frame( time = c( 4, 5, 9, 10, 12, 13, 10, 23, 28, 28, 28, 29, 31, 32, 37, 41, 41, 57, 62, 74, 100, 139, 20, 258, 269, 8, 10, 10, 12, 14, 20, 48, 70, 75, 99, 103, 162, 169, 195, 220, 161, 199, 217, 245, 8, 10, 11, 23, 25, 25, 28, 28, 31, 31, 40, 48, 89, 124, 143, 12, 159, 190, 196, 197, 205, 219), event = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0), group = factor(rep(1:3, c(25, 19, 22)), labels = as.roman(1:3))) ### Leton and Zuluaga (2002, p. 25, Table 6) ### Gehan, X^2_SG lt <- logrank_test(Surv(time, event) ~ group, data = leukemia, type = "Gehan") stopifnot(identical(lt@method, "K-Sample Gehan-Breslow Test")) stopifnot(all(-statistic(lt, "linear") == c(273, -170, -103))) isequal(round(statistic(lt), 3), 3.612) isequal(round(pvalue(lt), 4), 0.1643) ### Peto-Peto, X^2_SPP lt <- logrank_test(Surv(time, event) ~ group, data = leukemia, type = "Peto-Peto") stopifnot(identical(lt@method, "K-Sample Peto-Peto Test")) stopifnot(all(round(-statistic(lt, "linear"), 3) == c(4.171, -2.582, -1.589))) isequal(round(statistic(lt), 3), 3.527) isequal(round(pvalue(lt), 4), 0.1715) ### X^2_S1 lt <- logrank_test(Surv(time, event) ~ group, data = leukemia, type = "Prentice") stopifnot(identical(lt@method, "K-Sample Prentice Test")) stopifnot(all(round(-statistic(lt, "linear"), 3) == c(4.100, -2.503, -1.597))) isequal(round(statistic(lt), 3), 3.639) isequal(round(pvalue(lt), 4), 0.1621) ### LR Altshuler, X^2_SLRA lt <- logrank_test(Surv(time, event) ~ group, data = leukemia) stopifnot(identical(lt@method, "K-Sample Logrank Test")) stopifnot(all(round(-statistic(lt, "linear"), 3) == c(6.635, -3.693, -2.942))) isequal(round(statistic(lt), 3), 3.814) isequal(round(pvalue(lt), 4), 0.1485) ### X^2_S2 lt <- logrank_test(Surv(time, event) ~ group, data = leukemia, type = "Tarone-Ware") stopifnot(identical(lt@method, "K-Sample Tarone-Ware Test")) stopifnot(all(c(round(-statistic(lt, "linear")[1:2], 2), round(-statistic(lt, "linear")[3], 3)) == c(42.78, -26.42, -16.361))) isequal(round(statistic(lt), 3), 4.104) isequal(round(pvalue(lt), 4), 0.1285) coin/tests/Examples/0000755000176200001440000000000013763400162014124 5ustar liggesuserscoin/tests/Examples/coin-Ex.Rout.save0000644000176200001440000027567013763400162017257 0ustar liggesusers R Under development (unstable) (2020-08-20 r79057) -- "Unsuffered Consequences" Copyright (C) 2020 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > pkgname <- "coin" > source(file.path(R.home("share"), "R", "examples-header.R")) > options(warn = 1) > options(pager = "console") > library('coin') Loading required package: survival > > base::assign(".oldSearch", base::search(), pos = 'CheckExEnv') > base::assign(".old_wd", base::getwd(), pos = 'CheckExEnv') > cleanEx() > nameEx("CWD") > ### * CWD > > flush(stderr()); flush(stdout()) > > ### Name: CWD > ### Title: Coarse Woody Debris > ### Aliases: CWD > ### Keywords: datasets > > ### ** Examples > > ## Zeileis and Hothorn (2013, pp. 942-944) > ## Approximative (Monte Carlo) maximally selected statistics > CWD[1:6] <- 100 * CWD[1:6] # scaling (to avoid harmless warning) > mt <- maxstat_test(sample2 + sample3 + sample4 + + sample6 + sample7 + sample8 ~ trend, data = CWD, + distribution = approximate(nresample = 100000)) > > ## Absolute maximum of standardized statistics (t = 3.08) > statistic(mt) [1] 3.079268 > > ## 5% critical value (t_0.05 = 2.86) > (c <- qperm(mt, 0.95)) [1] 2.855509 > > ## Only 'sample8' exceeds the 5% critical value > sts <- statistic(mt, type = "standardized") > idx <- which(sts > c, arr.ind = TRUE) > sts[unique(idx[, 1]), unique(idx[, 2]), drop = FALSE] sample8 x <= 62 2.931118 x <= 71 3.079268 > > > > cleanEx() > nameEx("ContingencyTests") > ### * ContingencyTests > > flush(stderr()); flush(stdout()) > > ### Name: ContingencyTests > ### Title: Tests of Independence in Two- or Three-Way Contingency Tables > ### Aliases: chisq_test chisq_test.formula chisq_test.table > ### chisq_test.IndependenceProblem cmh_test cmh_test.formula > ### cmh_test.table cmh_test.IndependenceProblem lbl_test lbl_test.formula > ### lbl_test.table lbl_test.IndependenceProblem > ### Keywords: htest > > ### ** Examples > > ## Example data > ## Davis (1986, p. 140) > davis <- matrix( + c(3, 6, + 2, 19), + nrow = 2, byrow = TRUE + ) > davis <- as.table(davis) > > ## Asymptotic Pearson chi-squared test > chisq_test(davis) Asymptotic Pearson Chi-Squared Test data: Var2 by Var1 (A, B) chi-squared = 2.5714, df = 1, p-value = 0.1088 > chisq.test(davis, correct = FALSE) # same as above Warning in chisq.test(davis, correct = FALSE) : Chi-squared approximation may be incorrect Pearson's Chi-squared test data: davis X-squared = 2.5714, df = 1, p-value = 0.1088 > > ## Approximative (Monte Carlo) Pearson chi-squared test > ct <- chisq_test(davis, + distribution = approximate(nresample = 10000)) > pvalue(ct) # standard p-value [1] 0.2849 99 percent confidence interval: 0.2733285 0.2966774 > midpvalue(ct) # mid-p-value [1] 0.151 99 percent confidence interval: 0.1419433 0.1603887 > pvalue_interval(ct) # p-value interval p_0 p_1 0.0171 0.2849 > size(ct, alpha = 0.05) # test size at alpha = 0.05 using the p-value [1] 0.0171 > > ## Exact Pearson chi-squared test (Davis, 1986) > ## Note: disagrees with Fisher's exact test > ct <- chisq_test(davis, + distribution = "exact") > pvalue(ct) # standard p-value [1] 0.2860301 > midpvalue(ct) # mid-p-value [1] 0.1527409 > pvalue_interval(ct) # p-value interval p_0 p_1 0.01945181 0.28603006 > size(ct, alpha = 0.05) # test size at alpha = 0.05 using the p-value [1] 0.01945181 > fisher.test(davis) Fisher's Exact Test for Count Data data: davis p-value = 0.1432 alternative hypothesis: true odds ratio is not equal to 1 95 percent confidence interval: 0.410317 65.723900 sample estimates: odds ratio 4.462735 > > > ## Laryngeal cancer data > ## Agresti (2002, p. 107, Tab. 3.13) > cancer <- matrix( + c(21, 2, + 15, 3), + nrow = 2, byrow = TRUE, + dimnames = list( + "Treatment" = c("Surgery", "Radiation"), + "Cancer" = c("Controlled", "Not Controlled") + ) + ) > cancer <- as.table(cancer) > > ## Exact Pearson chi-squared test (Agresti, 2002, p. 108, Tab. 3.14) > ## Note: agrees with Fishers's exact test > (ct <- chisq_test(cancer, + distribution = "exact")) Exact Pearson Chi-Squared Test data: Cancer by Treatment (Surgery, Radiation) chi-squared = 0.59915, p-value = 0.6384 > midpvalue(ct) # mid-p-value [1] 0.5006832 > pvalue_interval(ct) # p-value interval p_0 p_1 0.3629407 0.6384258 > size(ct, alpha = 0.05) # test size at alpha = 0.05 using the p-value [1] 0.01143318 > fisher.test(cancer) Fisher's Exact Test for Count Data data: cancer p-value = 0.6384 alternative hypothesis: true odds ratio is not equal to 1 95 percent confidence interval: 0.2089115 27.5538747 sample estimates: odds ratio 2.061731 > > > ## Homework conditions and teacher's rating > ## Yates (1948, Tab. 1) > yates <- matrix( + c(141, 67, 114, 79, 39, + 131, 66, 143, 72, 35, + 36, 14, 38, 28, 16), + byrow = TRUE, ncol = 5, + dimnames = list( + "Rating" = c("A", "B", "C"), + "Condition" = c("A", "B", "C", "D", "E") + ) + ) > yates <- as.table(yates) > > ## Asymptotic Pearson chi-squared test (Yates, 1948, p. 176) > chisq_test(yates) Asymptotic Pearson Chi-Squared Test data: Condition by Rating (A, B, C) chi-squared = 9.0928, df = 8, p-value = 0.3345 > > ## Asymptotic Pearson-Yates chi-squared test (Yates, 1948, pp. 180-181) > ## Note: 'Rating' and 'Condition' as ordinal > (ct <- chisq_test(yates, + alternative = "less", + scores = list("Rating" = c(-1, 0, 1), + "Condition" = c(2, 1, 0, -1, -2)))) Asymptotic Linear-by-Linear Association Test data: Condition (ordered) by Rating (A < B < C) Z = -1.5269, p-value = 0.06339 alternative hypothesis: less > statistic(ct)^2 # chi^2 = 2.332 [1] 2.33154 > > ## Asymptotic Pearson-Yates chi-squared test (Yates, 1948, p. 181) > ## Note: 'Rating' as ordinal > chisq_test(yates, + scores = list("Rating" = c(-1, 0, 1))) # Q = 3.825 Asymptotic Generalized Pearson Chi-Squared Test data: Condition by Rating (A < B < C) chi-squared = 3.8242, df = 4, p-value = 0.4303 > > > ## Change in clinical condition and degree of infiltration > ## Cochran (1954, Tab. 6) > cochran <- matrix( + c(11, 7, + 27, 15, + 42, 16, + 53, 13, + 11, 1), + byrow = TRUE, ncol = 2, + dimnames = list( + "Change" = c("Marked", "Moderate", "Slight", + "Stationary", "Worse"), + "Infiltration" = c("0-7", "8-15") + ) + ) > cochran <- as.table(cochran) > > ## Asymptotic Pearson chi-squared test (Cochran, 1954, p. 435) > chisq_test(cochran) # X^2 = 6.88 Asymptotic Pearson Chi-Squared Test data: Infiltration by Change (Marked, Moderate, Slight, Stationary, Worse) chi-squared = 6.8807, df = 4, p-value = 0.1423 > > ## Asymptotic Cochran-Armitage test (Cochran, 1954, p. 436) > ## Note: 'Change' as ordinal > (ct <- chisq_test(cochran, + scores = list("Change" = c(3, 2, 1, 0, -1)))) Asymptotic Linear-by-Linear Association Test data: Infiltration by Change (Marked < Moderate < Slight < Stationary < Worse) Z = -2.5818, p-value = 0.009829 alternative hypothesis: two.sided > statistic(ct)^2 # X^2 = 6.66 [1] 6.665691 > > > ## Change in size of ulcer crater for two treatment groups > ## Armitage (1955, Tab. 2) > armitage <- matrix( + c( 6, 4, 10, 12, + 11, 8, 8, 5), + byrow = TRUE, ncol = 4, + dimnames = list( + "Treatment" = c("A", "B"), + "Crater" = c("Larger", "< 2/3 healed", + ">= 2/3 healed", "Healed") + ) + ) > armitage <- as.table(armitage) > > ## Approximative (Monte Carlo) Pearson chi-squared test (Armitage, 1955, p. 379) > chisq_test(armitage, + distribution = approximate(nresample = 10000)) # chi^2 = 5.91 Approximative Pearson Chi-Squared Test data: Crater by Treatment (A, B) chi-squared = 5.9085, p-value = 0.1186 > > ## Approximative (Monte Carlo) Cochran-Armitage test (Armitage, 1955, p. 379) > (ct <- chisq_test(armitage, + distribution = approximate(nresample = 10000), + scores = list("Crater" = c(-1.5, -0.5, 0.5, 1.5)))) Approximative Linear-by-Linear Association Test data: Crater (ordered) by Treatment (A, B) Z = 2.2932, p-value = 0.0291 alternative hypothesis: two.sided > statistic(ct)^2 # chi_0^2 = 5.26 [1] 5.258804 > > > ## Relationship between job satisfaction and income stratified by gender > ## Agresti (2002, p. 288, Tab. 7.8) > > ## Asymptotic generalized Cochran-Mantel-Haenszel test (Agresti, p. 297) > (ct <- cmh_test(jobsatisfaction)) # CMH = 10.2001 Asymptotic Generalized Cochran-Mantel-Haenszel Test data: Job.Satisfaction by Income (<5000, 5000-15000, 15000-25000, >25000) stratified by Gender chi-squared = 10.2, df = 9, p-value = 0.3345 > > ## The standardized linear statistic > statistic(ct, type = "standardized") Very Dissatisfied A Little Satisfied Moderately Satisfied <5000 1.3112789 0.69201053 -0.2478705 5000-15000 0.6481783 0.83462550 0.5175755 15000-25000 -1.0958361 -1.50130926 0.2361231 >25000 -1.0377629 -0.08983052 -0.5946119 Very Satisfied <5000 -0.9293458 5000-15000 -1.6257547 15000-25000 1.4614123 >25000 1.2031648 > > ## The standardized linear statistic for each block > statistic(ct, type = "standardized", partial = TRUE) , , Female Very Dissatisfied A Little Satisfied Moderately Satisfied <5000 0.2698452 0.4922196 0.2175066 5000-15000 0.9959059 -0.3770330 0.7219631 15000-25000 -0.9314188 -0.8360078 -0.4647580 >25000 -0.6652991 0.9438798 -0.7745967 Very Satisfied <5000 -0.8543153 5000-15000 -1.0990044 15000-25000 1.8254610 >25000 0.4803845 , , Male Very Dissatisfied A Little Satisfied Moderately Satisfied <5000 2.6457513 0.5352855 -0.8355894 5000-15000 -0.5388159 2.1196904 -0.1323549 15000-25000 -0.5773503 -1.3627703 0.9117028 >25000 -0.8164966 -0.9636241 -0.1289343 Very Satisfied <5000 -0.3964690 5000-15000 -1.2350566 15000-25000 0.2018721 >25000 1.1419611 > > ## Asymptotic generalized Cochran-Mantel-Haenszel test (Agresti, p. 297) > ## Note: 'Job.Satisfaction' as ordinal > cmh_test(jobsatisfaction, + scores = list("Job.Satisfaction" = c(1, 3, 4, 5))) # L^2 = 9.0342 Asymptotic Generalized Cochran-Mantel-Haenszel Test data: Job.Satisfaction (ordered) by Income (<5000, 5000-15000, 15000-25000, >25000) stratified by Gender chi-squared = 9.0342, df = 3, p-value = 0.02884 > > ## Asymptotic linear-by-linear association test (Agresti, p. 297) > ## Note: 'Job.Satisfaction' and 'Income' as ordinal > (lt <- lbl_test(jobsatisfaction, + scores = list("Job.Satisfaction" = c(1, 3, 4, 5), + "Income" = c(3, 10, 20, 35)))) Asymptotic Linear-by-Linear Association Test data: Job.Satisfaction (ordered) by Income (<5000 < 5000-15000 < 15000-25000 < >25000) stratified by Gender Z = 2.4812, p-value = 0.01309 alternative hypothesis: two.sided > statistic(lt)^2 # M^2 = 6.1563 [1] 6.156301 > > ## The standardized linear statistic > statistic(lt, type = "standardized") 2.48119 > > ## The standardized linear statistic for each block > statistic(lt, type = "standardized", partial = TRUE) , , Female 1.271093 , , Male 2.317108 > > > > cleanEx() > nameEx("CorrelationTests") > ### * CorrelationTests > > flush(stderr()); flush(stdout()) > > ### Name: CorrelationTests > ### Title: Correlation Tests > ### Aliases: spearman_test spearman_test.formula > ### spearman_test.IndependenceProblem fisyat_test fisyat_test.formula > ### fisyat_test.IndependenceProblem quadrant_test quadrant_test.formula > ### quadrant_test.IndependenceProblem koziol_test koziol_test.formula > ### koziol_test.IndependenceProblem > ### Keywords: htest > > ### ** Examples > > ## Asymptotic Spearman test > spearman_test(CONT ~ INTG, data = USJudgeRatings) Asymptotic Spearman Correlation Test data: CONT by INTG Z = -1.1437, p-value = 0.2527 alternative hypothesis: true rho is not equal to 0 > > ## Asymptotic Fisher-Yates test > fisyat_test(CONT ~ INTG, data = USJudgeRatings) Asymptotic Fisher-Yates (Normal Quantile) Correlation Test data: CONT by INTG Z = -0.82479, p-value = 0.4095 alternative hypothesis: true rho is not equal to 0 > > ## Asymptotic quadrant test > quadrant_test(CONT ~ INTG, data = USJudgeRatings) Asymptotic Quadrant Test data: CONT by INTG Z = -1.0944, p-value = 0.2738 alternative hypothesis: true rho is not equal to 0 > > ## Asymptotic Koziol-Nemec test > koziol_test(CONT ~ INTG, data = USJudgeRatings) Asymptotic Koziol-Nemec Test data: CONT by INTG Z = -1.292, p-value = 0.1964 alternative hypothesis: true rho is not equal to 0 > > > > cleanEx() > nameEx("GTSG") > ### * GTSG > > flush(stderr()); flush(stdout()) > > ### Name: GTSG > ### Title: Gastrointestinal Tumor Study Group > ### Aliases: GTSG > ### Keywords: datasets > > ### ** Examples > > ## Plot Kaplan-Meier estimates > plot(survfit(Surv(time / (365.25 / 12), event) ~ group, data = GTSG), + lty = 1:2, ylab = "% Survival", xlab = "Survival Time in Months") > legend("topright", lty = 1:2, + c("Chemotherapy+Radiation", "Chemotherapy"), bty = "n") > > ## Asymptotic logrank test > logrank_test(Surv(time, event) ~ group, data = GTSG) Asymptotic Two-Sample Logrank Test data: Surv(time, event) by group (Chemotherapy+Radiation, Chemotherapy) Z = -1.1428, p-value = 0.2531 alternative hypothesis: true theta is not equal to 1 > > ## Asymptotic Prentice test > logrank_test(Surv(time, event) ~ group, data = GTSG, type = "Prentice") Asymptotic Two-Sample Prentice Test data: Surv(time, event) by group (Chemotherapy+Radiation, Chemotherapy) Z = -2.1687, p-value = 0.03011 alternative hypothesis: true theta is not equal to 1 > > ## Asymptotic test against Weibull-type alternatives (Moreau et al., 1992) > moreau_weight <- function(time, n.risk, n.event) + 1 + log(-log(cumprod(n.risk / (n.risk + n.event)))) > > independence_test(Surv(time, event) ~ group, data = GTSG, + ytrafo = function(data) + trafo(data, surv_trafo = function(y) + logrank_trafo(y, weight = moreau_weight))) Asymptotic General Independence Test data: Surv(time, event) by group (Chemotherapy+Radiation, Chemotherapy) Z = 2.4129, p-value = 0.01583 alternative hypothesis: two.sided > > ## Asymptotic test against crossing-curve alternatives (Shen and Le, 2000) > shen_trafo <- function(x) + ansari_trafo(logrank_trafo(x, type = "Prentice")) > > independence_test(Surv(time, event) ~ group, data = GTSG, + ytrafo = function(data) + trafo(data, surv_trafo = shen_trafo)) Asymptotic General Independence Test data: Surv(time, event) by group (Chemotherapy+Radiation, Chemotherapy) Z = -2.342, p-value = 0.01918 alternative hypothesis: two.sided > > > > cleanEx() > nameEx("IndependenceTest") > ### * IndependenceTest > > flush(stderr()); flush(stdout()) > > ### Name: IndependenceTest > ### Title: General Independence Test > ### Aliases: independence_test independence_test.formula > ### independence_test.table independence_test.IndependenceProblem > ### Keywords: htest > > ### ** Examples > > ## One-sided exact van der Waerden (normal scores) test... > independence_test(asat ~ group, data = asat, + ## exact null distribution + distribution = "exact", + ## one-sided test + alternative = "greater", + ## apply normal scores to asat$asat + ytrafo = function(data) + trafo(data, numeric_trafo = normal_trafo), + ## indicator matrix of 1st level of asat$group + xtrafo = function(data) + trafo(data, factor_trafo = function(x) + matrix(x == levels(x)[1], ncol = 1))) Exact General Independence Test data: asat by group (Compound, Control) Z = 1.4269, p-value = 0.07809 alternative hypothesis: greater > > ## ...or more conveniently > normal_test(asat ~ group, data = asat, + ## exact null distribution + distribution = "exact", + ## one-sided test + alternative = "greater") Exact Two-Sample van der Waerden (Normal Quantile) Test data: asat by group (Compound, Control) Z = 1.4269, p-value = 0.07809 alternative hypothesis: true mu is greater than 0 > > > ## Receptor binding assay of benzodiazepines > ## Johnson, Mercante and May (1993, Tab. 1) > benzos <- data.frame( + cerebellum = c( 3.41, 3.50, 2.85, 4.43, + 4.04, 7.40, 5.63, 12.86, + 6.03, 6.08, 5.75, 8.09, 7.56), + brainstem = c( 3.46, 2.73, 2.22, 3.16, + 2.59, 4.18, 3.10, 4.49, + 6.78, 7.54, 5.29, 4.57, 5.39), + cortex = c(10.52, 7.52, 4.57, 5.48, + 7.16, 12.00, 9.36, 9.35, + 11.54, 11.05, 9.92, 13.59, 13.21), + hypothalamus = c(19.51, 10.00, 8.27, 10.26, + 11.43, 19.13, 14.03, 15.59, + 24.87, 14.16, 22.68, 19.93, 29.32), + striatum = c( 6.98, 5.07, 3.57, 5.34, + 4.57, 8.82, 5.76, 11.72, + 6.98, 7.54, 7.66, 9.69, 8.09), + hippocampus = c(20.31, 13.20, 8.58, 11.42, + 13.79, 23.71, 18.35, 38.52, + 21.56, 18.66, 19.24, 27.39, 26.55), + treatment = factor(rep(c("Lorazepam", "Alprazolam", "Saline"), + c(4, 4, 5))) + ) > > ## Approximative (Monte Carlo) multivariate Kruskal-Wallis test > ## Johnson, Mercante and May (1993, Tab. 2) > independence_test(cerebellum + brainstem + cortex + + hypothalamus + striatum + hippocampus ~ treatment, + data = benzos, + teststat = "quadratic", + distribution = approximate(nresample = 10000), + ytrafo = function(data) + trafo(data, numeric_trafo = rank_trafo)) # Q = 16.129 Approximative General Independence Test data: cerebellum, brainstem, cortex, hypothalamus, striatum, hippocampus by treatment (Alprazolam, Lorazepam, Saline) chi-squared = 16.129, p-value = 0.0708 > > > > cleanEx() > nameEx("LocationTests") > ### * LocationTests > > flush(stderr()); flush(stdout()) > > ### Name: LocationTests > ### Title: Two- and K-Sample Location Tests > ### Aliases: oneway_test oneway_test.formula > ### oneway_test.IndependenceProblem wilcox_test wilcox_test.formula > ### wilcox_test.IndependenceProblem kruskal_test kruskal_test.formula > ### kruskal_test.IndependenceProblem normal_test normal_test.formula > ### normal_test.IndependenceProblem median_test median_test.formula > ### median_test.IndependenceProblem savage_test savage_test.formula > ### savage_test.IndependenceProblem > ### Keywords: htest > > ### ** Examples > ## Don't show: > options(useFancyQuotes = FALSE) > ## End(Don't show) > ## Tritiated Water Diffusion Across Human Chorioamnion > ## Hollander and Wolfe (1999, p. 110, Tab. 4.1) > diffusion <- data.frame( + pd = c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46, + 1.15, 0.88, 0.90, 0.74, 1.21), + age = factor(rep(c("At term", "12-26 Weeks"), c(10, 5))) + ) > > ## Exact Wilcoxon-Mann-Whitney test > ## Hollander and Wolfe (1999, p. 111) > ## (At term - 12-26 Weeks) > (wt <- wilcox_test(pd ~ age, data = diffusion, + distribution = "exact", conf.int = TRUE)) Exact Wilcoxon-Mann-Whitney Test data: pd by age (12-26 Weeks, At term) Z = -1.2247, p-value = 0.2544 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -0.76 0.15 sample estimates: difference in location -0.305 > > ## Extract observed Wilcoxon statistic > ## Note: this is the sum of the ranks for age = "12-26 Weeks" > statistic(wt, type = "linear") 12-26 Weeks 30 > > ## Expectation, variance, two-sided pvalue and confidence interval > expectation(wt) 12-26 Weeks 40 > covariance(wt) 12-26 Weeks 12-26 Weeks 66.66667 > pvalue(wt) [1] 0.2544123 > confint(wt) 95 percent confidence interval: -0.76 0.15 sample estimates: difference in location -0.305 > > ## For two samples, the Kruskal-Wallis test is equivalent to the W-M-W test > kruskal_test(pd ~ age, data = diffusion, + distribution = "exact") Exact Kruskal-Wallis Test data: pd by age (12-26 Weeks, At term) chi-squared = 1.5, p-value = 0.2544 > > ## Asymptotic Fisher-Pitman test > oneway_test(pd ~ age, data = diffusion) Asymptotic Two-Sample Fisher-Pitman Permutation Test data: pd by age (12-26 Weeks, At term) Z = -1.5225, p-value = 0.1279 alternative hypothesis: true mu is not equal to 0 > > ## Approximative (Monte Carlo) Fisher-Pitman test > pvalue(oneway_test(pd ~ age, data = diffusion, + distribution = approximate(nresample = 10000))) [1] 0.1311 99 percent confidence interval: 0.1225338 0.1400198 > > ## Exact Fisher-Pitman test > pvalue(ot <- oneway_test(pd ~ age, data = diffusion, + distribution = "exact")) [1] 0.1318681 > > ## Plot density and distribution of the standardized test statistic > op <- par(no.readonly = TRUE) # save current settings > layout(matrix(1:2, nrow = 2)) > s <- support(ot) > d <- dperm(ot, s) > p <- pperm(ot, s) > plot(s, d, type = "S", xlab = "Test Statistic", ylab = "Density") > plot(s, p, type = "S", xlab = "Test Statistic", ylab = "Cum. Probability") > par(op) # reset > > > ## Example data > ex <- data.frame( + y = c(3, 4, 8, 9, 1, 2, 5, 6, 7), + x = factor(rep(c("no", "yes"), c(4, 5))) + ) > > ## Boxplots > boxplot(y ~ x, data = ex) > > ## Exact Brown-Mood median test with different mid-scores > (mt1 <- median_test(y ~ x, data = ex, distribution = "exact")) Exact Two-Sample Brown-Mood Median Test data: y by x (no, yes) Z = 0.28284, p-value = 1 alternative hypothesis: true mu is not equal to 0 > (mt2 <- median_test(y ~ x, data = ex, distribution = "exact", + mid.score = "0.5")) Exact Two-Sample Brown-Mood Median Test data: y by x (no, yes) Z = 0, p-value = 1 alternative hypothesis: true mu is not equal to 0 > (mt3 <- median_test(y ~ x, data = ex, distribution = "exact", + mid.score = "1")) # sign change! Exact Two-Sample Brown-Mood Median Test data: y by x (no, yes) Z = -0.28284, p-value = 1 alternative hypothesis: true mu is not equal to 0 > > ## Plot density and distribution of the standardized test statistics > op <- par(no.readonly = TRUE) # save current settings > layout(matrix(1:3, nrow = 3)) > s1 <- support(mt1); d1 <- dperm(mt1, s1) > plot(s1, d1, type = "h", main = "Mid-score: 0", + xlab = "Test Statistic", ylab = "Density") > s2 <- support(mt2); d2 <- dperm(mt2, s2) > plot(s2, d2, type = "h", main = "Mid-score: 0.5", + xlab = "Test Statistic", ylab = "Density") > s3 <- support(mt3); d3 <- dperm(mt3, s3) > plot(s3, d3, type = "h", main = "Mid-score: 1", + xlab = "Test Statistic", ylab = "Density") > par(op) # reset > > > ## Length of YOY Gizzard Shad > ## Hollander and Wolfe (1999, p. 200, Tab. 6.3) > yoy <- data.frame( + length = c(46, 28, 46, 37, 32, 41, 42, 45, 38, 44, + 42, 60, 32, 42, 45, 58, 27, 51, 42, 52, + 38, 33, 26, 25, 28, 28, 26, 27, 27, 27, + 31, 30, 27, 29, 30, 25, 25, 24, 27, 30), + site = gl(4, 10, labels = as.roman(1:4)) + ) > > ## Approximative (Monte Carlo) Kruskal-Wallis test > kruskal_test(length ~ site, data = yoy, + distribution = approximate(nresample = 10000)) Approximative Kruskal-Wallis Test data: length by site (I, II, III, IV) chi-squared = 22.852, p-value < 1e-04 > > ## Approximative (Monte Carlo) Nemenyi-Damico-Wolfe-Dunn test (joint ranking) > ## Hollander and Wolfe (1999, p. 244) > ## (where Steel-Dwass results are given) > it <- independence_test(length ~ site, data = yoy, + distribution = approximate(nresample = 50000), + ytrafo = function(data) + trafo(data, numeric_trafo = rank_trafo), + xtrafo = mcp_trafo(site = "Tukey")) > > ## Global p-value > pvalue(it) [1] 0.00068 99 percent confidence interval: 0.0004171853 0.0010419603 > > ## Sites (I = II) != (III = IV) at alpha = 0.01 (p. 244) > pvalue(it, method = "single-step") # subset pivotality is violated Warning in .local(object, ...) : p-values may be incorrect due to violation of the subset pivotality condition II - I 0.94868 III - I 0.00876 IV - I 0.00700 III - II 0.00084 IV - II 0.00068 IV - III 0.99996 > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("MarginalHomogeneityTests") > ### * MarginalHomogeneityTests > > flush(stderr()); flush(stdout()) > > ### Name: MarginalHomogeneityTests > ### Title: Marginal Homogeneity Tests > ### Aliases: mh_test mh_test.formula mh_test.table mh_test.SymmetryProblem > ### Keywords: htest > > ### ** Examples > > ## Performance of prime minister > ## Agresti (2002, p. 409) > performance <- matrix( + c(794, 150, + 86, 570), + nrow = 2, byrow = TRUE, + dimnames = list( + "First" = c("Approve", "Disprove"), + "Second" = c("Approve", "Disprove") + ) + ) > performance <- as.table(performance) > diag(performance) <- 0 # speed-up: only off-diagonal elements contribute > > ## Asymptotic McNemar Test > mh_test(performance) Asymptotic Marginal Homogeneity Test data: response by conditions (First, Second) stratified by block chi-squared = 17.356, df = 1, p-value = 3.099e-05 > > ## Exact McNemar Test > mh_test(performance, distribution = "exact") Exact Marginal Homogeneity Test data: response by conditions (First, Second) stratified by block chi-squared = 17.356, p-value = 3.716e-05 > > > ## Effectiveness of different media for the growth of diphtheria > ## Cochran (1950, Tab. 2) > cases <- c(4, 2, 3, 1, 59) > n <- sum(cases) > cochran <- data.frame( + diphtheria = factor( + unlist(rep(list(c(1, 1, 1, 1), + c(1, 1, 0, 1), + c(0, 1, 1, 1), + c(0, 1, 0, 1), + c(0, 0, 0, 0)), + cases)) + ), + media = factor(rep(LETTERS[1:4], n)), + case = factor(rep(seq_len(n), each = 4)) + ) > > ## Asymptotic Cochran Q test (Cochran, 1950, p. 260) > mh_test(diphtheria ~ media | case, data = cochran) # Q = 8.05 Asymptotic Marginal Homogeneity Test data: diphtheria by media (A, B, C, D) stratified by case chi-squared = 8.0526, df = 3, p-value = 0.04494 > > ## Approximative Cochran Q test > mt <- mh_test(diphtheria ~ media | case, data = cochran, + distribution = approximate(nresample = 10000)) > pvalue(mt) # standard p-value [1] 0.0536 99 percent confidence interval: 0.04796230 0.05966731 > midpvalue(mt) # mid-p-value [1] 0.0439 99 percent confidence interval: 0.03883667 0.04939715 > pvalue_interval(mt) # p-value interval p_0 p_1 0.0342 0.0536 > size(mt, alpha = 0.05) # test size at alpha = 0.05 using the p-value [1] 0.0342 > > > ## Opinions on Pre- and Extramarital Sex > ## Agresti (2002, p. 421) > opinions <- c("Always wrong", "Almost always wrong", + "Wrong only sometimes", "Not wrong at all") > PreExSex <- matrix( + c(144, 33, 84, 126, + 2, 4, 14, 29, + 0, 2, 6, 25, + 0, 0, 1, 5), + nrow = 4, + dimnames = list( + "Premarital Sex" = opinions, + "Extramarital Sex" = opinions + ) + ) > PreExSex <- as.table(PreExSex) > > ## Asymptotic Stuart test > mh_test(PreExSex) Asymptotic Marginal Homogeneity Test data: response by conditions (Premarital.Sex, Extramarital.Sex) stratified by block chi-squared = 271.92, df = 3, p-value < 2.2e-16 > > ## Asymptotic Stuart-Birch test > ## Note: response as ordinal > mh_test(PreExSex, scores = list(response = 1:length(opinions))) Asymptotic Marginal Homogeneity Test for Ordered Data data: response (ordered) by conditions (Premarital.Sex, Extramarital.Sex) stratified by block Z = 16.454, p-value < 2.2e-16 alternative hypothesis: two.sided > > > ## Vote intention > ## Madansky (1963, pp. 107-108) > vote <- array( + c(120, 1, 8, 2, 2, 1, 2, 1, 7, + 6, 2, 1, 1, 103, 5, 1, 4, 8, + 20, 3, 31, 1, 6, 30, 2, 1, 81), + dim = c(3, 3, 3), + dimnames = list( + "July" = c("Republican", "Democratic", "Uncertain"), + "August" = c("Republican", "Democratic", "Uncertain"), + "June" = c("Republican", "Democratic", "Uncertain") + ) + ) > vote <- as.table(vote) > > ## Asymptotic Madansky test (Q = 70.77) > mh_test(vote) Asymptotic Marginal Homogeneity Test data: response by conditions (July, August, June) stratified by block chi-squared = 70.763, df = 4, p-value = 1.565e-14 > > > ## Cross-over study > ## http://www.nesug.org/proceedings/nesug00/st/st9005.pdf > dysmenorrhea <- array( + c(6, 2, 1, 3, 1, 0, 1, 2, 1, + 4, 3, 0, 13, 3, 0, 8, 1, 1, + 5, 2, 2, 10, 1, 0, 14, 2, 0), + dim = c(3, 3, 3), + dimnames = list( + "Placebo" = c("None", "Moderate", "Complete"), + "Low dose" = c("None", "Moderate", "Complete"), + "High dose" = c("None", "Moderate", "Complete") + ) + ) > dysmenorrhea <- as.table(dysmenorrhea) > > ## Asymptotic Madansky-Birch test (Q = 53.76) > ## Note: response as ordinal > mh_test(dysmenorrhea, scores = list(response = 1:3)) Asymptotic Marginal Homogeneity Test for Ordered Data data: response (ordered) by conditions (Placebo, Low.dose, High.dose) stratified by block chi-squared = 53.762, df = 2, p-value = 2.117e-12 > > ## Asymptotic Madansky-Birch test (Q = 47.29) > ## Note: response and measurement conditions as ordinal > mh_test(dysmenorrhea, scores = list(response = 1:3, + conditions = 1:3)) Asymptotic Marginal Homogeneity Test for Ordered Data data: response (ordered) by conditions (Placebo < Low.dose < High.dose) stratified by block Z = 6.8764, p-value = 6.138e-12 alternative hypothesis: two.sided > > > > cleanEx() > nameEx("MaximallySelectedStatisticsTests") > ### * MaximallySelectedStatisticsTests > > flush(stderr()); flush(stdout()) > > ### Name: MaximallySelectedStatisticsTests > ### Title: Generalized Maximally Selected Statistics > ### Aliases: maxstat_test maxstat_test.formula maxstat_test.table > ### maxstat_test.IndependenceProblem > ### Keywords: htest > > ### ** Examples > > ## Don't show: > options(useFancyQuotes = FALSE) > ## End(Don't show) > ## Tree pipit data (Mueller and Hothorn, 2004) > ## Asymptotic maximally selected statistics > maxstat_test(counts ~ coverstorey, data = treepipit) Asymptotic Generalized Maximally Selected Statistics data: counts by coverstorey maxT = 4.3139, p-value = 0.0001796 alternative hypothesis: two.sided sample estimates: "best" cutpoint: <= 40 > > ## Asymptotic maximally selected statistics > ## Note: all covariates simultaneously > mt <- maxstat_test(counts ~ ., data = treepipit) > mt@estimates$estimate "best" cutpoint: <= 280 covariable: fdist > > > ## Malignant arrythmias data (Hothorn and Lausen, 2003, Sec. 7.2) > ## Asymptotic maximally selected statistics > maxstat_test(Surv(time, event) ~ EF, data = hohnloser, + ytrafo = function(data) + trafo(data, surv_trafo = function(y) + logrank_trafo(y, ties.method = "Hothorn-Lausen"))) Asymptotic Generalized Maximally Selected Statistics data: Surv(time, event) by EF maxT = 3.5691, p-value = 0.004286 alternative hypothesis: two.sided sample estimates: "best" cutpoint: <= 39 > > > ## Breast cancer data (Hothorn and Lausen, 2003, Sec. 7.3) > ## Asymptotic maximally selected statistics > data("sphase", package = "TH.data") > maxstat_test(Surv(RFS, event) ~ SPF, data = sphase, + ytrafo = function(data) + trafo(data, surv_trafo = function(y) + logrank_trafo(y, ties.method = "Hothorn-Lausen"))) Asymptotic Generalized Maximally Selected Statistics data: Surv(RFS, event) by SPF maxT = 2.4033, p-value = 0.1555 alternative hypothesis: two.sided sample estimates: "best" cutpoint: <= 107 > > > ## Job satisfaction data (Agresti, 2002, p. 288, Tab. 7.8) > ## Asymptotic maximally selected statistics > maxstat_test(jobsatisfaction) Asymptotic Generalized Maximally Selected Statistics data: Job.Satisfaction by Income (<5000, 5000-15000, 15000-25000, >25000) stratified by Gender maxT = 2.3349, p-value = 0.2993 alternative hypothesis: two.sided sample estimates: "best" cutpoint: {<5000, 5000-15000} vs. {15000-25000, >25000} > > ## Asymptotic maximally selected statistics > ## Note: 'Job.Satisfaction' and 'Income' as ordinal > maxstat_test(jobsatisfaction, + scores = list("Job.Satisfaction" = 1:4, + "Income" = 1:4)) Asymptotic Generalized Maximally Selected Statistics data: Job.Satisfaction (ordered) by Income (<5000 < 5000-15000 < 15000-25000 < >25000) stratified by Gender maxT = 2.9983, p-value = 0.007662 alternative hypothesis: two.sided sample estimates: "best" cutpoint: {<5000, 5000-15000} vs. {15000-25000, >25000} > > > > cleanEx() > nameEx("NullDistribution") > ### * NullDistribution > > flush(stderr()); flush(stdout()) > > ### Name: NullDistribution > ### Title: Specification of the Reference Distribution > ### Aliases: asymptotic approximate exact > ### Keywords: htest > > ### ** Examples > > ## Approximative (Monte Carlo) Cochran-Mantel-Haenszel test > > ## Serial operation > set.seed(123) > cmh_test(disease ~ smoking | gender, data = alzheimer, + distribution = approximate(nresample = 100000)) Approximative Generalized Cochran-Mantel-Haenszel Test data: disease by smoking (None, <10, 10-20, >20) stratified by gender chi-squared = 23.316, p-value = 0.00052 > > ## Not run: > ##D ## Multicore with 8 processes (not for MS Windows) > ##D set.seed(123, kind = "L'Ecuyer-CMRG") > ##D cmh_test(disease ~ smoking | gender, data = alzheimer, > ##D distribution = approximate(nresample = 100000, > ##D parallel = "multicore", ncpus = 8)) > ##D > ##D ## Automatic PSOCK cluster with 4 processes > ##D set.seed(123, kind = "L'Ecuyer-CMRG") > ##D cmh_test(disease ~ smoking | gender, data = alzheimer, > ##D distribution = approximate(nresample = 100000, > ##D parallel = "snow", ncpus = 4)) > ##D > ##D ## Registered FORK cluster with 12 processes (not for MS Windows) > ##D fork12 <- parallel::makeCluster(12, "FORK") # set-up cluster > ##D parallel::setDefaultCluster(fork12) # register default cluster > ##D set.seed(123, kind = "L'Ecuyer-CMRG") > ##D cmh_test(disease ~ smoking | gender, data = alzheimer, > ##D distribution = approximate(nresample = 100000, > ##D parallel = "snow")) > ##D parallel::stopCluster(fork12) # clean-up > ##D > ##D ## User-specified PSOCK cluster with 8 processes > ##D psock8 <- parallel::makeCluster(8, "PSOCK") # set-up cluster > ##D set.seed(123, kind = "L'Ecuyer-CMRG") > ##D cmh_test(disease ~ smoking | gender, data = alzheimer, > ##D distribution = approximate(nresample = 100000, > ##D parallel = "snow", cl = psock8)) > ##D parallel::stopCluster(psock8) # clean-up > ## End(Not run) > > > > cleanEx() > nameEx("PermutationDistribution-methods") > ### * PermutationDistribution-methods > > flush(stderr()); flush(stdout()) > > ### Name: PermutationDistribution-methods > ### Title: Computation of the Permutation Distribution > ### Aliases: dperm dperm-methods dperm,NullDistribution-method > ### dperm,IndependenceTest-method pperm pperm-methods > ### pperm,NullDistribution-method pperm,IndependenceTest-method qperm > ### qperm-methods qperm,NullDistribution-method > ### qperm,IndependenceTest-method rperm rperm-methods > ### rperm,NullDistribution-method rperm,IndependenceTest-method support > ### support-methods support,NullDistribution-method > ### support,IndependenceTest-method > ### Keywords: methods htest distribution > > ### ** Examples > > ## Two-sample problem > dta <- data.frame( + y = rnorm(20), + x = gl(2, 10) + ) > > ## Exact Ansari-Bradley test > at <- ansari_test(y ~ x, data = dta, distribution = "exact") > > ## Support of the exact distribution of the Ansari-Bradley statistic > supp <- support(at) > > ## Density of the exact distribution of the Ansari-Bradley statistic > dens <- dperm(at, x = supp) > > ## Plotting the density > plot(supp, dens, type = "s") > > ## 95% quantile > qperm(at, p = 0.95) [1] 1.669331 > > ## One-sided p-value > pperm(at, q = statistic(at)) [1] 0.698635 > > ## Random number generation > rperm(at, n = 5) [1] 0.9105443 0.4552721 0.7587869 0.1517574 0.1517574 > > > > cleanEx() > nameEx("ScaleTests") > ### * ScaleTests > > flush(stderr()); flush(stdout()) > > ### Name: ScaleTests > ### Title: Two- and K-Sample Scale Tests > ### Aliases: taha_test taha_test.formula taha_test.IndependenceProblem > ### klotz_test klotz_test.formula klotz_test.IndependenceProblem > ### mood_test mood_test.formula mood_test.IndependenceProblem ansari_test > ### ansari_test.formula ansari_test.IndependenceProblem fligner_test > ### fligner_test.formula fligner_test.IndependenceProblem conover_test > ### conover_test.formula conover_test.IndependenceProblem > ### Keywords: htest > > ### ** Examples > > ## Serum Iron Determination Using Hyland Control Sera > ## Hollander and Wolfe (1999, p. 147, Tab 5.1) > sid <- data.frame( + serum = c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99, + 101, 96, 97, 102, 107, 113, 116, 113, 110, 98, + 107, 108, 106, 98, 105, 103, 110, 105, 104, + 100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99), + method = gl(2, 20, labels = c("Ramsay", "Jung-Parekh")) + ) > > ## Asymptotic Ansari-Bradley test > ansari_test(serum ~ method, data = sid) Asymptotic Two-Sample Ansari-Bradley Test data: serum by method (Ramsay, Jung-Parekh) Z = -1.3363, p-value = 0.1815 alternative hypothesis: true ratio of scales is not equal to 1 > > ## Exact Ansari-Bradley test > pvalue(ansari_test(serum ~ method, data = sid, + distribution = "exact")) [1] 0.1880644 > > > ## Platelet Counts of Newborn Infants > ## Hollander and Wolfe (1999, p. 171, Tab. 5.4) > platelet <- data.frame( + counts = c(120, 124, 215, 90, 67, 95, 190, 180, 135, 399, + 12, 20, 112, 32, 60, 40), + treatment = factor(rep(c("Prednisone", "Control"), c(10, 6))) + ) > > ## Approximative (Monte Carlo) Lepage test > ## Hollander and Wolfe (1999, p. 172) > lepage_trafo <- function(y) + cbind("Location" = rank_trafo(y), "Scale" = ansari_trafo(y)) > > independence_test(counts ~ treatment, data = platelet, + distribution = approximate(nresample = 10000), + ytrafo = function(data) + trafo(data, numeric_trafo = lepage_trafo), + teststat = "quadratic") Approximative General Independence Test data: counts by treatment (Control, Prednisone) chi-squared = 9.3384, p-value = 0.0042 > > ## Why was the null hypothesis rejected? > ## Note: maximum statistic instead of quadratic form > ltm <- independence_test(counts ~ treatment, data = platelet, + distribution = approximate(nresample = 10000), + ytrafo = function(data) + trafo(data, numeric_trafo = lepage_trafo)) > > ## Step-down adjustment suggests a difference in location > pvalue(ltm, method = "step-down") Location Scale Control 0.0035 0.4665 > > ## The same results are obtained from the simple Sidak-Holm procedure since the > ## correlation between Wilcoxon and Ansari-Bradley test statistics is zero > cov2cor(covariance(ltm)) Control:Location Control:Scale Control:Location 1 0 Control:Scale 0 1 > pvalue(ltm, method = "step-down", distribution = "marginal", type = "Sidak") Location Scale Control 0.00349714 0.4665 > > > > cleanEx() > nameEx("SurvivalTests") > ### * SurvivalTests > > flush(stderr()); flush(stdout()) > > ### Name: SurvivalTests > ### Title: Two- and K-Sample Tests for Censored Data > ### Aliases: surv_test logrank_test logrank_test.formula > ### logrank_test.IndependenceProblem > ### Keywords: htest survival > > ### ** Examples > > ## Example data (Callaert, 2003, Tab. 1) > callaert <- data.frame( + time = c(1, 1, 5, 6, 6, 6, 6, 2, 2, 2, 3, 4, 4, 5, 5), + group = factor(rep(0:1, c(7, 8))) + ) > > ## Logrank scores using mid-ranks (Callaert, 2003, Tab. 2) > with(callaert, + logrank_trafo(Surv(time))) [1] -0.8666667 -0.8666667 0.1148962 1.1148962 1.1148962 1.1148962 [7] 1.1148962 -0.6358974 -0.6358974 -0.6358974 -0.5358974 -0.3136752 [13] -0.3136752 0.1148962 0.1148962 > > ## Asymptotic Mantel-Cox test (p = 0.0523) > survdiff(Surv(time) ~ group, data = callaert) Call: survdiff(formula = Surv(time) ~ group, data = callaert) N Observed Expected (O-E)^2/E (O-E)^2/V group=0 7 7 9.84 0.82 3.76 group=1 8 8 5.16 1.56 3.76 Chisq= 3.8 on 1 degrees of freedom, p= 0.05 > > ## Exact logrank test using mid-ranks (p = 0.0505) > logrank_test(Surv(time) ~ group, data = callaert, distribution = "exact") Exact Two-Sample Logrank Test data: Surv(time) by group (0, 1) Z = 1.9201, p-value = 0.05051 alternative hypothesis: true theta is not equal to 1 > > ## Exact logrank test using average-scores (p = 0.0468) > logrank_test(Surv(time) ~ group, data = callaert, distribution = "exact", + ties.method = "average-scores") Exact Two-Sample Logrank Test data: Surv(time) by group (0, 1) Z = 1.9865, p-value = 0.04678 alternative hypothesis: true theta is not equal to 1 > > > ## Lung cancer data (StatXact 9 manual, p. 213, Tab. 7.19) > lungcancer <- data.frame( + time = c(257, 476, 355, 1779, 355, + 191, 563, 242, 285, 16, 16, 16, 257, 16), + event = c(0, 0, 1, 1, 0, + 1, 1, 1, 1, 1, 1, 1, 1, 1), + group = factor(rep(1:2, c(5, 9)), + labels = c("newdrug", "control")) + ) > > ## Logrank scores using average-scores (StatXact 9 manual, p. 214) > with(lungcancer, + logrank_trafo(Surv(time, event), ties.method = "average-scores")) [1] 0.65870518 1.02537185 0.02537185 1.52537185 1.02537185 -0.57740593 [7] 0.52537185 -0.46629482 -0.17462815 -0.80648518 -0.80648518 -0.80648518 [13] -0.34129482 -0.80648518 > > ## Exact logrank test using average-scores (StatXact 9 manual, p. 215) > logrank_test(Surv(time, event) ~ group, data = lungcancer, + distribution = "exact", ties.method = "average-scores") Exact Two-Sample Logrank Test data: Surv(time, event) by group (newdrug, control) Z = 2.9492, p-value = 0.000999 alternative hypothesis: true theta is not equal to 1 > > ## Exact Prentice test using average-scores (StatXact 9 manual, p. 222) > logrank_test(Surv(time, event) ~ group, data = lungcancer, + distribution = "exact", ties.method = "average-scores", + type = "Prentice") Exact Two-Sample Prentice Test data: Surv(time, event) by group (newdrug, control) Z = 2.7813, p-value = 0.002997 alternative hypothesis: true theta is not equal to 1 > > > ## Approximative (Monte Carlo) versatile test (Lee, 1996) > rho.gamma <- expand.grid(rho = seq(0, 2, 1), gamma = seq(0, 2, 1)) > lee_trafo <- function(y) + logrank_trafo(y, ties.method = "average-scores", + type = "Fleming-Harrington", + rho = rho.gamma["rho"], gamma = rho.gamma["gamma"]) > > it <- independence_test(Surv(time, event) ~ group, data = lungcancer, + distribution = approximate(nresample = 10000), + ytrafo = function(data) + trafo(data, surv_trafo = lee_trafo)) > pvalue(it, method = "step-down") rho = 0, gamma = 0 rho = 1, gamma = 0 rho = 2, gamma = 0 newdrug 0.0028 0.0052 0.0103 rho = 0, gamma = 1 rho = 1, gamma = 1 rho = 2, gamma = 1 newdrug 0.0097 0.0028 0.0028 rho = 0, gamma = 2 rho = 1, gamma = 2 rho = 2, gamma = 2 newdrug 0.016 0.0103 0.0061 > > > > cleanEx() > nameEx("SymmetryTest") > ### * SymmetryTest > > flush(stderr()); flush(stdout()) > > ### Name: SymmetryTest > ### Title: General Symmetry Test > ### Aliases: symmetry_test symmetry_test.formula symmetry_test.table > ### symmetry_test.SymmetryProblem > ### Keywords: htest > > ### ** Examples > > ## One-sided exact Fisher-Pitman test for paired observations > y1 <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) > y2 <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) > dta <- data.frame( + y = c(y1, y2), + x = gl(2, length(y1)), + block = factor(rep(seq_along(y1), 2)) + ) > > symmetry_test(y ~ x | block, data = dta, + distribution = "exact", alternative = "greater") Exact General Symmetry Test data: y by x (1, 2) stratified by block Z = 2.1948, p-value = 0.01367 alternative hypothesis: greater > > ## Alternatively: transform data and set 'paired = TRUE' > delta <- y1 - y2 > y <- as.vector(rbind(abs(delta) * (delta >= 0), abs(delta) * (delta < 0))) > x <- factor(rep(0:1, length(delta)), labels = c("pos", "neg")) > block <- gl(length(delta), 2) > > symmetry_test(y ~ x | block, + distribution = "exact", alternative = "greater", + paired = TRUE) Exact General Symmetry Test data: y by x (pos, neg) stratified by block Z = 2.1948, p-value = 0.01367 alternative hypothesis: greater > > > ### Example data > ### Gerig (1969, p. 1597) > gerig <- data.frame( + y1 = c( 0.547, 1.811, 2.561, + 1.706, 2.509, 1.414, + -0.288, 2.524, 3.310, + 1.417, 0.703, 0.961, + 0.878, 0.094, 1.682, + -0.680, 2.077, 3.181, + 0.056, 0.542, 2.983, + 0.711, 0.269, 1.662, + -1.335, 1.545, 2.920, + 1.635, 0.200, 2.065), + y2 = c(-0.575, 1.840, 2.399, + 1.252, 1.574, 3.059, + -0.310, 1.553, 0.560, + 0.932, 1.390, 3.083, + 0.819, 0.045, 3.348, + 0.497, 1.747, 1.355, + -0.285, 0.760, 2.332, + 0.089, 1.076, 0.960, + -0.349, 1.471, 4.121, + 0.845, 1.480, 3.391), + x = factor(rep(1:3, 10)), + b = factor(rep(1:10, each = 3)) + ) > > ### Asymptotic multivariate Friedman test > ### Gerig (1969, p. 1599) > symmetry_test(y1 + y2 ~ x | b, data = gerig, teststat = "quadratic", + ytrafo = function(data) + trafo(data, numeric_trafo = rank_trafo, + block = gerig$b)) # L_n = 17.238 Asymptotic General Symmetry Test data: y1, y2 by x (1, 2, 3) stratified by b chi-squared = 17.238, df = 4, p-value = 0.001738 > > ### Asymptotic multivariate Page test > (st <- symmetry_test(y1 + y2 ~ x | b, data = gerig, + ytrafo = function(data) + trafo(data, numeric_trafo = rank_trafo, + block = gerig$b), + scores = list(x = 1:3))) Asymptotic General Symmetry Test data: y1, y2 by x (1 < 2 < 3) stratified by b maxT = 3.5777, p-value = 0.0006887 alternative hypothesis: two.sided > pvalue(st, method = "step-down") y1 y2 0.0139063 0.0006886767 > > > > cleanEx() > nameEx("SymmetryTests") > ### * SymmetryTests > > flush(stderr()); flush(stdout()) > > ### Name: SymmetryTests > ### Title: Symmetry Tests > ### Aliases: sign_test sign_test.formula sign_test.SymmetryProblem > ### wilcoxsign_test wilcoxsign_test.formula > ### wilcoxsign_test.SymmetryProblem friedman_test friedman_test.formula > ### friedman_test.SymmetryProblem quade_test quade_test.formula > ### quade_test.SymmetryProblem > ### Keywords: htest > > ### ** Examples > > ## Example data from ?wilcox.test > y1 <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) > y2 <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) > > ## One-sided exact sign test > (st <- sign_test(y1 ~ y2, distribution = "exact", + alternative = "greater")) Exact Sign Test data: y by x (pos, neg) stratified by block Z = 1.6667, p-value = 0.08984 alternative hypothesis: true mu is greater than 0 > midpvalue(st) # mid-p-value [1] 0.0546875 > > ## One-sided exact Wilcoxon signed-rank test > (wt <- wilcoxsign_test(y1 ~ y2, distribution = "exact", + alternative = "greater")) Exact Wilcoxon-Pratt Signed-Rank Test data: y by x (pos, neg) stratified by block Z = 2.0732, p-value = 0.01953 alternative hypothesis: true mu is greater than 0 > statistic(wt, type = "linear") pos 40 > midpvalue(wt) # mid-p-value [1] 0.01660156 > > ## Comparison with R's wilcox.test() function > wilcox.test(y1, y2, paired = TRUE, alternative = "greater") Wilcoxon signed rank exact test data: y1 and y2 V = 40, p-value = 0.01953 alternative hypothesis: true location shift is greater than 0 > > > ## Data with explicit group and block information > dta <- data.frame(y = c(y1, y2), x = gl(2, length(y1)), + block = factor(rep(seq_along(y1), 2))) > > ## For two samples, the sign test is equivalent to the Friedman test... > sign_test(y ~ x | block, data = dta, distribution = "exact") Exact Sign Test data: y by x (pos, neg) stratified by block Z = 1.6667, p-value = 0.1797 alternative hypothesis: true mu is not equal to 0 > friedman_test(y ~ x | block, data = dta, distribution = "exact") Exact Friedman Test data: y by x (1, 2) stratified by block chi-squared = 2.7778, p-value = 0.1797 > > ## ...and the signed-rank test is equivalent to the Quade test > wilcoxsign_test(y ~ x | block, data = dta, distribution = "exact") Exact Wilcoxon-Pratt Signed-Rank Test data: y by x (pos, neg) stratified by block Z = 2.0732, p-value = 0.03906 alternative hypothesis: true mu is not equal to 0 > quade_test(y ~ x | block, data = dta, distribution = "exact") Exact Quade Test data: y by x (1, 2) stratified by block chi-squared = 4.2982, p-value = 0.03906 > > > ## Comparison of three methods ("round out", "narrow angle", and "wide angle") > ## for rounding first base. > ## Hollander and Wolfe (1999, p. 274, Tab. 7.1) > rounding <- data.frame( + times = c(5.40, 5.50, 5.55, + 5.85, 5.70, 5.75, + 5.20, 5.60, 5.50, + 5.55, 5.50, 5.40, + 5.90, 5.85, 5.70, + 5.45, 5.55, 5.60, + 5.40, 5.40, 5.35, + 5.45, 5.50, 5.35, + 5.25, 5.15, 5.00, + 5.85, 5.80, 5.70, + 5.25, 5.20, 5.10, + 5.65, 5.55, 5.45, + 5.60, 5.35, 5.45, + 5.05, 5.00, 4.95, + 5.50, 5.50, 5.40, + 5.45, 5.55, 5.50, + 5.55, 5.55, 5.35, + 5.45, 5.50, 5.55, + 5.50, 5.45, 5.25, + 5.65, 5.60, 5.40, + 5.70, 5.65, 5.55, + 6.30, 6.30, 6.25), + methods = factor(rep(1:3, 22), + labels = c("Round Out", "Narrow Angle", "Wide Angle")), + block = gl(22, 3) + ) > > ## Asymptotic Friedman test > friedman_test(times ~ methods | block, data = rounding) Asymptotic Friedman Test data: times by methods (Round Out, Narrow Angle, Wide Angle) stratified by block chi-squared = 11.143, df = 2, p-value = 0.003805 > > ## Parallel coordinates plot > with(rounding, { + matplot(t(matrix(times, ncol = 3, byrow = TRUE)), + type = "l", lty = 1, col = 1, ylab = "Time", xlim = c(0.5, 3.5), + axes = FALSE) + axis(1, at = 1:3, labels = levels(methods)) + axis(2) + }) > > ## Where do the differences come from? > ## Wilcoxon-Nemenyi-McDonald-Thompson test (Hollander and Wolfe, 1999, p. 295) > ## Note: all pairwise comparisons > (st <- symmetry_test(times ~ methods | block, data = rounding, + ytrafo = function(data) + trafo(data, numeric_trafo = rank_trafo, + block = rounding$block), + xtrafo = mcp_trafo(methods = "Tukey"))) Asymptotic General Symmetry Test data: times by methods (Round Out, Narrow Angle, Wide Angle) stratified by block maxT = 3.2404, p-value = 0.003456 alternative hypothesis: two.sided > > ## Simultaneous test of all pairwise comparisons > ## Wide Angle vs. Round Out differ (Hollander and Wolfe, 1999, p. 296) > pvalue(st, method = "single-step") # subset pivotality is violated Warning in .local(object, ...) : p-values may be incorrect due to violation of the subset pivotality condition Narrow Angle - Round Out 0.623934656 Wide Angle - Round Out 0.003358314 Wide Angle - Narrow Angle 0.053791966 > > > ## Strength Index of Cotton > ## Hollander and Wolfe (1999, p. 286, Tab. 7.5) > cotton <- data.frame( + strength = c(7.46, 7.17, 7.76, 8.14, 7.63, + 7.68, 7.57, 7.73, 8.15, 8.00, + 7.21, 7.80, 7.74, 7.87, 7.93), + potash = ordered(rep(c(144, 108, 72, 54, 36), 3), + levels = c(144, 108, 72, 54, 36)), + block = gl(3, 5) + ) > > ## One-sided asymptotic Page test > friedman_test(strength ~ potash | block, data = cotton, alternative = "greater") Asymptotic Page Test data: strength by potash (144 < 108 < 72 < 54 < 36) stratified by block Z = 2.6558, p-value = 0.003956 alternative hypothesis: greater > > ## One-sided approximative (Monte Carlo) Page test > friedman_test(strength ~ potash | block, data = cotton, alternative = "greater", + distribution = approximate(nresample = 10000)) Approximative Page Test data: strength by potash (144 < 108 < 72 < 54 < 36) stratified by block Z = 2.6558, p-value = 0.0027 alternative hypothesis: greater > > > ## Data from Quade (1979, p. 683) > dta <- data.frame( + y = c(52, 45, 38, + 63, 79, 50, + 45, 57, 39, + 53, 51, 43, + 47, 50, 56, + 62, 72, 49, + 49, 52, 40), + x = factor(rep(LETTERS[1:3], 7)), + b = factor(rep(1:7, each = 3)) + ) > > ## Approximative (Monte Carlo) Friedman test > ## Quade (1979, p. 683) > friedman_test(y ~ x | b, data = dta, + distribution = approximate(nresample = 10000)) # chi^2 = 6.000 Approximative Friedman Test data: y by x (A, B, C) stratified by b chi-squared = 6, p-value = 0.0502 > > ## Approximative (Monte Carlo) Quade test > ## Quade (1979, p. 683) > (qt <- quade_test(y ~ x | b, data = dta, + distribution = approximate(nresample = 10000))) # W = 8.157 Approximative Quade Test data: y by x (A, B, C) stratified by b chi-squared = 8.1571, p-value = 0.006 > > ## Comparison with R's quade.test() function > quade.test(y ~ x | b, data = dta) Quade test data: y and x and b Quade F = 8.3765, num df = 2, denom df = 12, p-value = 0.005284 > > ## quade.test() uses an F-statistic > b <- nlevels(qt@statistic@block) > A <- sum(qt@statistic@y^2) > B <- sum(statistic(qt, type = "linear")^2) / b > (b - 1) * B / (A - B) # F = 8.3765 [1] 8.376528 > > > > cleanEx() > nameEx("Transformations") > ### * Transformations > > flush(stderr()); flush(stdout()) > > ### Name: Transformations > ### Title: Functions for Data Transformation > ### Aliases: id_trafo rank_trafo normal_trafo median_trafo savage_trafo > ### consal_trafo koziol_trafo klotz_trafo mood_trafo ansari_trafo > ### fligner_trafo logrank_trafo logrank_weight maxstat_trafo > ### fmaxstat_trafo ofmaxstat_trafo f_trafo of_trafo zheng_trafo trafo > ### mcp_trafo > ### Keywords: manip > > ### ** Examples > > ## Dummy matrix, two-sample problem (only one column) > f_trafo(gl(2, 3)) 1 1 1 2 1 3 1 4 0 5 0 6 0 > > ## Dummy matrix, K-sample problem (K columns) > x <- gl(3, 2) > f_trafo(x) 1 2 3 1 1 0 0 2 1 0 0 3 0 1 0 4 0 1 0 5 0 0 1 6 0 0 1 attr(,"assign") [1] 1 1 1 attr(,"contrasts") attr(,"contrasts")$x [1] "contr.treatment" > > ## Score matrix > ox <- as.ordered(x) > of_trafo(ox) [,1] 1 1 2 1 3 2 4 2 5 3 6 3 > of_trafo(ox, scores = c(1, 3:4)) [,1] 1 1 2 1 3 3 4 3 5 4 6 4 > of_trafo(ox, scores = list(s1 = 1:3, s2 = c(1, 3:4))) s1 s2 1 1 1 2 1 1 3 2 3 4 2 3 5 3 4 6 3 4 > zheng_trafo(ox, increment = 1/3) gamma = (0.0000, 0.0000, 1.0000) gamma = (0.0000, 0.3333, 1.0000) 1 0 0.0000000 2 0 0.0000000 3 0 0.3333333 4 0 0.3333333 5 1 1.0000000 6 1 1.0000000 gamma = (0.0000, 0.6667, 1.0000) gamma = (0.0000, 1.0000, 1.0000) 1 0.0000000 0 2 0.0000000 0 3 0.6666667 1 4 0.6666667 1 5 1.0000000 1 6 1.0000000 1 > > ## Normal scores > y <- runif(6) > normal_trafo(y) [1] -0.5659488 -0.1800124 0.1800124 1.0675705 -1.0675705 0.5659488 > > ## All together now > trafo(data.frame(x = x, ox = ox, y = y), numeric_trafo = normal_trafo) x.1 x.2 x.3 ox y 1 1 0 0 1 -0.5659488 2 1 0 0 1 -0.1800124 3 0 1 0 2 0.1800124 4 0 1 0 2 1.0675705 5 0 0 1 3 -1.0675705 6 0 0 1 3 0.5659488 attr(,"assign") [1] 1 1 1 2 3 > > ## The same, but allows for fine-tuning > trafo(data.frame(x = x, ox = ox, y = y), var_trafo = list(y = normal_trafo)) x.1 x.2 x.3 ox y 1 1 0 0 1 -0.5659488 2 1 0 0 1 -0.1800124 3 0 1 0 2 0.1800124 4 0 1 0 2 1.0675705 5 0 0 1 3 -1.0675705 6 0 0 1 3 0.5659488 attr(,"assign") [1] 1 1 1 2 3 > > ## Transformations for maximally selected statistics > maxstat_trafo(y) x <= 0.202 x <= 0.266 x <= 0.372 x <= 0.573 x <= 0.898 1 0 1 1 1 1 2 0 0 1 1 1 3 0 0 0 1 1 4 0 0 0 0 0 5 1 1 1 1 1 6 0 0 0 0 1 > fmaxstat_trafo(x) {1} vs. {2, 3} {1, 2} vs. {3} {1, 3} vs. {2} 1 1 1 1 2 1 1 1 3 0 1 0 4 0 1 0 5 0 0 1 6 0 0 1 > ofmaxstat_trafo(ox) {1} vs. {2, 3} {1, 2} vs. {3} 1 1 1 2 1 1 3 0 1 4 0 1 5 0 0 6 0 0 > > ## Apply transformation blockwise (as in the Friedman test) > trafo(data.frame(y = 1:20), numeric_trafo = rank_trafo, block = gl(4, 5)) [1,] 1 [2,] 2 [3,] 3 [4,] 4 [5,] 5 [6,] 1 [7,] 2 [8,] 3 [9,] 4 [10,] 5 [11,] 1 [12,] 2 [13,] 3 [14,] 4 [15,] 5 [16,] 1 [17,] 2 [18,] 3 [19,] 4 [20,] 5 attr(,"assign") [1] 1 > > ## Multiple comparisons > dta <- data.frame(x) > mcp_trafo(x = "Tukey")(dta) 2 - 1 3 - 1 3 - 2 1 -1 -1 0 2 -1 -1 0 3 1 0 -1 4 1 0 -1 5 0 1 1 6 0 1 1 attr(,"assign") [1] 1 1 1 attr(,"contrast") Multiple Comparisons of Means: Tukey Contrasts 1 2 3 2 - 1 -1 1 0 3 - 1 -1 0 1 3 - 2 0 -1 1 > > ## The same, but useful when specific contrasts are desired > K <- rbind("2 - 1" = c(-1, 1, 0), + "3 - 1" = c(-1, 0, 1), + "3 - 2" = c( 0, -1, 1)) > mcp_trafo(x = K)(dta) 2 - 1 3 - 1 3 - 2 1 -1 -1 0 2 -1 -1 0 3 1 0 -1 4 1 0 -1 5 0 1 1 6 0 1 1 attr(,"assign") [1] 1 1 1 attr(,"contrast") Multiple Comparisons of Means: User-defined Contrasts 1 2 3 2 - 1 -1 1 0 3 - 1 -1 0 1 3 - 2 0 -1 1 > > > > cleanEx() > nameEx("alpha") > ### * alpha > > flush(stderr()); flush(stdout()) > > ### Name: alpha > ### Title: Genetic Components of Alcoholism > ### Aliases: alpha > ### Keywords: datasets > > ### ** Examples > > ## Boxplots > boxplot(elevel ~ alength, data = alpha) > > ## Asymptotic Kruskal-Wallis test > kruskal_test(elevel ~ alength, data = alpha) Asymptotic Kruskal-Wallis Test data: elevel by alength (short, intermediate, long) chi-squared = 8.8302, df = 2, p-value = 0.01209 > > ## Asymptotic Kruskal-Wallis test using midpoint scores > kruskal_test(elevel ~ alength, data = alpha, + scores = list(alength = c(2, 7, 11))) Asymptotic Linear-by-Linear Association Test data: elevel by alength (short < intermediate < long) Z = 2.9263, p-value = 0.00343 alternative hypothesis: two.sided > > ## Asymptotic score-independent test > ## Winell and Lindbaeck (2018) > (it <- independence_test(elevel ~ alength, data = alpha, + ytrafo = function(data) + trafo(data, numeric_trafo = rank_trafo), + xtrafo = function(data) + trafo(data, factor_trafo = function(x) + zheng_trafo(as.ordered(x))))) Asymptotic General Independence Test data: elevel by alength (short, intermediate, long) maxT = 2.9651, p-value = 0.008184 alternative hypothesis: two.sided > > ## Extract the "best" set of scores > ss <- statistic(it, type = "standardized") > idx <- which(abs(ss) == max(abs(ss)), arr.ind = TRUE) > ss[idx[1], idx[2], drop = FALSE] gamma = (0.0, 0.4, 1.0) 2.96508 > > > > cleanEx() > nameEx("alzheimer") > ### * alzheimer > > flush(stderr()); flush(stdout()) > > ### Name: alzheimer > ### Title: Smoking and Alzheimer's Disease > ### Aliases: alzheimer > ### Keywords: datasets > > ### ** Examples > > ## Spineplots > op <- par(no.readonly = TRUE) # save current settings > layout(matrix(1:2, ncol = 2)) > spineplot(disease ~ smoking, data = alzheimer, + subset = gender == "Male", main = "Male") > spineplot(disease ~ smoking, data = alzheimer, + subset = gender == "Female", main = "Female") > par(op) # reset > > ## Asymptotic Cochran-Mantel-Haenszel test > cmh_test(disease ~ smoking | gender, data = alzheimer) Asymptotic Generalized Cochran-Mantel-Haenszel Test data: disease by smoking (None, <10, 10-20, >20) stratified by gender chi-squared = 23.316, df = 6, p-value = 0.0006972 > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("asat") > ### * asat > > flush(stderr()); flush(stdout()) > > ### Name: asat > ### Title: Toxicological Study on Female Wistar Rats > ### Aliases: asat > ### Keywords: datasets > > ### ** Examples > > ## Proof-of-safety based on ratio of medians (Pflueger and Hothorn, 2002) > ## One-sided exact Wilcoxon-Mann-Whitney test > wt <- wilcox_test(I(log(asat)) ~ group, data = asat, + distribution = "exact", alternative = "less", + conf.int = TRUE) > > ## One-sided confidence set > ## Note: Safety cannot be concluded since the effect of the compound > ## exceeds 20 % of the control median > exp(confint(wt)$conf.int) [1] 0.000000 1.337778 attr(,"conf.level") [1] 0.95 > > > > cleanEx() > nameEx("coin-package") > ### * coin-package > > flush(stderr()); flush(stdout()) > > ### Name: coin-package > ### Title: General Information on the 'coin' Package > ### Aliases: coin-package coin > ### Keywords: package > > ### ** Examples > > ## Not run: > ##D ## Generate doxygen documentation if you are interested in the internals: > ##D ## Download source package into a temporary directory > ##D tmpdir <- tempdir() > ##D tgz <- download.packages("coin", destdir = tmpdir, type = "source")[2] > ##D ## Extract contents > ##D untar(tgz, exdir = tmpdir) > ##D ## Run doxygen (assuming it is installed) > ##D wd <- setwd(file.path(tmpdir, "coin")) > ##D system("doxygen inst/doxygen.cfg") > ##D setwd(wd) > ##D ## Have fun! > ##D browseURL(file.path(tmpdir, "coin", "inst", > ##D "documentation", "html", "index.html")) > ## End(Not run) > > > > cleanEx() > nameEx("expectation-methods") > ### * expectation-methods > > flush(stderr()); flush(stdout()) > > ### Name: expectation-methods > ### Title: Extraction of the Expectation, Variance and Covariance of the > ### Linear Statistic > ### Aliases: expectation expectation-methods > ### expectation,IndependenceLinearStatistic-method > ### expectation,IndependenceTest-method variance variance-methods > ### variance,Variance-method variance,CovarianceMatrix-method > ### variance,IndependenceLinearStatistic-method > ### variance,IndependenceTest-method covariance covariance-methods > ### covariance,CovarianceMatrix-method > ### covariance,IndependenceLinearStatistic-method > ### covariance,QuadTypeIndependenceTestStatistic-method > ### covariance,IndependenceTest-method > ### Keywords: methods > > ### ** Examples > ## Don't show: > suppressWarnings(RNGversion("3.5.2")); set.seed(711109) > ## End(Don't show) > ## Example data > dta <- data.frame( + y = gl(3, 2), + x = sample(gl(3, 2)) + ) > > ## Asymptotic Cochran-Mantel-Haenszel Test > ct <- cmh_test(y ~ x, data = dta) > > ## The linear statistic, i.e., the contingency table... > (T <- statistic(ct, type = "linear")) 1 2 3 1 1 0 1 2 0 2 0 3 1 0 1 > > ## ...and its expectation... > (mu <- expectation(ct)) 1 2 3 1 0.6666667 0.6666667 0.6666667 2 0.6666667 0.6666667 0.6666667 3 0.6666667 0.6666667 0.6666667 > > ## ...and variance... > (sigma <- variance(ct)) 1 2 3 1 0.3555556 0.3555556 0.3555556 2 0.3555556 0.3555556 0.3555556 3 0.3555556 0.3555556 0.3555556 > > ## ...and covariance... > (Sigma <- covariance(ct)) 1:1 2:1 3:1 1:2 2:2 3:2 1:1 0.35555556 -0.17777778 -0.17777778 -0.17777778 0.08888889 0.08888889 2:1 -0.17777778 0.35555556 -0.17777778 0.08888889 -0.17777778 0.08888889 3:1 -0.17777778 -0.17777778 0.35555556 0.08888889 0.08888889 -0.17777778 1:2 -0.17777778 0.08888889 0.08888889 0.35555556 -0.17777778 -0.17777778 2:2 0.08888889 -0.17777778 0.08888889 -0.17777778 0.35555556 -0.17777778 3:2 0.08888889 0.08888889 -0.17777778 -0.17777778 -0.17777778 0.35555556 1:3 -0.17777778 0.08888889 0.08888889 -0.17777778 0.08888889 0.08888889 2:3 0.08888889 -0.17777778 0.08888889 0.08888889 -0.17777778 0.08888889 3:3 0.08888889 0.08888889 -0.17777778 0.08888889 0.08888889 -0.17777778 1:3 2:3 3:3 1:1 -0.17777778 0.08888889 0.08888889 2:1 0.08888889 -0.17777778 0.08888889 3:1 0.08888889 0.08888889 -0.17777778 1:2 -0.17777778 0.08888889 0.08888889 2:2 0.08888889 -0.17777778 0.08888889 3:2 0.08888889 0.08888889 -0.17777778 1:3 0.35555556 -0.17777778 -0.17777778 2:3 -0.17777778 0.35555556 -0.17777778 3:3 -0.17777778 -0.17777778 0.35555556 > > ## ...and its inverse > (SigmaPlus <- covariance(ct, invert = TRUE)) 1:1 2:1 3:1 1:2 2:2 3:2 1:1 0.5555556 -0.2777778 -0.2777778 -0.2777778 0.1388889 0.1388889 2:1 -0.2777778 0.5555556 -0.2777778 0.1388889 -0.2777778 0.1388889 3:1 -0.2777778 -0.2777778 0.5555556 0.1388889 0.1388889 -0.2777778 1:2 -0.2777778 0.1388889 0.1388889 0.5555556 -0.2777778 -0.2777778 2:2 0.1388889 -0.2777778 0.1388889 -0.2777778 0.5555556 -0.2777778 3:2 0.1388889 0.1388889 -0.2777778 -0.2777778 -0.2777778 0.5555556 1:3 -0.2777778 0.1388889 0.1388889 -0.2777778 0.1388889 0.1388889 2:3 0.1388889 -0.2777778 0.1388889 0.1388889 -0.2777778 0.1388889 3:3 0.1388889 0.1388889 -0.2777778 0.1388889 0.1388889 -0.2777778 1:3 2:3 3:3 1:1 -0.2777778 0.1388889 0.1388889 2:1 0.1388889 -0.2777778 0.1388889 3:1 0.1388889 0.1388889 -0.2777778 1:2 -0.2777778 0.1388889 0.1388889 2:2 0.1388889 -0.2777778 0.1388889 3:2 0.1388889 0.1388889 -0.2777778 1:3 0.5555556 -0.2777778 -0.2777778 2:3 -0.2777778 0.5555556 -0.2777778 3:3 -0.2777778 -0.2777778 0.5555556 > > ## The standardized contingency table... > (T - mu) / sqrt(sigma) 1 2 3 1 0.559017 -1.118034 0.559017 2 -1.118034 2.236068 -1.118034 3 0.559017 -1.118034 0.559017 > > ## ...is identical to the standardized linear statistic > statistic(ct, type = "standardized") 1 2 3 1 0.559017 -1.118034 0.559017 2 -1.118034 2.236068 -1.118034 3 0.559017 -1.118034 0.559017 > > ## The quadratic form... > U <- as.vector(T - mu) > U %*% SigmaPlus %*% U [,1] [1,] 5 > > ## ...is identical to the test statistic > statistic(ct, type = "test") [1] 5 > > > > cleanEx() > nameEx("glioma") > ### * glioma > > flush(stderr()); flush(stdout()) > > ### Name: glioma > ### Title: Malignant Glioma Pilot Study > ### Aliases: glioma > ### Keywords: datasets > > ### ** Examples > > ## Grade III glioma > g3 <- subset(glioma, histology == "Grade3") > > ## Plot Kaplan-Meier estimates > op <- par(no.readonly = TRUE) # save current settings > layout(matrix(1:2, ncol = 2)) > plot(survfit(Surv(time, event) ~ group, data = g3), + main = "Grade III Glioma", lty = 2:1, + ylab = "Probability", xlab = "Survival Time in Month", + xlim = c(-2, 72)) > legend("bottomleft", lty = 2:1, c("Control", "Treated"), bty = "n") > > ## Exact logrank test > logrank_test(Surv(time, event) ~ group, data = g3, + distribution = "exact") Exact Two-Sample Logrank Test data: Surv(time, event) by group (Control, RIT) Z = -2.1711, p-value = 0.02877 alternative hypothesis: true theta is not equal to 1 > > > ## Grade IV glioma > gbm <- subset(glioma, histology == "GBM") > > ## Plot Kaplan-Meier estimates > plot(survfit(Surv(time, event) ~ group, data = gbm), + main = "Grade IV Glioma", lty = 2:1, + ylab = "Probability", xlab = "Survival Time in Month", + xlim = c(-2, 72)) > legend("topright", lty = 2:1, c("Control", "Treated"), bty = "n") > par(op) # reset > > ## Exact logrank test > logrank_test(Surv(time, event) ~ group, data = gbm, + distribution = "exact") Exact Two-Sample Logrank Test data: Surv(time, event) by group (Control, RIT) Z = -3.2215, p-value = 0.0001588 alternative hypothesis: true theta is not equal to 1 > > > ## Stratified approximative (Monte Carlo) logrank test > logrank_test(Surv(time, event) ~ group | histology, data = glioma, + distribution = approximate(nresample = 10000)) Approximative Two-Sample Logrank Test data: Surv(time, event) by group (Control, RIT) stratified by histology Z = -3.6704, p-value < 1e-04 alternative hypothesis: true theta is not equal to 1 > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("hohnloser") > ### * hohnloser > > flush(stderr()); flush(stdout()) > > ### Name: hohnloser > ### Title: Left Ventricular Ejection Fraction > ### Aliases: hohnloser > ### Keywords: datasets > > ### ** Examples > > ## Asymptotic maximally selected logrank statistics > maxstat_test(Surv(time, event) ~ EF, data = hohnloser) Asymptotic Generalized Maximally Selected Statistics data: Surv(time, event) by EF maxT = 3.5647, p-value = 0.004554 alternative hypothesis: two.sided sample estimates: "best" cutpoint: <= 39 > > > > cleanEx() > nameEx("jobsatisfaction") > ### * jobsatisfaction > > flush(stderr()); flush(stdout()) > > ### Name: jobsatisfaction > ### Title: Income and Job Satisfaction > ### Aliases: jobsatisfaction > ### Keywords: datasets > > ### ** Examples > > ## Approximative (Monte Carlo) linear-by-linear association test > lbl_test(jobsatisfaction, distribution = approximate(nresample = 10000)) Approximative Linear-by-Linear Association Test data: Job.Satisfaction (ordered) by Income (<5000 < 5000-15000 < 15000-25000 < >25000) stratified by Gender Z = 2.5736, p-value = 0.0104 alternative hypothesis: two.sided > > ## Not run: > ##D ## Approximative (Monte Carlo) score-independent test > ##D ## Winell and Lindbaeck (2018) > ##D (it <- independence_test(jobsatisfaction, > ##D distribution = approximate(nresample = 10000), > ##D xtrafo = function(data) > ##D trafo(data, factor_trafo = function(x) > ##D zheng_trafo(as.ordered(x))), > ##D ytrafo = function(data) > ##D trafo(data, factor_trafo = function(y) > ##D zheng_trafo(as.ordered(y))))) > ##D > ##D ## Extract the "best" set of scores > ##D ss <- statistic(it, type = "standardized") > ##D idx <- which(abs(ss) == max(abs(ss)), arr.ind = TRUE) > ##D ss[idx[1], idx[2], drop = FALSE] > ## End(Not run) > > > > cleanEx() > nameEx("malformations") > ### * malformations > > flush(stderr()); flush(stdout()) > > ### Name: malformations > ### Title: Maternal Drinking and Congenital Sex Organ Malformation > ### Aliases: malformations > ### Keywords: datasets > > ### ** Examples > > ## Graubard and Korn (1987, Tab. 3) > > ## One-sided approximative (Monte Carlo) Cochran-Armitage test > ## Note: midpoint scores (p < 0.05) > midpoints <- c(0, 0.5, 1.5, 4.0, 7.0) > chisq_test(malformation ~ consumption, data = malformations, + distribution = approximate(nresample = 1000), + alternative = "greater", + scores = list(consumption = midpoints)) Approximative Linear-by-Linear Association Test data: malformation by consumption (0 < <1 < 1-2 < 3-5 < >=6) Z = 2.5632, p-value = 0.017 alternative hypothesis: greater > > ## One-sided approximative (Monte Carlo) Cochran-Armitage test > ## Note: midrank scores (p > 0.05) > midranks <- c(8557.5, 24375.5, 32013.0, 32473.0, 32555.5) > chisq_test(malformation ~ consumption, data = malformations, + distribution = approximate(nresample = 1000), + alternative = "greater", + scores = list(consumption = midranks)) Approximative Linear-by-Linear Association Test data: malformation by consumption (0 < <1 < 1-2 < 3-5 < >=6) Z = 0.59208, p-value = 0.269 alternative hypothesis: greater > > ## One-sided approximative (Monte Carlo) Cochran-Armitage test > ## Note: equally spaced scores (p > 0.05) > chisq_test(malformation ~ consumption, data = malformations, + distribution = approximate(nresample = 1000), + alternative = "greater") Approximative Linear-by-Linear Association Test data: malformation by consumption (0 < <1 < 1-2 < 3-5 < >=6) Z = 1.352, p-value = 0.117 alternative hypothesis: greater > > ## Not run: > ##D ## One-sided approximative (Monte Carlo) score-independent test > ##D ## Winell and Lindbaeck (2018) > ##D (it <- independence_test(malformation ~ consumption, data = malformations, > ##D distribution = approximate(nresample = 1000, > ##D parallel = "snow", > ##D ncpus = 8), > ##D alternative = "greater", > ##D xtrafo = function(data) > ##D trafo(data, ordered_trafo = zheng_trafo))) > ##D > ##D ## Extract the "best" set of scores > ##D ss <- statistic(it, type = "standardized") > ##D idx <- which(ss == max(ss), arr.ind = TRUE) > ##D ss[idx[1], idx[2], drop = FALSE] > ## End(Not run) > > > > cleanEx() > nameEx("mercuryfish") > ### * mercuryfish > > flush(stderr()); flush(stdout()) > > ### Name: mercuryfish > ### Title: Chromosomal Effects of Mercury-Contaminated Fish Consumption > ### Aliases: mercuryfish > ### Keywords: datasets > > ### ** Examples > > ## Coherence criterion > coherence <- function(data) { + x <- as.matrix(data) + matrix(apply(x, 1, function(y) + sum(colSums(t(x) < y) == ncol(x)) - + sum(colSums(t(x) > y) == ncol(x))), ncol = 1) + } > > ## Asymptotic POSET test > poset <- independence_test(mercury + abnormal + ccells ~ group, + data = mercuryfish, ytrafo = coherence) > > ## Linear statistic (T in the notation of Rosenbaum, 1994) > statistic(poset, type = "linear") control -237 > > ## Expectation > expectation(poset) control 0 > > ## Variance > ## Note: typo in Rosenbaum (1994, p. 371, Sec. 2, last paragraph) > variance(poset) control 3097.954 > > ## Standardized statistic > statistic(poset) [1] -4.258051 > > ## P-value > pvalue(poset) [1] 2.062169e-05 > > ## Exact POSET test > independence_test(mercury + abnormal + ccells ~ group, + data = mercuryfish, ytrafo = coherence, + distribution = "exact") Exact General Independence Test data: mercury, abnormal, ccells by group (control, exposed) Z = -4.2581, p-value = 4.486e-06 alternative hypothesis: two.sided > > ## Asymptotic multivariate test > mvtest <- independence_test(mercury + abnormal + ccells ~ group, + data = mercuryfish) > > ## Global p-value > pvalue(mvtest) [1] 0.007140628 99 percent confidence interval: 0.006371664 0.007909593 > > ## Single-step adjusted p-values > pvalue(mvtest, method = "single-step") mercury abnormal ccells control 0.007991569 0.01726738 0.03830126 > > ## Step-down adjusted p-values > pvalue(mvtest, method = "step-down") mercury abnormal ccells control 0.007187993 0.0111254 0.0152947 > > > > cleanEx() > nameEx("neuropathy") > ### * neuropathy > > flush(stderr()); flush(stdout()) > > ### Name: neuropathy > ### Title: Acute Painful Diabetic Neuropathy > ### Aliases: neuropathy > ### Keywords: datasets > > ### ** Examples > > ## Conover and Salsburg (1988, Tab. 2) > > ## One-sided approximative Fisher-Pitman test > oneway_test(pain ~ group, data = neuropathy, + alternative = "less", + distribution = approximate(nresample = 10000)) Approximative Two-Sample Fisher-Pitman Permutation Test data: pain by group (control, treat) Z = -1.3191, p-value = 0.09 alternative hypothesis: true mu is less than 0 > > ## One-sided approximative Wilcoxon-Mann-Whitney test > wilcox_test(pain ~ group, data = neuropathy, + alternative = "less", + distribution = approximate(nresample = 10000)) Approximative Wilcoxon-Mann-Whitney Test data: pain by group (control, treat) Z = -0.98169, p-value = 0.1661 alternative hypothesis: true mu is less than 0 > > ## One-sided approximative Conover-Salsburg test > oneway_test(pain ~ group, data = neuropathy, + alternative = "less", + distribution = approximate(nresample = 10000), + ytrafo = function(data) + trafo(data, numeric_trafo = consal_trafo)) Approximative Two-Sample Fisher-Pitman Permutation Test data: pain by group (control, treat) Z = -1.8683, p-value = 0.0334 alternative hypothesis: true mu is less than 0 > > ## One-sided approximative maximum test for a range of 'a' values > it <- independence_test(pain ~ group, data = neuropathy, + alternative = "less", + distribution = approximate(nresample = 10000), + ytrafo = function(data) + trafo(data, numeric_trafo = function(y) + consal_trafo(y, a = 2:7))) > pvalue(it, method = "single-step") a = 2 a = 3 a = 4 a = 5 a = 6 a = 7 control 0.2377 0.0994 0.062 0.0511 0.0483 0.0492 > > > > cleanEx() > nameEx("ocarcinoma") > ### * ocarcinoma > > flush(stderr()); flush(stdout()) > > ### Name: ocarcinoma > ### Title: Ovarian Carcinoma > ### Aliases: ocarcinoma > ### Keywords: datasets > > ### ** Examples > > ## Exact logrank test > lt <- logrank_test(Surv(time, event) ~ stadium, data = ocarcinoma, + distribution = "exact") > > ## Test statistic > statistic(lt) [1] 2.337284 > > ## P-value > pvalue(lt) [1] 0.01819758 > > > > cleanEx() > nameEx("photocar") > ### * photocar > > flush(stderr()); flush(stdout()) > > ### Name: photocar > ### Title: Multiple Dosing Photococarcinogenicity Experiment > ### Aliases: photocar > ### Keywords: datasets > > ### ** Examples > > ## Plotting data > op <- par(no.readonly = TRUE) # save current settings > layout(matrix(1:3, ncol = 3)) > with(photocar, { + plot(survfit(Surv(time, event) ~ group), + lty = 1:3, xmax = 50, main = "Survival Time") + legend("bottomleft", lty = 1:3, levels(group), bty = "n") + plot(survfit(Surv(dmin, tumor) ~ group), + lty = 1:3, xmax = 50, main = "Time to First Tumor") + legend("bottomleft", lty = 1:3, levels(group), bty = "n") + boxplot(ntumor ~ group, main = "Number of Tumors") + }) > par(op) # reset > > ## Approximative multivariate (all three responses) test > it <- independence_test(Surv(time, event) + Surv(dmin, tumor) + ntumor ~ group, + data = photocar, + distribution = approximate(nresample = 10000)) > > ## Global p-value > pvalue(it) [1] <1e-04 99 percent confidence interval: 0.0000000000 0.0005296914 > > ## Why was the global null hypothesis rejected? > statistic(it, type = "standardized") Surv(time, event) Surv(dmin, tumor) ntumor A 2.327338 2.178704 0.2642120 B 4.750336 4.106039 0.1509783 C -7.077674 -6.284743 -0.4151904 > pvalue(it, method = "single-step") Surv(time, event) Surv(dmin, tumor) ntumor A 0.129 0.1850 1.000 B <0.001 0.0003 1.000 C <0.001 <0.0001 0.999 > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("pvalue-methods") > ### * pvalue-methods > > flush(stderr()); flush(stdout()) > > ### Name: pvalue-methods > ### Title: Computation of the p-Value, Mid-p-Value, p-Value Interval and > ### Test Size > ### Aliases: pvalue pvalue-methods pvalue,PValue-method > ### pvalue,NullDistribution-method pvalue,ApproxNullDistribution-method > ### pvalue,IndependenceTest-method pvalue,MaxTypeIndependenceTest-method > ### midpvalue midpvalue-methods midpvalue,NullDistribution-method > ### midpvalue,ApproxNullDistribution-method > ### midpvalue,IndependenceTest-method pvalue_interval > ### pvalue_interval-methods pvalue_interval,NullDistribution-method > ### pvalue_interval,IndependenceTest-method size size-methods > ### size,NullDistribution-method size,IndependenceTest-method > ### Keywords: methods htest > > ### ** Examples > > ## Two-sample problem > dta <- data.frame( + y = rnorm(20), + x = gl(2, 10) + ) > > ## Exact Ansari-Bradley test > (at <- ansari_test(y ~ x, data = dta, distribution = "exact")) Exact Two-Sample Ansari-Bradley Test data: y by x (1, 2) Z = 0.45527, p-value = 0.7102 alternative hypothesis: true ratio of scales is not equal to 1 > pvalue(at) [1] 0.710234 > midpvalue(at) [1] 0.6564821 > pvalue_interval(at) p_0 p_1 0.6027301 0.7102340 > size(at, alpha = 0.05) [1] 0.03830999 > size(at, alpha = 0.05, type = "mid-p-value") [1] 0.05633376 > > > ## Bivariate two-sample problem > dta2 <- data.frame( + y1 = rnorm(20) + rep(0:1, each = 10), + y2 = rnorm(20), + x = gl(2, 10) + ) > > ## Approximative (Monte Carlo) bivariate Fisher-Pitman test > (it <- independence_test(y1 + y2 ~ x, data = dta2, + distribution = approximate(nresample = 10000))) Approximative General Independence Test data: y1, y2 by x (1, 2) maxT = 2.6084, p-value = 0.011 alternative hypothesis: two.sided > > ## Global p-value > pvalue(it) [1] 0.011 99 percent confidence interval: 0.008496613 0.013980169 > > ## Joint distribution single-step p-values > pvalue(it, method = "single-step") y1 y2 1 0.011 0.9998 > > ## Joint distribution step-down p-values > pvalue(it, method = "step-down") y1 y2 1 0.011 0.979 > > ## Sidak step-down p-values > pvalue(it, method = "step-down", distribution = "marginal", type = "Sidak") y1 y2 1 0.0110692 0.979 > > ## Unadjusted p-values > pvalue(it, method = "unadjusted") y1 y2 1 0.0055 0.979 > > > ## Length of YOY Gizzard Shad (Hollander and Wolfe, 1999, p. 200, Tab. 6.3) > yoy <- data.frame( + length = c(46, 28, 46, 37, 32, 41, 42, 45, 38, 44, + 42, 60, 32, 42, 45, 58, 27, 51, 42, 52, + 38, 33, 26, 25, 28, 28, 26, 27, 27, 27, + 31, 30, 27, 29, 30, 25, 25, 24, 27, 30), + site = gl(4, 10, labels = as.roman(1:4)) + ) > > ## Approximative (Monte Carlo) Fisher-Pitman test with contrasts > ## Note: all pairwise comparisons > (it <- independence_test(length ~ site, data = yoy, + distribution = approximate(nresample = 10000), + xtrafo = mcp_trafo(site = "Tukey"))) Approximative General Independence Test data: length by site (I, II, III, IV) maxT = 3.953, p-value = 1e-04 alternative hypothesis: two.sided > > ## Joint distribution step-down p-values > pvalue(it, method = "step-down") # subset pivotality is violated Warning in .local(object, ...) : p-values may be incorrect due to violation of the subset pivotality condition II - I 0.4284 III - I 0.0213 IV - I 0.0148 III - II 0.0002 IV - II 0.0001 IV - III 0.8817 > > > > cleanEx() > nameEx("rotarod") > ### * rotarod > > flush(stderr()); flush(stdout()) > > ### Name: rotarod > ### Title: Rotating Rats > ### Aliases: rotarod > ### Keywords: datasets > > ### ** Examples > > ## One-sided exact Wilcoxon-Mann-Whitney test (p = 0.0186) > wilcox_test(time ~ group, data = rotarod, distribution = "exact", + alternative = "greater") Exact Wilcoxon-Mann-Whitney Test data: time by group (control, treatment) Z = 2.4389, p-value = 0.01863 alternative hypothesis: true mu is greater than 0 > > ## Two-sided exact Wilcoxon-Mann-Whitney test (p = 0.0373) > wilcox_test(time ~ group, data = rotarod, distribution = "exact") Exact Wilcoxon-Mann-Whitney Test data: time by group (control, treatment) Z = 2.4389, p-value = 0.03727 alternative hypothesis: true mu is not equal to 0 > > ## Two-sided asymptotic Wilcoxon-Mann-Whitney test (p = 0.0147) > wilcox_test(time ~ group, data = rotarod) Asymptotic Wilcoxon-Mann-Whitney Test data: time by group (control, treatment) Z = 2.4389, p-value = 0.01473 alternative hypothesis: true mu is not equal to 0 > > > > cleanEx() > nameEx("statistic-methods") > ### * statistic-methods > > flush(stderr()); flush(stdout()) > > ### Name: statistic-methods > ### Title: Extraction of the Test Statistic and the Linear Statistic > ### Aliases: statistic statistic-methods > ### statistic,IndependenceLinearStatistic-method > ### statistic,IndependenceTestStatistic-method > ### statistic,IndependenceTest-method > ### Keywords: methods > > ### ** Examples > > ## Example data > dta <- data.frame( + y = gl(4, 5), + x = gl(5, 4) + ) > > ## Asymptotic Cochran-Mantel-Haenszel Test > ct <- cmh_test(y ~ x, data = dta) > > ## Test statistic > statistic(ct) [1] 38 > > ## The unstandardized linear statistic... > statistic(ct, type = "linear") 1 2 3 4 1 4 0 0 0 2 1 3 0 0 3 0 2 2 0 4 0 0 3 1 5 0 0 0 4 > > ## ...is identical to the contingency table > xtabs(~ x + y, data = dta) y x 1 2 3 4 1 4 0 0 0 2 1 3 0 0 3 0 2 2 0 4 0 0 3 1 5 0 0 0 4 > > ## The centered linear statistic... > statistic(ct, type = "centered") 1 2 3 4 1 3 -1 -1 -1 2 0 2 -1 -1 3 -1 1 1 -1 4 -1 -1 2 0 5 -1 -1 -1 3 > > ## ...is identical to > statistic(ct, type = "linear") - expectation(ct) 1 2 3 4 1 3 -1 -1 -1 2 0 2 -1 -1 3 -1 1 1 -1 4 -1 -1 2 0 5 -1 -1 -1 3 > > ## The standardized linear statistic, illustrating departures from the null > ## hypothesis of independence... > statistic(ct, type = "standardized") 1 2 3 4 1 3.774917 -1.258306 -1.258306 -1.258306 2 0.000000 2.516611 -1.258306 -1.258306 3 -1.258306 1.258306 1.258306 -1.258306 4 -1.258306 -1.258306 2.516611 0.000000 5 -1.258306 -1.258306 -1.258306 3.774917 > > ## ...is identical to > (statistic(ct, type = "linear") - expectation(ct)) / sqrt(variance(ct)) 1 2 3 4 1 3.774917 -1.258306 -1.258306 -1.258306 2 0.000000 2.516611 -1.258306 -1.258306 3 -1.258306 1.258306 1.258306 -1.258306 4 -1.258306 -1.258306 2.516611 0.000000 5 -1.258306 -1.258306 -1.258306 3.774917 > > > > cleanEx() > nameEx("treepipit") > ### * treepipit > > flush(stderr()); flush(stdout()) > > ### Name: treepipit > ### Title: Tree Pipits in Franconian Oak Forests > ### Aliases: treepipit > ### Keywords: datasets > > ### ** Examples > > ## Asymptotic maximally selected statistics > maxstat_test(counts ~ age + coverstorey + coverregen + meanregen + + coniferous + deadtree + cbpiles + ivytree, + data = treepipit) Asymptotic Generalized Maximally Selected Statistics data: counts by age, coverstorey, coverregen, meanregen, coniferous, deadtree, cbpiles, ivytree maxT = 4.3139, p-value = 0.0006596 alternative hypothesis: two.sided sample estimates: "best" cutpoint: <= 40 covariable: coverstorey > > > > cleanEx() > nameEx("vision") > ### * vision > > flush(stderr()); flush(stdout()) > > ### Name: vision > ### Title: Unaided Distance Vision > ### Aliases: vision > ### Keywords: datasets > > ### ** Examples > > ## Asymptotic Stuart test (Q = 11.96) > diag(vision) <- 0 # speed-up > mh_test(vision) Asymptotic Marginal Homogeneity Test data: response by conditions (Right.Eye, Left.Eye) stratified by block chi-squared = 11.957, df = 3, p-value = 0.007533 > > ## Asymptotic score-independent test > ## Winell and Lindbaeck (2018) > (st <- symmetry_test(vision, + ytrafo = function(data) + trafo(data, factor_trafo = function(y) + zheng_trafo(as.ordered(y))))) Asymptotic General Symmetry Test data: response by conditions (Right.Eye, Left.Eye) stratified by block maxT = 3.4484, p-value = 0.003294 alternative hypothesis: two.sided > ss <- statistic(st, type = "standardized") > idx <- which(abs(ss) == max(abs(ss)), arr.ind = TRUE) > ss[idx[1], idx[2], drop = FALSE] eta = (0.0, 0.3, 0.7, 1.0) Right.Eye -3.448397 > > > > ### *