coin/0000755000176200001440000000000013531465157011214 5ustar liggesuserscoin/NAMESPACE0000644000176200001440000001201513436244173012427 0ustar liggesusersuseDynLib(coin, .registration = TRUE) importFrom("survival", is.Surv) importFrom("methods", callGeneric, callNextMethod, getSlots, new, validObject) importMethodsFrom("methods", initialize, show) importFrom("parallel", clusterApply, clusterSetRNGStream, 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.Rd0000644000176200001440000004675713401471036015124 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{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", "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{"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 Prentice test, the Prentice-Marek test, the Andersen-Borgan-Gill-Keiding test, the Fleming-Harrington 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 Prentice test (\code{"Prentice"}) is another 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 \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 and \deqn{ \hat{S}_k = \prod_{j = 0}^{k - 1} \frac{n_j - d_j}{n_j}, \quad \hat{S}_0 \equiv 1 }{ Shat_k = prod(j = 0, \dots, k - 1) (n_j - d_j) / n_j, Shat_0 := 1 } is the \emph{left-continuous} Kaplan-Meier estimator of the survival function; \eqn{\rho = 0} and \eqn{\gamma = 0} lead to the standard logrank 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. 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) := 1 } 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. 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.Rd0000644000176200001440000000727612557641056021002 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, varonly = FALSE, \dots)} where \code{object} is an object of class \code{"\linkS4class{IndependenceTestProblem}"}, \code{varonly} is a logical indicating that slot \code{covariance} (see \sQuote{Slots}) should only contain the diagonal elements of the covariance matrix. } \section{Slots}{ \describe{ \item{\code{linearstatistic}:}{ Object of class \code{"numeric"}. The linear statistic. } \item{\code{expectation}:}{ Object of class \code{"numeric"}. The expectation of the linear statistic. } \item{\code{covariance}:}{ Object of class \code{"\linkS4class{VarCovar}"}. The covariance or variance of the linear statistic. } \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.Rd0000644000176200001440000002137513401471036020757 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 binary factor response and a univariable ordered 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.Rd0000644000176200001440000000520513401471036015073 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. } } } \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.Rd0000644000176200001440000001177513401471036016673 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.Rd0000644000176200001440000000476513401471036015727 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 Linear Statistic} \description{ Methods for extraction of the test statistic and linear statistic. } \usage{ \S4method{statistic}{IndependenceLinearStatistic}(object, type = c("test", "linear", "centered", "standardized"), \dots) \S4method{statistic}{IndependenceTestStatistic}(object, type = c("test", "linear", "centered", "standardized"), \dots) \S4method{statistic}{IndependenceTest}(object, type = c("test", "linear", "centered", "standardized"), \dots) } \arguments{ \item{object}{ an object from which the test statistic or linear statistic can be extracted. } \item{type}{ a character, 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{\dots}{ further arguments (currently ignored). } } \details{ The method \code{statistic} extracts the 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. } \value{ The test statistic or the unstandardized, centered or standardized linear statistic extracted from \code{object}. A numeric vector or matrix. } \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.Rd0000644000176200001440000002234413401471036017235 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. 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.Rd0000644000176200001440000002467213401471036015561 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) cmh_test(jobsatisfaction) # CMH = 10.2001 ## 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 } \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.Rd0000644000176200001440000001570513435754645016620 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/DESCRIPTION0000644000176200001440000000353013531465156012722 0ustar liggesusersPackage: coin Version: 1.3-1 Date: 2019-08-22 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. Depends: R (>= 3.4.0), survival Imports: methods, parallel, stats, stats4, utils, libcoin (>= 1.0-0), matrixStats (>= 0.54.0), modeltools (>= 0.2-9), mvtnorm (>= 1.0-5), multcomp Suggests: xtable, e1071, vcd, TH.data (>= 1.0-7) LinkingTo: libcoin (>= 1.0-0) LazyData: yes NeedsCompilation: yes ByteCompile: yes License: GPL-2 URL: http://coin.r-forge.r-project.org Packaged: 2019-08-27 09:16:05 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: 2019-08-28 11:50:06 UTC coin/build/0000755000176200001440000000000013531172324012302 5ustar liggesuserscoin/build/vignette.rds0000644000176200001440000000076313531172324014647 0ustar liggesusers}To0N !$i;!ƩTijaWy)buO+ϋ&L99ŃNԍii8ѣgHх\g(Q9V+ ?qgZ%*__NoZWsp-MP+`0˘SXyQe`;y \oC 6) e@Рe_&Asb0kzr2g0% ,jnč6w/yYuKn*vݖ?j4%8UKcP4Vg;ўuO|= F|ϓޝ&n?hՙ>0 3 mZ93Ꮬ9:3 s %n!sZPi.X3'Tuy wFց# y#كsN[zEVJ_ W|?`xukbUn’,44z3)vcdÇ^I3jEcoin/build/partial.rdb0000644000176200001440000061250313531172257014443 0ustar liggesusersxɖ& B$e(GI%oC#%*(UޮNI2$*ĺ}}txޛ7owvw޾5o_o?I) v髬9q0_ٝH$;%IߙD8>$z=}q'~c)YX$=swv7]'瘫oG ~}b'roӿU`/M[WrModvJdMXEӭŲ3?~7}q{`.~[WHxqï*aVm_Qh/TDxqbFVqCq c{[7+&E+2򄳐g+rgu/t*0gc&p&L3ku"ԳnXٱsz{TSg އ|_2w]#۫[|5xm˭x1 3^VX VeCX/@.::kיU嫎7-cyg^$ծnIKZ;;M 2,BeM*KGFG&瘥ܺhҨ+w^Zkfs赯KA߭g2 js~}ppd)#.uS}ql׋٧+_j>9BmzOZ"`Pz!@e2e:F#b0}X,9?pWqYￒ71sV"3sպ>TZ 7Z1y*d!J gVn)arFݐղ}y.cOj9409d٩D*g/ 3Ҽƒo=gS-TN>V57U;==Y޶/d_t3tvd|,5<:9&ϜdǽTgwffbz8 Y-YOs^|kp"-=MEB]w*ܑBmuP3oxħlӥ'lR)CC޿I`ǫ2S*!ΪCyViS"mr /]/428r1nmbfDMc?ЩKDl+k۵ w5|{Oc|jZ@O?r訙~wxfwEsZ5 nԚƎ<8翿ek7b~gîRt;q;&5ԓ`Esivb_B7fw,_/q[鍽hEz_ꋄYZ`r&*1Պg*m^3ܺY܊##R{KHm.&G CV_*KQ!㖽"76, ԗ;00LX*Ɋ_b*J[=ᑡl&3>:126ݖI?i$IqxyG|vc=%:6|\E4齈ofWL{VO/EY=mZFNhrIWޱt"-l'HWF&ЭմZAbSwڥ#qeCV[|76!SS{A킥4I6ۼ2['jP㙿bL| U.c,_&[M[*+D=Eٰh@@1l^M@P 3WgOĈ )d‡ CiDϔgܳ)V `rF^|B,r?&ahQxܱ[NC֨7$ȦR» 'G)O> 4c.iڲ'931fGƦR@:ߖE\7<2\[Ķc/:vP/F5Vƨvrsz)1jcԊ6rBY Mc?:h>,c&ΘlCO}y"dI#ᕵ_u!o>}lZ^LrZxڥEȗ עʹy߭Y$>|W:IQYb }/C׎rG$sOcYʦSVձZiJ+NE+xyPQ܊SU6/£j =s+~ZӕwbrT1! xtoc$NBr=&WMeS䪧FبpL@2@>vAт\u&32>0#Xf$gs[檩r'WMl9zĦ\us3-W}\iU륨#WQ+r M6LSMgf&Sn+'㾛4u/ިxoMt]:r_F(\ߕwEE.\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}qoOR̋UV 1 --l+ XZ^ap=^; zdğћs] >0Gj(&+JU}mpI; d0N\'eŞ][>!w̐bUf#Å?]gF%o+3<Ϡ1} sZcy|eg&څT|oR-W<i8yuS-GҙI\iB 쯑(VI}DC~/Qv/yr>xeR,ΌyNOgGxeer^?&*,Fj[4jh4itWயwͥ-L{T AIZ5iIV(kMsI]sHCW K2qt-u|ӻd y=~_ϫI`5d~w̓gw!LaqڦIߨ Qܪ$oKۛwٛ|6+.=\7row\\^֪}ps /WJFϦVy 6}dW yFK;\@QO?ܽsbvVg٭Az ,WKI4|gײkFKky-ֻnk5؜0^.svWmn|T*ܷ\:xNJ\.uGv,o]f* Ut~'{Y/Ld =oŞl=_Oٳ!*6ԐF2f ^?u_}gpGtfgV:UZKnűMUg5Нw,voU t6M[vw\|6NQi"fSlmU̢73ifFRr&FD9+w~hpV1VJ^_0 hXEt9J-zv]/}.Nfk746o/t 7[l@`s/ڰZ7w\w(qf2bԖZ+BVxIĻ{_(78ݛ[*BJihM#UTkY=G^n,_<돖FW;|u"f5dVBѝwߋRqqM-c,\@0Z,MOKaώwR4xn)7M ';=JJ{ :Tu3 Ckehi]7sh)?n vwo2T)-~1o,|mhoቩѕ1R l&⾲y)I⒔ljMֲylM\>D 1c+z [֐oVP·oBDQ/ˆ1ufSZX>#Lo]RMGTsU#x-Vͦ1cvifw:j8 ?N/V7B­]*-r~#̟9yNKTtOF;&YTN&{ɠ Z!>jɨ4NȽVkwyX[~TnFK Ū&Vz>]z¼q816 q޽=a3HhMdkߏrk4ClQoƛk]X5xNDžXFV D=ߙh8ClןkFvSZ꽜E*/̮Fj/|"ߔB=! Q&;nR2nd!Yj]Idۀ jZx~W{zE%MCP=P 'ڠn$WC!]Na 3"9"v'::`)v 5:R$G=Pa;G=PaG*GrdFPa;GPaG5:5ը:v:ȼQzG㋦vyӔyrlQ(%zwC>MIȒ!_Ma!^H5 7KY*msQJYH=0̒YQ[_8d!gۢ>ppFŏpG?J^Jl ׵sVwA*mׁD-ċ:]$9ģI_G®5-zE*#>= l[ttz!<\uD3huMtv{fꅱ9ň?%x;tYY.^!׆o ݚqGR]tb`Lɡ-oUU^۬dQ 㲝I1Ҫ؎+|ah,iYd RGxmWGk!ItbtDKG9-$$E' ;֣Nz@r=CD"KtƱ<8/oճߺ%ې|q)SPG6S cPnaa㩸GyD`yiѻNIEA.{~o2[~$'!KATl?2˝AD p\,ӊtLKzLd}kxOgЇ$t.Og`;Cן ph'CVcг[m[L9{ï#lk z!pbPb{ ؁}h JŠ=w{22¶Ơ,C J1Ş!U^K %3cuĶ'8e4cwU>SO5 ??A2) _Ы<2KAe.^Rq-zBxH|* k lpAvp{8p1RYR| KfI{UuF4qGQg 4Iv H6^:]br ܆,)w NԲ*;˂+*U5 .γ '20)' Ȭ5/l0:mpĸUe >:QNAje:i;dV\EQ*11dVQ(4D0l{qpe1Ӎb;P=v*EˏjakB[/P}KUeD z&`o!ot[7?fbձ̿tE:Ur/4 ;UyIG K$6^PqW՗0512&a=OdX4h2X k 5R'[E׿٨cJ LB;J]M)Sqہi L?$j؉g7`Dpة؉Ro$:hA'.mW$"jթxa3j,U4~bz #.EBCd,Y><;wT]ۉ;}*>N,nӧۍb;~dk$ h폁Zv1b+thn_\F Kbe" /BַLkmXMŅ'BV_}U ,g9jѭ޸cFJ_cnfBZ+ÝOwm UzH һ(솊<Y{KM4G@Ӊ5%YC##'t\C<D26#D@~LwmzWMY],W+^-f̵7td${)Zǁ':I}pNeO@ d\cToõh!Fi' }kS4clGe 1CVl-曊Yrs6w@vjtr^VrsUZ&.Z9"EvJ5p=oO(Yf\isU Okpuj5ZnjQbop$"Em)Zc66k bm!Z!΍Mu'~xrފHol*FxD(F!w0#i.B(i5&Z~3s;<*6P)dG*Z*lNP乳tj =.2̍"=2Q_K~!_V*NQ:'u^Vk~^7,B'O9j<}ej"σV=wn!MgSj7ԘP)hF\ɌrٱXE7575L8Y*޸fph{`&S7WQvٮzc$pTQlp )k O~MĒ~"5|Ym=b.^YazñM$X.P_$PDHdItb/jNdsk;6iKRgr͊ 1!9]S_DGVPqSǐg=8/jY_A!\Ё B}\'ĩxj01#⺁G!`$K1I֠ZϮG-.?=ܰ£1~Yž@>ˑ;1>ÉYDO@>z{⺁'!uw5ӐnU*p^ pΥ[(6TXvYHy& irneQF}cRM@9hTOe.=fJٝ򾒶o v"[5-CoLjuE>oKlo}[p\׮VZ$]1s-ߩ ^׮e`?A1oV+&&"Yb#jPQ ;&Km+؝֪YprvI.m7b~KR>!AWb;O25ԓ'RIH3ob_;%.%J*f)͟E[d ѷ.֭t[!pƁ7mvyF/rGn=qEp7b39< YjgOApVNs(}pL*#"d3b/A;M`f'Rѱ\ ,޴5xLL]QƁ ^o5uEls˰H]y+[+ўKQGJVJ2mljySL]ָdSWU5(-jňi՗}O? }7:+;P A Â'i(\Ll+A6(BvU4]6,蠈p{1&Gvx -eG@~$5u2vA-w֋gP&Ɏd4 {?nv/C,z5GlpȰfhH4z)jcԊ<6rBMd:CZ.6-H\+[M ~FzTxZ'L^ґ%m [-/-RyvNJ\?SdQN-j'IfK$Kd tf^b_[af !?TΣSL66I`2_(Ӣ ;:\GV£jr`73O K/) CetuC<2a|AQ10*&0X1Rg'OD*5<6*ޡ_q}ҔrˎfʍjUi?rL :6m\}*7|K4"ڳ[z)nicԊ6rBM7]jyS\ZMg}VըՊ"5./;fKmK4Qa _ A? I6nkNQBO<%> &y.@^Pcy:x?1+J5o>嚆k7@pCn<]u(Ճ֝GGi8pR3kr<{ThmFxTb)(j =Y CQ1)(*s68NdRIMlp\צO~/FYYCѴWǘm c=닟x5OM鯔d^:A"д]o/STG{eb)ݶJ#R+VvZ3by&P_[,-gvNfJtpo귂PVd(I7>BI];؞ڪ3d&V=iM̒eh!\\K,Ly5߾Sv윙:o%r(Eru*iYq(o7S_'H;h:>}}oLʎ2=z'5"* x4Ş]c|O@>Q1);*$840ǧ2D&#lj)`V[ѱ4iGcTj.B^ۚ#O9OeXƖM[#m[#h>O5Rԑƨt#?=*f<֓D_6OJ_rAwfz>;b+;3nQC=)}Ջ0$dF}{El rNk]-{lp,SSAF+iJ֌C<ƀ5j#&YC ' KݞP!T*;)~љ>@qW?+Э]yh_hd,M 掩ߖ"\7<2l[EĶc/:6`\hX쵩߲kED+=I$6FHi#'4$]13S^Z3}i`7_=KuJ+]˩ؾOmBb&1+KGkfSV{,v]0}RGSYc:f)gA?HlTav!J]U?t/.ܹ$Cģ8p( 5WE?QqGpG,;@8}nXѨ8֛a^?.!T浏FO8^+t? 'Yv*XRDCޯLQ*9kvlO 3`Ex ]P8ad9zf놛$ ?=/A!y/wsY3F\+V-%KR0$YC/ψ:|H؈O,]'d9qPf<;.0(=2c~e 3`K8y+Pvz q \v7V1x:0g*&5=2%(NBq49f9~(o?ybufԚ(9VY6f oA\WFj* V( ')+„ H^|U𥢕|ydZ#TۅѸYtB'/mO :uZk}AdFnx֚IgRd)3* k5.pÿe g.=´#f gi'=vŜ&f4,gsefEa?IB? JFF1b-/n  !CoI}h-GA ??q;34(>Z}XZe[Y|¶Z egQo7 =1ҚiX.8N*?;P_ͱѭXl`82${nH:;"n[Ch>lB}S}d+I6,>Xn Ԟ̎%w&Ē= B/[y:>[)N@Pmq4 ) :+x!^!<Y$l?wLR4K~bnYY3$_2~ >p%BΪ'r?8gRű 3OԽpq?; %rvoq2zd$vAR&rkG X{ a;L1{H} mGP_y6p"ׯt!('7usSg<5(ˈLOs B:PURÃɬ w Q  R d^g鑑aadWOQvz\+&O,BUExayP nSd ~dE7 %0z?IO W_8 7:Ч%S9V{=bv(QR Vɿ 1Vi*T]p 5X~ cعu(")(")-[iADz q7@Pzp)%rVD}+HRL#9?hԈ8"Q+>qɦd&}YŧE%oEEG!ԗ9G  egΛ``W$&_X%F%#XLv\S&Pμ5mIMTvL"?$ْ% wO=(v*8xzg&xd>o9:2&ޚ oB\#(ڛ}3''y_<eG4jM8EN;B ?B0D*~~Rk'?8m*Vpzk?F4Jeނ|K6gþ?>.U1S eoZy4Cw*hsB[Y%\J{al `M/=E^4tC>dX_wZa#GO2olRSb~B}s7gLb!£p~=*N Z]n/x͛|GB?#24Aۑ'lxhGÐ[q/HP_@n>Me||zFmG'̧HmBP%x,ϵ? @MqSc@K1521%޾=S멺Sf1=ζFϩ?䜌1KzTV>>>D}vwN<[I2]<*5@ms/(8+اy5x9%q׭2[1+Mľi0Tjj 0,o2U4Yyeק!78\CR ^I?LA}6|w8W c” l˱`?JgFF6oXF;N vc+X%oZHg `>FEn+WdtGLRGA}T=(JAS/ČG}+|>곕qPCK[ چ-59:=w>)`3Wٱa\/e3$V&za_|W/Dg:umAJwwRw-47^{0m@L4A{!\l&sğmvBwz_zLkCbyh׆'WWGW#PζJCE44[gn:lX`nde"'cʁY0"H .hbyG!sw槵.|殺[pVRĶuiW\\x+Jh)_+Ul檵_{[NWWm_W1* cu UrGㄏ(;疽g[ 1FN.aȇeEcٛ}Qu0EQ4Ѥ# INZ05 |  _F,kѤzXʛeJrc̢z!m^ 8yڢrGZQsۡ CA/x!cvv酊?!MzӋ| D-l~9!M9G~/C]8aDֺ]8ģ+j$vqO;9C\f$\/3V;gg95jH톆aj^_XvA.a呏j8Hz a;9Cu!lg4f ;p7; B MJMr6-Zٞ+1%oF~iѤ3Ilj~УvkQ[lC? Q )<>B"Aw}q?6͢A$d}V v0vOs7v_;3%Hr6.{Jk1EorJ9GW޼-TУ_ xT *VzEF.P'9#.U:4!VciWY\O+9 jt{e8tӢԹ]b 6Cڻ7ݜcc.\l]t4^"Kl~i_{EyY-UP_f]3ةbdL5 ?"UTMu907ww>Z\ۮ]K/pG^yW:;9ɧG"2f}51MFxTv=ηx uxT&7ڎfeݎZW 4Q+L%xh͐N2vI6FwQ3# 8Yq/JTz3ϔMH@")O߯v]dKG-^,zN 1%րMll7j{J8nW4dtQH_/R`r}|t ;bypmŸo+.b:{Azs&2G${[=۳'Ssv%3r@:ۙD}Φa=F8Yߢ-:4 P~-_Z-j|oX1]_Wc`ߡLqOqm {8y΄BU&"ApF4/kx6NLq`[' Jbiϸx*nI<xl$^O]N O&-^ؐB31LЏ&LCNρPC#p D`8Y=bgjex Z |o2D((@l;yb<%` 3:إt6 1%t6¶f.~f. ;yb;y Jbw,W]OO8k;FVCh/xT͂u8o: _#6^`>eΈ!($9Ai '(KtҨ# u)ްg+;Rp➂}/|NӐ妏 ^WB?C1rs(lې'iNƁ!_WvI ކ|[Fh!xڡY#ȏth1E},Qx \nZ+c1\>vo%.anK*2ʪFKy5Fљvp]x}_/V^>a^/s%a7J1WJ8Ot@O۵B˧TeC 2 f>nU>(*r:Fd9T1Rs9B1 5?mK peH6A7@p)7AgTd%C/vhP~OfG|l rF۞ a4cwUZ^W,NzXmڢ8 ]z#^j /]C;b݇0dcx;XaL""F.;5\GUuoP%^UCQBC۹uٗ{-t5` rT%`z,˛A=SulQ14ieL2X.y511ʴ׭7*Ph` !.$&lc4BCI7`4Bpةhd -?' n@vU꙼ւmt,ȑU.\p]QNCȦ_8Aq`$F;50r Z80WaJ0,VRU8!E-krc*g90y/Ua1+bOCkkU_`߈ny* Ҿ\vZӈ_*,:I,d}HcG*nxeEIRbiR]eBȲi+`svbY)1]ēJQ[ !6h} E8]'j+ZmLTE eL36S\sZ†D &:DlE !#WW!K.p.Fp qoCø~~^kvQwF\BV٬],W+4n&ݭz6dn՗Vg&OB~1mNYn vDf7|*n; dܞx?ĬLe7YW,Asn,zDAAQֻw{w{UF4rGQo )7!^|MGX%VS:hBrNQLcP\V3+ 3l@pQ#Z#w30*,p"0(48Ӎb;P=v*\3- WzkDI,jh֞F+A0bV ╆Eﻞ=ѧAҴh0•(<dougbrx 2,wzdd~N!jv8 eXq ;凌Y)Ō'T6GwZAއ|_Y-;?f)H<CV#B|hG=))`0/FO%j j3=xb<Yn*NO>qҰx@:$l㴀"niahyU-lHF4z (*Bģz gZ4Kpkp^,x+wgQ,d+b>ށ,HSqW5DWlӧL}!YaSFtT|N?5_QZ;iwj=>Dp>&ʐW^-7)"S%!.DB{fj,9!-`ǢnJ7\7k++T!/P -+3~ӌ;s+n ˟C yNgԳlr1v$t"P? Ś[ο#VTF5gŇrL< u-rx ︟yn ;55\isqNe#9{m̭yr=_k^&"lGfpJ`1>r˽+sk7n4J7ўUjB27n8e㐥^sDe Hi;3:WEo@{s{V .R4Xk0ԯ%ZH?DjpB{"3@Pi0!k~4ˎRّ1EDp #U-uXqz9QiMU+4!F:˨a''5@لr^+[47 CޯIbV^^wPMPm^jo!82LY-R@{34B<iF.SSK9?I8ycZ1I0Fhc^DkjAȭk0}(P0:n+KchRL^ȽJQ&-;Ua7prU>bٯl+ՅB0n*; Tm*,ÓQmXNAV_L"5|Ymy" &:G¬T$XvrCل' r8^l/ J z _7HdiZ/X|BnԎ"N ܆8; LAVSwzxH6nVH,5|Y꒫Ŭ>*.nc':&Ν(BVA)9ǹG.o?O@pbJOBSBn)rl߈Mo.XKB+%9!v)U: wq(=la%jGǐE;\OK訣8TsGTXMTx}fBGFAZ ,A&Gؾ%TZ7PI(- 8@y mc*'w u D*09 Iõ If,X" e4a|J'R/Mguv6ǒQz(zs%OCyY, <U۳GJ~%v2i63fʱE:+YبYcG(D=1O&\_Kͤkh{A_ .!`ZL4I۵:F#AnIvY&׾H2nis|;ޅ,uL@c-.9DD."gQ6kWca\Z`D6P#b(t{dWD:)dtn곰qE$mEc=* x4 &$6e؅|L' PV`Rc^,ԅOo׽._䓞[Z3TBߪv^F,o[{[6L d2јZ~BL@Aسyw#9JT7Gb{c}]uG|55.t4[TА 5}k٪-nf{(6g{;(Q-4^e#g~qbi#J˛ds|[SMiY;A2]npYUbb-VLL<Fo79w$]j[\V͂.{?٥_fs#t-q|%MgP!ŷX 777.DC<~i҉}7y"88D< L}AJ" St!Ke(7{700}=~?F`٧Uk {Mp,qd !+qe')u$*2Lf;C%Z~șh5QzráV߀=0xd7:ܓ@!'o:JF@[z{2w^K=9e X>Gq֪X脊P-:ٔZ[8;`+!~)eKsDeٿ=AkNGMe~1Ǩ~~?OXԹ.CK76u_]]ɎC9* yQlHI:lX`ndaÄ阮sjݐ&Og7OKMÝT_?n2ŅgRoRFDZʻՕwUo;=^ _yG(FM9wϾ*mr3T^HЈgu A'(rJ!oJ>Rf{ Kjd;eDGPBw[!ݰZdtxĹwM>H\Zy/)zW æ%!Jo'OF=m=TcW˂|B؇*VԶCEW!_mkTW*zsGUtvpgUrtCcgα52+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$]Ͱ]IQ_q> s wNxmXɮDEPTg{J?zGj=Ey^( msb`ǫP9u*Q+F.Ԙ6IW$EBgN0},MJ#yҵi} Kż7 [W؃!_[G2ӍV,vS?5/(&+#fǻt+rp:n|Z]d[$?|cW"S4ޞe;crQ@ {;(uqGcyW:H'k!Q] v=63-өW{0q, s,=^*</ b#c1O͎;A<zɲpm w*pmOĞ!ߟdoG9U*9\AL΄?[0R~bk< 1³*'rq7$Y.-/I4`p|z)װ<1nbXڻ)aP'1p8A % h0Z>ݨEo ДS-"w 5'YelRk$ѿgPB}T\Qvz4QԸX3/LkZ(F4 ӡ;J^.aBίoYԂP=٢Q>TXvL)XKtyWBnU"I؁/W-;?ҵw0LvԼAsQFJyE)4 r҄\,XlӟcϚ%oqs?IǛ O4/[lS%6k Kwkf#V7#>~ȹ6 ,JTγ桅vvAkx9t=fb~Ty#Npë.l 8\{m7Q8y&<]@!~p"H~S$7~|"8~Ի.6!7c֔]6r!2gZU8IwqG2׹;)5+'{ B>M/_m'jsCW x 2? o4ggg=/=S3u~צ/#Cbyh׆uS㫫+c(g[Q"OӦ_~͟5y,x 0Ͻ%PbMRMn|6y?۾5~^ &Ķd ˝ ~%W kؽi斪5_{m)l2읞aZW"+d^#r:ޫ6y*(?)qvCYe`QCtCsg\3f An"C3η[: ,啣myhVDIv e[@3yvJx]g>ysk55b{Yʻ+~9oW.*ʍ%'_~W߿.l_K-gW[P: dY;:yZc;`|Ļa?*J׀C:ѕ3,וoIWH`4dYhڏδ?p%M:KŠA,7_4XjV$^5Qr.N20:uom~=_9Tƨ*cwWMOx -jů79Z_K /aRaIrf x3Ҵk<.cz:2`O-T暼 /X]oe=zwBn9b="'n^Jǣ =e־Ay%ȗ:1+hs;[ۃ6? PP>A 8JH"G,: M4ZIμT/rt@uTUgDxuvtZO2(KwG2>N{}M}?[)ع^ޅ|WsW(Dŝރ|OY;u1EHAS&Cv%Ȅ_kdA]YQ "{{!KI1AާOW K9@8Hx5QG52fyx19 >׀I^oKdr]$ <^Oratƀ5eY,o@ބ|SYxH.B^TGM@.Z%d'oKT8]<;ՉT|\^]~=3+4uRQ>q~*xzr.%fqxD+ eWq9"zxz pHebeUw&((V_xOpZyhanVH0MԗE&$e +hqGQa\U(8bXp[};=Ts:n MgnEgU P l/nSnZt;e@zߒ`ʈA(i#xe[6s9#\Ee2WbU]3f쎹jYb:SOl#0u^򉆗a}j /]C;"|Hx45qpApة[)7zX&*AؗP}׫3qC<:<^hxw(kaE.LA|9]*0 9,oUk􅪙g9~G܆O ?Q8DfΦdih0$KK 5zu2j_ l6N4uNT|hv$@> =QUZ(Ħ$$X[7#W1{d7]#oO3Ӣ0h5JAٻ59Ja>mhomA|B>#/|NYGgD`ҳ& s(26X(p|{vyAݿ O!KQDRpf_]- #4Үp!Qǐ?n! %j mcӉc%=(7ov b$7Ҙߍb;7R=v*n̢峪Z2nU` TZ3;8qC<[sv)o`Z(4n&/3J^d)Zapr~*.TX%!fTG)1{D4 ,s_l @= SԲ]dW_hY)1]:R֢4 !T;A+ʖ5!jL*px덉K&3j,U@:,ZM!/vdX0/!{8ԻDY$Df!Ke"K}r*u/p)kC1v0{8TD5Q;KK4$'TwTULKjgg wKN?Ž[aiո -N^8i3C[osϣ:`cTdгB$t"V!1Sہ{5(Dv@֗8~YjR)AÐ7.*ɨ90rLI:k1]ݗ T.`xйUGSR*4 ݅1qJJQx7SS{h{ZzJ!S/= ~I ?)}h~%SR `Tm`'Tc`g` RہR-_ED8%ߓ))Q9|f))JtvJJ2fJJdn:%ǁǔv|J0Pٔ(qJJqJJvrJJvrJ]\))un))aUcrc)ĩ>%U>hPϔv0%-E/H+XEL\\R1rdv&]\)h=W͡9@~Y`@ < Y} Чv?9Y:'SU`*Q; 7wN.PTOlh oy#|o8wFߩ;5/Tbo}݊Z/p}{(j,۔qޔ^4vDi/BYYdF(iBhxPN;=%Zpim8yPKJ*xZ=Sqہ KP}FIV?Bg﷕. | YBAkcMbnx]^*.Ar6-T$*6^%&jǸ=C!w yk lc(H#y7`(HpةP9Z6Ro F/P=.j9"E-= tqG)2~Z'mW4+vexZɛ O~&Q5>1<0 *CiYeE}MK|oU:_Ik B~Uh䫪"2h:hq*xO@>lWVދz fL(0)fkrQ"Χu$UhEp.yʊUq gÿt Sb)GE5X'dh`ğnVM׋K8Wqo R0WL񾎚|=SSS2L*N6 ɧ|\3B5gq~hQ ʕ/@DBӁ6\4+(%8|Tc3bAV?q g2~?0)ɮ3_ګמ>|Y}%0)x1Bof2KԽ%{ab K=܈K,37*2pz}s`x='يYym.xCZjk9dY{rxܚ /{ /H6CL,wz3 BV#,W,p8pY^@zO1pPB%+5ADnoALg tBm ? 1 d1J`>q$ "ݐb݃,t/M('q 1 <Y}f-<(B3gl2iѯRpMڴ+n鵴7XqMU0}e7Zuʣ봃 A.&7mj;Ѩ_4 Ð՗ _H@7{[|D)N\-w컨D ~q/7,*kefXteGiPddFėdVL T!}a 5Z^V!]p"rx֛wx6p|bpMBB.b/AKT7eW:9 '"iPvz;r4(dcڍO!_oJƁ7 P PB{]ŧT=}cx48 ⺁ǒ^FI{)icT 0 9E]AԇB[-R-oAgղWpU7ܽ.u(Ðr !JJqt$Bŝ^|6K^,^=z^>g fxLs甹.z @ $%F`v52*bWYh '\\a;Uh,iJҼEp\[xKp%<҃Xέ[;{.ݎ6 P/,bJހ>.) %"7!?_‹fܺ׫SsFbR ~aٳgaE^$xJ`-c,wtRVM3] ~mKVdnץ S;UQH^ղO b5O/.i֨ZrG(> w v?=nIVֱWwn5Όq;QBUq |Y=5NAƼБyɠp=HznI.dlZ,P_1YGgR o[IK 5*ѫe★!Z/P B -=ଖYZTx\U2yj?;Ut$ *BYݧd \pA%t,E'$1^Cu5{]ُRZFA-M,ą ?j*?n`]LY#$A? '!;a/CnAjXCMCV {q^Բ~zdN|ٰ B-|[~ {X l;1*XM OB;4rzrxԚbq@V?p0o|&p"FO ҁs%/Gz$tX,z'm;;X|7A_!Ts+9z RZ(6Td]jQNCnQF}cRM@9ﺅhTdr:z!V*!ꑢC7X1./HtR]9=t~a"8-D3%ҚI֎ Ű0 叾nA{&ki:Px jW!a wx =HQk" 7N?Oadyl,Gxc'e-ĭx[  < 2 S6`쵁V)tet E|ߑsy݌eң1ݒFE/FyݢEDGã_nZx4J' !QlڽUI<┬Iؓ_y[ 0 I6f3i,iLMqKgO5aP/J]bp+f1ҴGjh:2DCށ|GcK Y >NBOۇ_!?4wg$[qߊ] w߁$HG{2 <Yn#_S7e^@w_wI/zZ3TBߪv^F,o[/8ͤ٩ɡL&3Wё8]~BLO O֑gS.{̃ϻ)\S1߈f4zZD1OVf.=fJٝ򾛶vj[55G)6g{;(ҍyc/ݲ38r1krJ˛+~޵t"Ml'XWVk-O;?=fj ń/Zl]>:jvof-@}Z[d;UF[>{o_ j[ SN3_tIא נN*A%Zثt*1/8|癿 oA >7WZ4+SÎ3+3ܦ.סCֹj6&E1bO@>ޏE?!]axCרw x܋P}IM%FD"09#MI[E=#Ctdiy˜U, | Yx9LsF ؘ~-gHmhHgRԑ-ƨ"m䄦z$nx@,Ҿv+}]l5@_*OeǏ,.}ڙh."OO3D> 5ԓ!g쑽^rRH;$3ݞY9: %SS#!SI:ԃpr}O wrRpYq]1Bk"B"]&#Z߈>,qiQ6˿k\  r(ǜ maά`Cw]jۖ]4V*1>_Ǥ';9(_ð.]k4#EQT\7P,-f/=ZuµLv|{R㙉odƦRcewx' ֱ1$W\Ko')/UԞKQGKVJmoR+t|;d_5F^ik9Xzyo-֡Z1~LNґrp:n|Z]d[j?LQڝ+MA$1]/| f𸿉t/kȽ oF=!+ 2Ao#N|>Gp}Ð u_ɖRqG /f32J Mx H )+ˏFldl$^Ld2;&$Pl +ouAq' PⶄőO7 _ވ_0o{) Z<Ǐ$3%Z ߊ#<D"= Y%YѼ}v^N/p `n]?؝NC&[.вv JL'B)D/ʘl4m0oGE /aƝ%S~A6F^50 t)^3ֶ^y8ywnh2ښ&mm h-:⦁3g44u8J e=' \-,{ Nq# 63/vDh.HԻ҉=w%!Q4/\ 3Zy3}u{aԲJS`p?Lc -!5HYA5*;lͱ$]gä0))ulOAoNi|u3滽M$UW _ldfd*T^|QT/iӛ:8dk#( ]Ѝ.&< SUkj϶&Aj5̈́'NzJ:(n5 g *s^_jx Y\J#€h2?D]~oG:d@xî_źgu]ju[o.㏣$Ny=ϋ%9,YfRf'dld4t ґ lhOʶ!8i#mjXπYgI^Inςڑϡx qey ֓h 2-;;v>%_kLL1pP o#S^N|K6G'y p 2i(2xc&6K61=J翥^7ve(ŪTz<}2=a2_ =s 5frF%_S@8Qq\^; :1bQzEDialذOrZzEG3vw_ fg:N ^! }?۾A~^ KwlN*կOl3"<}k³_UB3Z7}os)4}C[}w-=fgV+=ds@pCib#A#%VCB}Ө x!bX6 5Hs3_K/]0KG^>^om:!< d F>k~Ѥs~AgѱW fQPW=eȗ۠0"E.]Q^[Fm.CqTa58N/>ntBN̄qPvB?qa NAGp}$e.-W.(6Ca^1^OA6 ROCs/J pGXn( d)w#Pd9,*~C:!lN;jq~}臰>CAGPsWƚ)Bq 8*0}I餭>tBAGşPlO[}:,wtRVh绁W&UZ%rSr*~C/\]JRźU)2:^|-W D.EQ8ģkXA.H(BxQh dLѤJr [Ut j9<]*qGvמ< fM2J:ݲt!dYDş93?֓ h ڠa C<4/|gJ4ܧM',rb<@BR}NiqoTD$6Di.uSA1ǔMhY3'\#̶\PSSgRZeK(%[iW8ģӡy?x[eAG~ U`U/#܈-{?4t36+Gu `Z>xRtюwp\w^7w)q8 y}]N@D")Scyp -;Ɖ9&ތD((w4۳T(Xpl.iG/uFoMќ]ZM[nf<\gԘx#W/ h_b\܉~G^ہ[/SÐ^"m1Dq;=E{Vp\z=;\ԉ^OC~^A6 z` QG}J<G OQIȓSD` 8 y#)gØC |oD(VhJl;0mb%` -lIg0&:m8mtAE+cA]:txe:ƚ 9|x_@^Qp}Kf)5ar}C IꁋxBlQxcx1N&> 2GmF"'> g9`G"la| FF[4lmFdO W+'0&@@;/ RYWD Tx>!I38JZ/xT͂u8$dR (AALhN3Z(ܹEGaem7Jν><09l_(Cŝ=*^D\B?C1cmCF'p:^|]Y'i Ym{h&.7!?\8MJq?卨#J-f.T\(ʪ9Kp 6xs xܙ\Q.dK8 y=@[zPYE{7CW&xz[;@W`0MXU '"n]=7{8v-\G_W–xe$BUF48ģG~$yZU(V)l0|{MhnhSCCU-l=y VHpO^hP-nc':v *IiF6E qC<. ̈q^Q/ڻ\J/)= |Y=SxZ=Sq_Oө"ǁƁZ7Hpة Zwk(%@> =4*uGQisRfYUmMԽ`_qjߟzQ?qګD45ʊUJS 1]-)j! -1EO4dw"B\ƀS0GↀӐ 1Ŕ 9nAS"Z~QU [*%A>Թ8¡7aKl]@8O|2>_7'& QLT@~zL>.|M ` mtԙQl]2a\33U-lE%AEWUoD(xܺ9&UZ8ZAw( s.$_fL'VK$zrbNQL˟xupYm$)H]iCLd џ4҅F؅֍MxiK [,/LT /.Rk@>Ͷ4e50u8YjQqgG=(1`!TE agQl*N+_AEU [+k$BzGg (8!E= V`p]k+ M7w=O/-OvWxB}MsJFxx,6zTFx &G K])6pPq}㐏++`=2ILzLJ?'g2QRc m?凌Y)Ō'TFwZAއ|_Y-;?f)DH<CW&C.VY.\'|ǬVAt0H-,ujW < YZz᨜?< Y= "."S@Սb;/OةhojaST.uO: W~ |/D2BOއ`mtQl>áӏ,ur͗D=> v7A!vJǠvO 4/ߒ)1*sT\70d ѲHTZ_b@:H\1ǀܥQ`~B`B(żˍq[j& r;CK4jFԧR77!Oz>W!1ѧRqNT*>wNl36T*PO.sQ ˭NR7oG7iMl+;++o4QKTn@Vuu{n:ER4Jl:j%XO ^#3JԋuR27Ɤ%X Ke`O0 *ʫZt t&_ێګmzzhLԄpr23Ҍ`Ys,d,vÅh.qf򪻲؅W)SxUTPۻwT/ªSSSiv;a7n&T`!NM2I [5'Nh{ Ճ ~7~ӌ;s+n ˟ŷC 0} SϲYŔ <\D8c~ʨ B"XY3+oP Z¹8ZBW4ww<$+,;2JeG$PοYk'+9so(U Qi(@o0Y$x٥0J V㛠N8yF[,wF3qy|Y*J9s|eQ m_0]ݛDxcCm*xyk6gDCBu8Y!aW΅kV'Gգl7#H &ytoO.G#]#dJyy;bqxTtCǚКc=,Ey"* pAdG#=8F>.B^=}T[N` vbxI~q?9Lp{BT6 :fNB~r50Y?Ѡ} @WM, wG K}}=31ށ܆ T(.d;eV{ljڱ\.Yl'agFtİ{JCxeei Q{Joy(樊 Wc/̋u*)kZxcW! N1"$Dt?p6N3 ݁72* |Yj$)>1r9j )d1F[:iIz {(c4A 9 YŋPqǁ!_TVT_m.XMHd.G ˅;i0.]JҒ=Dx92ȬKuCV_s%4Zy=ոkA)٦6gbc%hoXK]MP~ > *dMibFŝ^,wK pŃgd:y=4F*D-& .0:Y է#-Pg[Q0ȥznʤ 6VeCU$S$zUj\BS킙/xf6[J?Jei 6!˽}C? XBlCB;B2\۷D^AU8@yD?ς,]S?t~6Lb[B4M)q-: LBn TQ` rJYcgq,xorɢVEǐy8_b:]}irv riE=K/I m'N׀Rf}֑ '$"FJ V @ʟN˔vc Nn%7Rm'*s%V1pR':TO:9MIVߔ>5JMM/@>|MQtz2`O 1o)_+CB_ZDmBM%WGG+f"!}!r" ܫ)CzUbՃ(\e*CV?bٯlVވ^P`&n*{GکfXiÓQȣiQqc96HR}dD͊H@Vw[X7ȳWRdSisMiV/=j/(X-Y bR0.u&׬7N %`L8 Y5^'(q7Է|E-뗠B_ 27uRaKzG KČ|T/'ǀ'!KBRj9 'Rq:o%&4+ h dˊ}JQO_2I_P鲺ÉYCHO@>z{⺁'!uN:2Ӑ6LF';z R+qprw* p z.up4QNC[elG j!Kj61| Qq NQQYN>O8r6ZW6l_ԓU !^SίLSo 4)1_ҺXwձr4F_ٺM8j&xx.XMAQ_1_އd[)=O?wCHQR!gGG|S/69W=k6QDΏsD$ڕ&- ]j?]f<\cEbڢ;M9 V ʟކ|[v,/tbN_hDAwqQVkAy!Qls=Ek_Kol*#x4Y]x*6d(2s0byQao/J3HK)FjB=+[f!KJ=!pT|)vx110225(HBVO`cl|r"ʤ{o>γ N-?3ߔ;[-TN>y5J*mg5!?mL: eѱ4y_GቩJ~BLM(ƞQ?ICO|#a kbU4ۺKOzRv`ǫ" O4)F(t1nșW]Ib'-:r\+[۵ w3V)&Zbj0Qnp催Vˋ,v粵jܨḋ]0}co7~K1k)АC+1\ڝ-AxGP6a.Je{ < έڧ-=Fݱ5{䌼Yrl1],1 [aG!ݯ1. :'悞.z_ $ 5ONۥ8{"ڰo~-tsfe΋ߎ"yO&?bB !7쫶r=KU07e.Nb d}7Y\ߡ'~*Qe#L H>;f(:@uy(6V̓gw2~g"KDۻKw~S(da醴-`C<<&.\`ip ;j_9sleEoԜ]6%a 6L8YԭǾ6LՇ`hJreynh:;(Lw*arF|?IQ1ҫ4b =Dx e~i*ޚȤ'?d?3JLQ7DZ1Ԁ>dWYO6k3Ik6f8;I«υNL5:3hc1 g?éq4_IOOdc&:s#q"MO@! /zZ7v)5gJV9[jA"dDU%|Aː/+=@`) qծ?x]!?׻4vsߡ.k##`J8yHj|`VpdH_Jgϗ>+(xsB}+~lK(q0$Y7<^>\cj1\H ?+qAa0ğqo(W\Uޗd481_@$|Pvz t7P:No &2+l{8kp{z5<͋+πʟiIXY0!ܧ T*ρR29lAp/dDx (;D=}Gm#mY?vKza q{yK7 ` @/|P%p$<;DCfPx5+(;D=f{3ۙ),wtRVÄy8|^v SW_EGՉw[?7KN^ԡÐgeMo)Ygek%|Ko6IM'B!1ӵS۠ExzciV_1# vS>.]A>Q}sޛnVeßE:MxKy[_] WW>w2nɀˆ3PӎiRa#L ^XPЊscO%@p2cîV?ճ${S0VH]-N&$! oC\aEʂlѱW WZ;90L L(ៃ?)&'Pvz,qe <Rt$L_ʿԪC՗ dymGl4&'7ҍ%xMH" H_Ⱦdӻ G%_$LAN)sx%oQ8aCCz=(߃dɕ7zSVou@$d#uQvzt7]6Rjζ=?fiir'(V|YI} oB\^-ek!G'v *=Lc6@P_|}mA?km󱷶ykq[k%[7Jkya3)CjH͈|ٚB$DI-QY:) L*5B;=EHV @I}g3=N4a8g{g^;}⾰oc{޵}pH @u@s@fg&lbnfQf Z+,%F$#mC=ԆkA`9 :{m,S޼jx(S5V8T*XPi )]O$# Xc٨|DMcDb9>`<0d o16,߃o*{*ۑA&vxx0FOnfXNA3~dH!IeBˡOy>h'_S66M܂U k 'a;"o"Wڬ7,X9J߿au1wCVuA!][t.FްO W Vjgv.;Vɺ)޿Iݮ1uKhS\/mx)yԼKyW< Khn~vve\=;?v>u%]ۈ~5r-;puk+_dnQ[ c<ȿN Cqo^&+E~tc?B}UhiӾGpn+`L{s47p5=^E Rȹg mñ^jQ^]k;M,ȯݲm7~odSɞ:tTQ<`gWUfVFPz(U^XOiUl)cT?龞vOU}J lJ0q<J8jm{W;hCutY1jq5,:NNগnRɗ-vr4wtٞLc)nRZ\N\j:Ο/&s@gJw0ztl<vg)[J)eyeI؂G\Yk5MG,9v7ͽ˗C9sHr"Gk=4.ώeh=sl43/3(:Bյ'k=4PtA[ P otFJPp/8RclB=颲ӍSYYY>BVa%lu5M6`}PR8c 6ŕ?^ѤqZR"?}ofg9;WHF&L;zlO˛785N˔ߩa-'54O]Y}N9d[x e'ڝU 敒Pi^Gk=4z[YxV5>/K(%(/R"k=4-<KBuHAfZ_~.MZ%XߪgӅJ} 7#4]H}ѣI#Ybɗ#bteBE=4fbJoP@Q3(Й(Yi32X˱8g1So~TqeEe>$BAN It GFo7lPI(:I^]W25~osu\( > ZlZ劓 OL.gF Vqp;@T]7ҿyȜ:E+-vv Vʝ'7X-v u#F|֏MaW޶&o'g~awѵU*_˖#O?k߽Y=ҏ+!vn/?G^ǯ8yWn֥Uc=kYք! GF=^Xњa^{UHպm;VUފV٤ZBc&=I%m {BmmYcpmCǐmD=It!le4Ok [m.8dY2#<]/Еtt.Hh+Bx (Kֆ3]<&́?;uXʺŬ]*hF7$FLCa7Mbhf-7YEX8aSq~6ad2?* C9\rjzTlvAD㲹FRv6RcFg笜U<Ӟ~afx*n6$ +dK, +8T-Fܔִرhʄ+k8U+34r[9AkHY(SU+ Ryȸk~ZJR|gM[̳K6U- $e1O>¡y)QƷ͖n9ttZ^e$< Y髫uR@+9%{ \gcbtbIQ(B<|mTG1E@Q!W& HԑuRG?FVP Q ~2: hv6dt 8 yR١qrn4v!)\B_ƻR'Dhbmmj@ldjU\:]Ζ+8dY*=<|;*RhJydrjt@=-Jģx U%R{8yU 33bRŷV ;{ms_ϽO[C᩷TUen~}qR#:ģic|htKt7(kKa9L~v8> 0Y)G}n^!uǁij9 3L3[UlrU@<8dV~6EoBi"T,@@<-C9ítl% &U}?bƐlU¬.kf F' 6e:*2gn|dCʚ{Ρld{i>[J٥ijV>Μr@q@:-.LF )E`S9h ZϪjfjw V:oMwQWY7p7daK-#`O걜b4s4Wg:aq47y'8c '6R%`II]+4 ¹n9m&#ģiǛA%;묬,`/De̥mXtÅk C~ZN,W~P'fe}afhytsqՇ d%⚁[\Pe66Kv5dK3pF[7Pةkhn3B3Ņ%lkVKlRh +K.G!jn?ט|4/ODg xmZ]OLp":hzˎS qK^c݅bʹ vBEZ9&j_!+At]&tEu Djx]c{)?9Fe=C5O+9% ?!]υͱ]tBm;KvutqJ,G]>DV]+"coRkt˨Z 7*Yuls )?ko[w傏Heހ|`'Fm !I]rL> VB €OujI}֝K8RGAvtv FGء<2ytƹ^^Mz^2$4 MR yQYs_89\%^[W0~$d9ލ8VQD纀x ٮku xRwլ$[ȇg{(_ Žӌ`t~L mou1a'V6.!M-Uᡡa9+5JAufb%gk%J1(<[>"/[r~m1[&iޑfUVNZ]sI΃9{aMq4jNi-/^VEͬ%7 \ނl`䔔Ԥ6d);Kgiד*2c4P57|Bdm_- J c=A&#G#Y"gs)36[ί3H,S|V= &`5Ξ?Ϟ6nY=>@^ElVr_J%Ͼjsz-@P3>+(^ QCxKHxZn㫰U6g-QG|~>綞HF3ldť sށvMK 妽s^3^})c6 Ł/ ?L-7<Hߐ5Z{5TU}î׍``c{E|3{ -oa/ۊP-7`ne|Wm8*)MPwJsEnR߭H,AV؁xO+ < Q.4܄\J a~6vҩy xE`&4:GLL'nAJ -hIWuђ Bn!Ȥ,d+A8lP!:ׁG~+HŒ ݇^Zlށ0RMQޅٕ;-"r~%# 4#en4?H]'p'dJP CL+ VXd0:i\?!4]iA-/ %\7+l'G!WF)[:qBs+ўQ/L-btz /~] n4T[v ([or$r|JDj'* ]^Zқn i,Ym-n9~Bs\ +8_a;Ф|%u")ʻ+b/oTǁ' ]+v ^@vT@ ,pr $p ~]i(!OQ8QPD~eE' it GF㣜]M>OBǘIv,Wh&(mR! ZڥKY"LEz@1Ib}ssI?GEP_~߃b._ŬL~Mh,ΨMK{q /`n5!ugMt{ҡ?jjRW% )T=hk%",&µ,Th2[I6odmϷקCwȾuv=u[,BᖋVG(MY-BΟ?mOb~mFiӊtdg_l0b F-1` 0N'p1QhIc?Q+VVb~йaY!R&6g?t+-M_*+/oa  w~-2j3_e7| 3CCCT}𫱡f`Z+af&Oj˰lf`×&\}5-3 9\[]Tea5y=x0ͿxL/MtӶ$ߖ@rh`]~"aб uINvSjS+]1<&VB{PQ{xmm{loH@Of,ɤRQ޿Z S  {a8e,isfl]Uήɯ[Ćw&{ ,ִM\wMǥ-sKMkIIJ{v6zUN Tp < Τ4"dO RW|l<mZLtp!ږN-=_oz_ɗk^.Sܻ\qo}^vݼ?==$1}`w67E;ce^G&#tP1;Ofn=YyNgd_bXy'L*ۯdg4XO=F i[̬'l\.ӃӮ:\ߚٴ.*v1{g[?h2F%Rnzt[׃vZt0ѠNَ%?okkç|.]"SVXJ2ֆ1h/59wl. ]kkki~IKΊy7voYX g\+Or H%jnvH'abVCOh!]̮cH[9m]B خ%/X`j:W.dxr 2##Tfd4k$ fJo v-–EvHĭ^WgJaJ&#SFw¬_,+\()+ΊW:,KJx B`r:̘S=>VUW@0dKJꅳ7 " YE=Xeo])4drG d}F ǐ:3ٕDNzVG.d4`,<"sal|,JWu9Gad?)x:(t1o0mDx FF ؎jڨN!7lOh"QdQ3EII[ւvY|( N9j} -uWئ]e5ٜ %.מV'^fAseW8NP&h^8zy9++Ǐ/[/m[nWx 9cKL\Tܒ둛<พ=A^pAg, kCZLFh:uC07c0& YjxҩӛO9FA1ZP<6!_{? MJ\C7 OMMťfC>Զ4Dl//.m(F6|Q6cuR41ƨcFf$n Юj8hHj}w,ӝovfFn$nO;Ld}_}їdS.vzėP{Z< U4yrխbccyi/yngZm cȏ_8]7-X"~RZw>A/CVJAewH `rR6X%% Sٝa>1JoewH]8y\ Tj4#&љރfCGNیfy:g Qid[!}>ֱ}ĺ'h֊NЬ}_6c|R41ƨ9c䤆f$nC^h&Ol~w ߷KE _&{lmSmFLl(0~(fC/U e~+o3W*D_FTL>c_]s6OΤl*?ٓ[[=~o\N~Oٷa}KxfF}]WW׮!}[B~n])IWa7ncZo8)±_* @fLq-R-;~4VzO>)C=Ch.|[AwfX++[3Oa/^6 HM8yЌayNFy̐0]}~WtDOiOj,(\p-7YECm(ɞYi6,x)BsYzAۖF Az$}~+Bsx_B?*O&H0k@X|?Qp Ն >p"< 6QR#.s!۟G)@~ /Bh?!5 ?Zeeߐ-P@r~tǔGQ0\tGGp;l.sQf<{vofGdEQ$;mO4Y4+O?@Vv-xT D ӐHHq('4 Lowl80> d)>ɗς/d_F[Bo;C殙#Jڅ1vMƤ_O8u #4򚯜ECM MO!̴iN|"EQπ3)m6RVvѳkg? Aς75 +_ /se+W 9$4T/8zϲ*?~沿(܏ZQi$½;Q&/Q +EZބЧ*oUf,OxMA/AwʅeFy B)>٢g;ʞUü[> M8 Y} Ug)ρA $IIZ1<.oJG +-z *#jÆMP͡7 )[;*ң'C \ o^ↅ-W,|ͅ þ  -B|I<K^rjlG HxmWDPNh.[tZlkW_ʳO4m^뱍9N$Rz>| ϡ;BɨLt욚 P#d6͓MgCRD.]9ExImn$WkSԯt.Fa@!_:ᇐ?lgaFQ A٠"7 Ch.P՝rVNNƃL)g&RIyVݞTxԚz.߱or6~ g6ɗńc =xSɈ"7qy4 ((KP r#CQN\6C |$@@r;2>0>{XɯcTY;YW7YA~U6ޢoZnh[`}lQB%O NhnVqT?h Fmh4"_ȳu=+tGhֿiA7 XjĄ|@\#7/"撁@w?qv{r%.M :f2jt˗/EۯJ`h ࿩t)"/&47Kt8yk1Bv6!W#JAB>k)- WҎD k2JL'2=2GEX[KPك=sϽ+C "rѐ@qLO@%7%䭬+:V97g}P.riUYi+?g)Sͺ/Y&gόҿאַ=i '!Ok/@_$<E('47Z[K0$47*{%L-]D oケĸ|+%LCNk6;\XuY} ;F&8 []% tGZH+l o:d,XEcrNx㢆Lhq[f߁.(Qm-eZ70&<¾%_k_8_ uz&}殑JRDs½=uXzn jj-=ɿ"ģV{Mg?*H|:n/+G}_Nָ!^xo\( > ZlZ~rf̺Nq`p7 th + A <Y)1P7 : < YiZߍ vyͭk|JۍQ !MIW]c&KY]+՟e؞ASD[7"'hš" wC הڶaF%Ե}``ƫ]$hk}$^I@Do@֯Yn.@rz~mO=/=v՞[AH֙Wq =XnvP8jJ:R%`z#iM8u;tMF4 hfz! Z7d[-߷}YB7Xl d b@VZ)^ B֟b'B` 8 YJ"avB%kbi ca ,'bG!_6滻NQ^c&!7SJ@<ͮn+0 YP!!!Cmh/>α}'j:}'R%`NI|R N;/ 캁J$EGhYٲ%y^ O@Ct oJyM3  ɾQ &'E7q$=+نOA>#/|ZFDPXu:c됯kJ$>pB4+CKخ'@h7rohPÐkۦs@Aţ ' +[fj ]AgtxyUa7Pkmgv@pD㰀x4 XQ=ʳb%߸L&YtNdj'\VV}9Μ2_`+ɶ26_CzZ!J[o5 oCm]~g; ڄUeAc9X-˻t @YOY_ S|iφD.!7ߙH9 mH36S;-Σc&j!kKR)fU]eݥC|ig-,);<YiqAQ1F!yJȹ/^6wl)(E%j4]BQ 8<oBǸ Ym:¾WT6ǐ~>pFWUʖi|7 ~%!þZm댇pPB OC֟y ʏ~ Z0 mALFDخJ~J `)rB6Bmb`{N6eҶloQJ!kVle|q/4 >Ъg=!X$]Cm: `7xx䜀x NJrn%ww!mÈfhVZ#*q- J:ZR%`ƵPtZ_U!=(OZ!M+]#z3o5is%/ԑa= /hzwx5iBŊƪ}̪4R r>YK/~*I]=n1 [:Aw jݹT%utGɡ@<.0|Ӻ. ;zq[/ozyk-cDWK.rN!jMi^E۳gAk7.[:]MW~0z&x /h :V +Yv @|+o~IhnK<#d\ 2k~guXlv5MgvgS\MJY [fyy_.YVT?= ^ʮ9?0-&K. )w_tRN@VT_kLj]NB?PWuv"5\Xͥo5*f ]~b̲9ٗ"-F^j!R*Te$! .jYXd=#+VsxEȋouaOm>]꼰5+9oN>?@Vw70}{ᆛK%UP8;۽B} >nBUkK7P+u$O%ujdgA4=#Lp (9 dYkrx"=gEg!oAOCLBԞCoS1 /A--?Uq ppk2p=n% @ -7 "7B5& sm"7 `Vؠ̓C.>|g= >b" Y)W)W=H]'pdE⧷hA`XeZNѯ-dV > %<͏yeޡ^`7p~K'\V~Uϭ|¦(H*E +jEY| ?$օ/d;Xa3uHcfSo.QX۾M87-݅Hv!JHx4iXÔ}$ަ5)ȩv'"2 4 RC6r %WDj8Y?v]Y"ٵJʮa:%Kp1fӤCZp I  7|fxn d][p#h{x֍ h[p[bu򎲕c!4B%"''!l~%uS 4Hi Kh,uR"g!/ /t˒[[!C p8I'1h&$oI\o@a,u'r,B 9#u JzI"1d}cjCNbWϱ}CN"rxr Z,Rx~#% ǀ % 7yZcղvǛ ERPDyQBvucG=܎ϲEڪ+;^ aˊ%\VBY?xd՛ N"U"< Y)sie 1:LCnԝBԶjl%/_S!d uw_mo|ٸ˝6Y# YۼyQ$6pJM^:'VzKLMM aM!/juů ko}ބ!_~IPIYlxhՂ 0p˖#}GoAh-j ; wWh,1&:;c(-1&mnFRFѝv j ntB>NG3~GBVprJ꺁 kNqjkO9; p򀱢ر^u4߃Cz #kaVҥ'!g 4x0[wNq괲-Ra1>}ֹؤ#eo~\7{ x&(XMB67;ǹܐ1/A֟W}4;쒺 C-4@ö% )T=+ZR!^ݥKElf eY K$Y}^Vor>+:qFzZZJWcC L:¦#՜gQvJg@qckeyj{_%? \PR64(zI>@.A6ԝ^?4$ 7z & fBO[[7$$uSOihhÊko|ޘO8(D]p:= ?QhjLT;!<ܰT}hksTGv"\!RɪIͤ7-zHi0% fw; ѓs}=lm{!'m@sS?6.:_Ե9[*;g* 4 R}WJ&W +]'>W!_vnVUd]q xKBr4qyq v *n 7b[!u@>nQAJؘiXcbX?3d#TjdxHS$dkWs3tj}3TeKZryusw67Jg?S#yUkvΓ[Ob޵Yz{!}cEB=;W_N, ض[764[+K`]ouM@_1myR.Fu|O0^l__HҌ饹rӋ$;=$[UvM췃;m;s N٥c)"ߺ&7815&'9My3{վݾy^VLؽfb1>|=_xK_b.diHX1hffE'ٳpb"<[8nҤpPhRbY]튔}_ ?w枖N(h+oMC>/Vb3}G6GlA6=&GNg!/G*~N@<-O%r.n`3nҋI7N$Yf8JeF&+6 <Y}az됯4-M*c{_&bA/hKOh"gQ3{II 2%UUpz;jOry"2dφj}ü3Ҷۏr &ro7fJ/U ~+o3*čѯ kEdW～]mO2p^=h{V9cNe~/@8ô?"={ WD^iȧ TO 2{~@:kd1)JR5H*=%&\^[3Brܡ̣k"3cPBjzhhjjLmM$c'YP_"*cD/7&MͿY&5#ij0lč YM/;k"my6|;eܗ"ߺ&78ryDYjM/U y~+o3k'@^aŨ"@& ^ ϦɼٵJʮ^!7ʏ}i[ "Eg-)X[Yբ˯XByß?oQHuTzn+Zy3#[L'Q-oB_ETsK@<|C! >Rw8 A#w<9ㄩ062>JL_{)iɡe unFFb^aVl/ptEhiV^X_Raۅ|P[Z7ZڗZ3xf)cԌ 1rRyE7Nv]%V;cyݹO4>rta"Eתu&y;$ĥtЯ CmMdTwxy$7@7ac][ħx ѲH]'ڑ1ݙTsH!Ʉ&FR1 q9 2'c9{0<2418<62<1:V )JI?TiZL!3ֱݮ+Q2E,,-1>1KDfO-17x*6oB)R͛^0ofFnkI;L$L__oIK[[qS$KԞVH~cXh&Er9'|H{P)wL%Hk?X-.?w!~mn D{  IO/te~H 3}WʓIG?p Ѳmnh|PʌK8e`;ж; w(hFfxjr2V S6JÐ-M##*:e )-ٔ11KDfl\-Q\2islw`7xK #76&R6߯R6}K6s~+nwF|#)փ*Iȏ~+tꍎꇣsLv0 ;*"z v1x$8{_aOxӿ>ڼ+tSU(mRZ+헌ZŲd}-| pK=dlZvxc/Z@YR>b_vY0±sNq-;^eBRtʎm\}~0Җ5g7#~Y!p7:gT6$T*5<<)%27i9u5% &bK'p*hgd,wNrÔ,\' d9 FKSĶO`ݧ: lIS w%lOӚh"MkQ3Ҵt'Co]Uhvw-|L5aO߼Sv?SdΠ 9(~=1c{(Bn-=[] }ov7/W{ ޮ;g_Gz@Y& L Qbt>pN>+c!CMi:-߾k+n5vwfYCƼ{)2F%M<a\&g3϶Y)9e1QqϑI(1AȃڬP*tsdҔh&!')$A5(gJp;,뾰=zz2,k؃C/AVto4ƨ/7dms,SVv+~l?^|QmPfWSM8W 6BÀk s$Ma/dAwfj(f݂}V^)Zyit G!65 bӨkmh,qZ|}K/$3=*o/Kn{ ̿ [ם^_)&~_zwGFekT-$) y1Xzn H-="ģVg_yvBw{w]?{ꌓ5~k+˅歅o >'WVF3#`u8X jw zzqCfeJJڥDP-ItžѲ ?(s55Rfc{T1wCt Q`O-B ǔE)mM{ H7[ kQH~2%;[D$tboC"BG` =RJ;G`@)_{A dooW])2*e^RB)SRP[9 7 6Z$JTOGi]:Q#ģY*'cz'HK4Fn-6]"TަXeVBJ+eۣUmXt +o" !~.zI&PuX6P]@έK^$u[աnDk-LZ) N.N=nBDإ\1ЋյB!++po=hDgfڇi>PK`{4#eWytn=ZU50{F;(B⧓a×] ([Zzɦ&:a떂a5voxy  h2Y6FrMoAmݬ?6lsy-MYx&{@Y.!ȇ,n+rӸ ~o*\b3 /*ǁ!_Զ|o]{ݲv\8)v'Զ7ElWoJ8 |!nJ,8EH;Y>a)cIǁ 61>zp ZujHa nTT%ZDB[ ,Qk8_ lakAjZ.Z tаʎO7p'MEh w;[Z`D^-l}Y 'B;K3vel{}ts8Yi\%u灣̈M2oRY'cQYk 8yN~}Bh~̭|#6;!+%k]*=Om|U`/d||%9 dEv3D3欨X 0 9i2=2j9W +-KoC_Ӱ[ p6lDpQuKvs: Q \uRx~!/$ -Qj8"]k8Fɧup8n(AfvBj.y6-%)5&kA،PdjSA d`t%i6T!a -r'Զ1ؒ.l3(xV _KjD㠀fV<.]Q>.io7 }apK-Qup؋OPs-ܗ/ۖ< )^4`E:ÐYg;NKP11O|XCMPJNm)hhVs;kh@ sJbs,rbK] =dA${!x&ץPotTGhfsg,WI|0w od_C[TyاwR1'/]{M./\ ]'x5BYeY޺kUC~ZSt s-ؤ-W<$+ gs=Ҍ=MP&Sm܂nB3^|)m6q>PxQ.^a:-HdJ4lkI]'0Z vZy"N'j#Q];͝MBVFnUO{GiSC ʖYHJRj{.hx|숍|՘v<|b|œM&gy Idu*91p 6gg64pҩf^|EHHU5Z?0fF10jpaWH]b0RZ^g;; aŜp$?!(I$z4i~M*03Z܇nB3C [O7Pkɮ\(!uhen yf ;4.^Kr}$dX|Yb#{v){WG"DϿE\{իu:Gcl`.yZ+:샬܏|M%q-YjaMt_Aj{GlƁ +W-yDnml%67Y2< mαr67ueAuF74ڮdي_ߔD~ W6<`M|(-;Rk}gtBY>*^گse/l{*T. 7M?'? HBhV$uH7ݿk)]1Z?C.2Sq 7Z'z:1΂"Nts6cLX`S-ekA||OKhkPeje<;a\ kE],|BzP}o5IW:¢RiR[ro7Q$4>v?\8G/f5 :Y) ?Am*_HڎSg$p.D/ {eB5,Tt[a͹Ӓ0!|Ettx uPX9F'0[){ ˲knQ bo 6&5v/; !|"u3VVɺ s7; wCM7rOu%LMrN\2}t4:<YiŧeCV:t~r3e(dsm%$hAtrwGK/ұf,}=-[oU->B>jpTT?NAߵ ۣsX&I a ֔^bw8 Yi7~> !d)ܮ`$[#|ʘF|SZ%Rw6̺ Ny=y+F!|,!ae- \,K:= SY3Cr~W^WtxR_ ' -P*KIgds"0 Y)I8yP,? &C+ilY)`f{I}x}. ^ox`F7J$LZgn;痍w],d_ŷgT#+^.B^.2[ek;eGz^ %HvbL9ƒ GtvrvL%)2^ޒOCQJ+R槰K6]8${N?xEy= Qm絙Im0x:=Lټp2?۟뾩]As!h,zV<:b]-^JYJō/ؕQTZ;.  "4x F;'A3he7Q{xIIG3Q9JͦO;SUgA/¿~97ז+N>ˮ>}s/ 3#~drGO14[+K`Ŵ@_QoWmعŨPqٳ~!?"\̶8cbn"oUU`ukGDK~#]e\⧻gmR]usG+oqLYej/9+vޯ }7voYX}Hnz̿$0_ܪHi6TL_fZe |`:Ȟ#_9 i<`ů i^|Iۅ%C0Ïx*E:`='+(& `;t_88+=x &Կl 81~]Svx:qhLsq#u R˸31d̨~dsU;6F с$ɌR#cD2p 6)4Brܡl/3:6829:<9d2c10G/ < JG?b{J`}J[^+׾+3Rsf)cԌܟ1rRE"xې_Ar1[{gmYW0~ŏ,]Y] RpbF;sK=1Y"a} SgCeq;#2瀭^ZouN$pd紉3~TwYѢAH{n w K/_P,͖^9* ;g}Ar.z ټe %P7r~_$̪tԏ ǐ:2 |Cn1YNR7?C R̄t|܆/BVs"ut9`:ؔ:6R|jKZN@si3PBwZcw6hpdW*71 {.M: m?NjUc-8c{/#ɜB/˯)ʻ g@CmҽeSPps^Ƚ! M9o:n]ud JuIa$wIxueWpg 4Hꦁ7!4]SEr y ZE3`]g[!FX[#8/3ɲ]^sؿAhn}%WѾRx#x(9R+^4U(H^Yý¶g+/[?*ۛFvM eDx*P1 |@63&Ɠj[c_4JF&29430M M ɡTS#Ó8S7\sDv x]Wot':vdN!7XuTm1R4f;2F.f\m"oY UdtlHSN} k)t,~ۣ37;c.߷;c-*C|5|Nbc/U`Kܫ=JoR۳ ʋa-HJR6B:ģv-C<NGG!z,jἰYp)f<_S-fr;W ؇*d4WAwfNE:d{PNL'Cα O6̰w›ojǵT}+| $Y^;˂`C𦲯]&+ܨݶW臯G=Xoqoa{/a10> zLJq3`3F5^ټm#K"75#4d#?;ZtL';T 33-Kw'[ɠa/beCMheiNPG?„_P`Lh.Q[g釰G?w ~$-!a?~uXʹŲW)-hbsx @׍zSs? ͒4`(IRDm& Yi:$-/]J{ &?EGk3' wol)u%j+4Nָ!^ 1X.-~6o-|c 70<15>2δU󷅖1=xX-@%_0|3+ƩA%*/Ztm>NZ{–wMNؾײGZwo2%Sŷ7k޽=nۮ)Zzk\7#HB= |lY7j b\Z}ЪuےwzsV%"4kUFJޒN',BxXG8ލohےذU!tuN֬ &hXtm.HZ !<\ ,|"cR;g*m+LAR4VP6 @@;&[:m'CNX7RA@ݷ]Vѷv& +UqIMCV9iهԟ!> +UrI[Ej‹պNZ"![^;ES r{a  +I1liaH!2A0QF!<Y)HF!<Y-hԟ! sEJFX` :s2}g@@<\-/œkiƧ sÜh0'[(m s94 v9R? 0Z/; X (k#DvX e#JiqųSx #\7PTsݜ]zaޖW^آn O!nzV.oX0BxR,mð Ij H) ?GN>oEYv,GP.[FDx hzPs6!<\}&m͓̓+(ߚar1te0n)ƨƊ1kjQ4棐tS*Wu #O)qg<o^%bÐk"З5\JG _2VۖN9_o5[[Blu!I;t(f3f3ӊwtUŊ9Y~)^Ok91G *W*wX\|$)Uϭ|fZNnuʗm/zDgjVK9zN 4pVUR! ]<ݙXE?ϟdϊ6muܤygj+;m07wgk1(3ҥKģ-~ga!E>+jb/.G"YS7:<`RxU-@s~C:ʲo56lյ_Yň C],~)%I#d'~!"X>ݩjgQ6} 1ҀAZQ΢[w? $4"ո3O7y߇?uDZWHW߀v:"MYvʧgЂliiJgA$ .p p X;N@&"Y\7b wfTNd&jWlT>?rb{؆Q9}\HqTNMVK^R t.tT~ Uܨu]A?6S[6Hph;CoCOA8=R0h rՖ+^ 5Z)f),UzR;| Y?UD )ReKR Ҩl/F(tߛ\?ÚYnv qʹB IȓD CA/A^ <Yi9 <.qo~09svvz" w 71 @Vjek0jkxoz 20 950hVᙨa)NAjCa6I]9 &FPta`K ce m2y`[ D)]66ޔf0F.8j.C (5_k]#_~ Q?q[*涮mK?W{&um Qtt[@<ɘ$iXdEEXŮ@Qnڌh͎рb(hS(k+ilg}bfy7\63䔱u)Rw6vrl  -Gy]&W AmTjGV8o8] q/啬C*$. W4CwYeS9^l"JAÐ[c~m *2k򑭂QvQ}bXmY"nYjOhWf[5!0 [De8y.FꆀӐͷ?ɜB)ϻDY":W&35NezҽhLAa5%P]G(GVh+ AP>*cք$Cߚ LZ? 0鯲c|D+[Pքw خ JEYx {PhP;a{5IN 5$z1)Lxuc1vyȆdrxdRw6d~N><70$Se6dR%`BG(tan)>ݺv#1ϮY n2\ey׬b.o1|;<[V*E~gK}'4?N/e;|Ϫ{Y$ީuS8m@1!F}$dRw4 4HM]2cI_Y߳Ngݔd9_g˞n o} DxIcoFG +ԝB6\tw' 8B:\jg:R%`+@C uWkn{7`!M+]hR\ hh=MX Za^b*;-ȷ V{Qކ|Q]ށ|GK}x6%8&a >Nmc']*Zw.UcIS(oGء<:=ե^| |[/7Y&> &|@,қI@%uo⩡]AVZ#oCimD&)SMi44K8y5fN@60S2$p*s`ݬқO.oh!+m74dSu62,PXfCr4̽IBy?%U, <Aos&`C&! )LS $Ys_89]3FeNQ<.l&~iBTR1xM ũw*z6eO3ʾGs_0v+tԃ2L36y<~s&.LԑO:/[^}e_c|>(b; B8}ib34*M)%7DJ4ˌR1i=;5I'V:B3iƞmXϳKmr Rד4t1s6_G|UP'Ns 5*B<0U-.xJ~DADn!kzȘj9` 70+_U?=MV|}H~sّ}'rϑ |RzFSxh4J? A. k,+w܌ RL5 IJ*6 K ǧ)!إǗs\6#$Qt Yc]vӪMM OӔћo#=M)TGhff6$ܰj"ᩫ84<?,鍑Kl8N+^p|gݗd/ĐsOo50;],r Y ]wBVHq^G6u|7REdw7zxiBw}_A7oRI':;&u!wkN ( KndJ)Xٯly:^a'p~$nzܗ7Yub [–ocQJ{[ p ⧇iLm _O4PDj8 Y?l=d=Ԓe[˽p,6,eyy2ԦQ׶}Q Hhn"r8λRK᡹>U&.U$Ƅѓn&(>܂-%n usv^ֳ>G !\HTmym~>JGX <N`/^NTulnS>rxAyC6A>jgF/hҭ1^t f]"42G3uZI_#' R < huAVBz+' 0@@p8R ,pr $p ~]i"QNCVgl孌{G]'f[J]AUJHx4i0>e˧=Lc hh!UH}xkv]:?m*6me3fXrrun.6^3>g ]wղ7]CZ/A?`KFO@~S!Yܗcfų_)*Q~EX8^l,zk`M麬osWfb6; <9 mk? 1l[71M%&ځ u Dxzx4KD~$I2 z#f[[*;F&*g!̹مZړ~9IфPd݉ @?M"gKV%XFa5Û~fܢj{Fi`rp(aV 7 REXJ֣>dUf0xI:&rO{cQjy%:?/vijcLV~ߖ]~T2g ƲŨބ|SGF;LDd''R񩡴t q9<;SUgt5/ }msyzzIc9;P:34948ΌM) OLżdGO۱9^feuWW%g1b}56z̿$0C_b:jQE39V4{N'i6l$ehc23i7wFQcҸAOac݇[nP)\@T=u |4D}s*9% \`0~ _$\B G|Z7; w--- fH]'p'd{ $T&ˌtb x c վxfh*3194rFbޯa.^8p tr$b;-Vaۛ\ؘK\oJ#ml h"dQ32HI IG u=hWL5TGkiFfݵD Kw&y;[$ti75fEEՓl.doď<~iy%~9iӤ K${ܣ|5Svy ,hBmO~+ރp;e֫b3ίe'OYeK~@,ƺE{ٵ[˞]?O.! 1y.Rw8YrS~R@< 1,X!h1 &R7dk㨰t F2TЇ^Idn!/jAthY;y4aPfbh0sr?3*9ڽ=橓T(]A5Ts8K_Cu2ɾfӟyi(̤OMDԆTghip|fO?Mtl2uO@V:x(L&uOj(8Om< ϡ5VvUwd]plѳ}d[?L~n>? kW7t%.Hyul- [8"nO-X7 |Y߾݌57'[37wVnI]S3PTɾzϧ)-WL 8a#Q џi~NuooDۼ)CH{RE<omĞu{ahٳoy{A˶Wpᎂ8y%M2ǵqsXd4ˌN$3koĎe3`J8yPcWS ~iflѹQuK:?soƲL&2CPQfq8I_8u׵_'3T@xjJ5^'75״az;LTz 1+G_44dH7Ph&5A* ͝uv^;!AX.4NZ>(}Oo%YJq5hyG@*d7PN7?otGh43k7hvI GOhũ}L8c7 ͉}(C?(V޾? wSExp{|K G?:/Iwt)D? I1y3gq!%o^}X) 6o\v"{P\_Is HxЛO}QyJ8yHRTJG +]zG?CaÙ#94t9SI?d&鯑_qBsMa(Y~RH%p$<&,{U.rP+At~.}E-ԏho I!{ (Կ 7!lGw@9a;#4dAx6`vZ: , "˛ 6DeZq)T|AB<ş-B"Ogx@]vY7Tq:Y$p Ӭ部ׇo; d%5oBwfjԄ#\\}B㨱 ' o˘ycY|BoKzX @}H^|6Tˈh+,揣cB]p.x۬lQӊ]q>yy/7#LڵϷ+<[[/3Ϧ i nٞf+_/VfUvÂ4| _a{=_.PkܢP8A?+އH&uL \ 33M4TWF sL8ݲ]JܗEf>ӯV+J҄$ BM6 G G ;B3_ ,X 6^Kfy6s˖Ss F0t2  ,pY;W3[ү_U!/j֣൲8p.m%urPAo l:u_ 4y !'£j{SK/XުSG5}ܹ*?{ASyjW$Bk^J/?"QQwZYטQv,=_^v z#|/B ZlZ~lrf̺Nq`y/NGE~>/V4P7T=O+ ' ӣRB+*/Zh/lO#<":a_˖#?k޽YUB˪Z;7|C]x|mWR` #hB=$ <q ƻ5y Z-YyǪ8w(Cz1dyw587L's#!400Fg{Kg|u9(&MJޒ4PBx F!3*1d @.키@!_l@uVX~@@Qd}W@pܳ% zvݶʱI;7ihҘ?ݙUw7w_ᡧlhgm߷u:lyg^~흶Z3_y/]R ŸmĮoxt$7o5SbBFٱumÔbRs"p_bhpKB5 $~:؏b7 $п۴e${i;k|r9s^SsH< 'څ'<>읪mb|m@b~yQvq):dL~7Wpr)2O^15kU|'h_.C^֧pIza{֪ENBV돋m ~ô,B sqV\+S̾s0DQ_uQ|1z[kS•~G >f,f.?~^[sU(XM05lI(QkbIm?0 YmCT%)`r`ޢ,#X;GoC@i]:- ]>ҙ" EEX:^ " ܣ:k3#Uģic,RL-B,uבWl9f7>g'UCCgR >80 Y)mtgrl  ϖu\O+l2Mz(9fUSu\B&v8a-1}9Oc^Ie]^ln֥SDY&;"+P> <*ːVU$RߵM璕}NDŽ)q 8 Y}rh:;ӵTz^oޛMBmZ׿|YEMpzBb27$tA- Y?lÃU"=ͭߪm$.6[pR.uC*2OtZVA__NKېok|]cbRD:''!4fSQ9 &dPYI-m;T" x < t5g3Ւ`,tCTc->4d1P,txucѥb;^[%zP*xV6ʒYcMT쇡]9c"dZIVAyHI!`/dx <r;0 mϠNDخMM]+4wzkn.JTpB'tE4 G^b`{N6LKݪ/X0" btx. m'! O{hϸ_e:bS$ds5) i$a.؞KU8Wyt" 6^|ŘM&p|ksyAQNEcMM]& HVDD0Q@M+w&Q-Lv' ,;]93"D) 4(_LdBV[jl1QLAVZ-WI9`rZ< N% s(=b7!le ]oU9P^NB% mʱ =X܏5!j-@s=ح*<1#mRe[<0 ĩ.-|tz:ʧifàAb;rR%` FMLo(PGtHbhZ@ t6IS͵q svx~30'2 60'*cIJM\Hz %s,4km 꾫YY >- 4קʒ~|'D8hYVۛ%WLVVĶ2+Kn۝%fevde`Kp+Cw$+KT.[%uDV &j̤tLJi]3Nmc']*Zw.UcIݧQڋ@<.E>UeA+w ,D^ ڻqIx]&J{ruA>mqVNɅ- QÂ=>|fzq>Eg,hlcU]a:S|4n,v|'1OᕄBWC˺O  n1x%~t)V~w%]vN1>t&jJr`Sp&rcbd ٷoѷ OX傳#ㅟGg9d+xp |9j ȾW"BHjDo1e7Y)387DR~tx0=5׌8c Ȗ٣z97ྶl{tMHZK ʟu%o,rA+_U-3on n`NI'-t4U)8dꁰLYT|w8Y? =e7V[V{u*IVÐk[g*ɜNnL>w_5leoX/d(>\McAdF,܊pdcÛgO:~JhETR8Y)՜J.oBi<*}&Dԫ5 dM_R t Z ir\D]sV6TJD 7٦TYf6< d=.cXЃy =E Z=Co[@ ۼh1}ހ*Ɉ"X a:BufLK Kf./$RΗn\lBҸ, i< 5JLy:T Ɋ f: <3MM2.jK[$.ې!^ḍMK B|AO!_`E֛NJ@ʾO!47Ip7dYɆ碟+yf v4̥,u5AV]zrq@ ېZb7 \mnZ0+Ȏ*01a7z=к5=A!GdvB>j;^Pi4BAf3>jFF^+dGJD5f6Y AmӰdumv2_}.@֏s; : p'dӨ]NMsG WLjk0&[+?/~ ~W׽Bi9BKgxL;ӥ䷗jzd++dFuxXA#l q"d}'fE,6 U8Q 2kzy 3)]G _0N)r*>;AIo!HEd&hU-ȯ#/@id`rƝSeNJ}e)!m]ն^`K8ukA]Ӓ@ q @hs^9 7h gӲμyE :< [y;\f%qo:~_zQqr!ԋu? TBƒf'%S Q9<Yk*>!+m~_2ڴ3T 6[HشHwSVYauxQc^o#KiW"Z 8yD iPza{֪ Q@ֿI{[;!]Ps6[sH]deJch :2Q_!o4L!ZsF޶rEE-(6ttw_md}(DQV^Q ;U^H*>oO H/N؎q$vĎt'88qzN8{yyI0 g(@Z/;{Ϲ{%^`?fVFtzBGxF%T 6{.=qM/A9 Լncx|U)B<Œi4 e(_b#@ZTT7"oTUeLgWvSb_2{>_1 ?'?J0 Y`=fc@wZ`)l+PCz$mw=cR4j|%Z/y=^%`̫w*n'w:_F_O/J~c}, 4s,xZ<Cگܼ. |12uvj [p2 jγ03D@u櫯h(d^xӪQQ堂950Bknb* ob"B7 K2CJ 6dʭ[4du'15 B9B<-6}Ð++il˨YՊQ7m2&U51b}rgbSH/Rt0bbܴȌoAVc%>%t:;W?z+Q&R[ g7?8IPY-'d”Z7d9?@SȜ" G!5,o-` si@P6>>hb_朗pGOǐ??&zsT=ʡRl|o-'!OjXvFRBG>v`8y쯃^ X )[ lI@J$`wԷ:4R՛XB;ӂA^|$rxr'.dɫTC GOou~Q- ֈV` F25ؾ= 7mZ +#f5tPQ"Ӑ M`?c,Av"=JE{pU e dt b(AunA*-*K[/|7Ey^{yqj9s?6*cK%f?F K5K1Ј'6Yp,{\oKd5}B3zH[MFO=zz7".7oj;8+1Zxo BxoŷqVM԰ٯ[?RG=;r,Ǜ**JssʴFE v"Էg5I0hSxQƿ, 5y䇑VTc9`0C)!Գq+;Q[!Kל2pOx͞bp pSVb oMg^.YCRpfZp p.JW": ߍ7~츉F/YdBTvwCޭ5dBmGY+f ߻B`9ʤN.;nUԤ^=w>pTJWtbߺywcc|bQXdB&.Jć=HǐW1c%R QA|wk~< Nx 5mUD|Y5gu @xҟ>n[3>_ дaWݤ92ҟb&]_3G̺Ư}ߗy6`Ӣ!@P=~u+~*'8xd)`R<YyM]sѰ7&(j!`r^[{DQ"VZ-Jnxz%\)wP[8Kb7"L.A.io ՜'k.<lhT,1Ra2W˛QDGP On0ޛeDѸz_+U*8i,vkexI0o([vD^p›| GWM'iti~iyd$]!^|Q[W/DU#$NyUW[Rr)5rBu#ꎝ @nOԎˌ8{]Hkyel i`rv"{*C׮ڹYS& _NnCeK%QkC1qֲ,3Â6CBZJm'd0+%]+ SBUf0:AV?7\O +1buxT&dc '5%u(|er~`r-9AVԏjE/ZщWz$»y)#b-MZfZD3a6w!op# qnr;"'KDh=~Dm~΄H!waGUguӧ>{_f? s#< 2U]? wIWxD'xo=CQ"6"DE oc(AB}wqUGDcSl7IL~)~ r:/?#Cw@iIUut1~=O(!Գh@&=M$wL)Pm'k0bw_3G K5Jb J0Y჉e (D oBVw0M17ױh4przqXEQR?"{;03H- qVh~<^ciVl }r?r%7)s֣c)z>:~u(٤~o<|">(P{5l*V_@AUbá?[O!J~c]DáIhV\Np* kJ釦UagdG "ܯmpto-C%"NC 6T.AV[֢ggybkƘ !T;#eIiHYHp: <Yꮏ1K1=:Ký<=5oy*{i1)xc,r&u_-'>N+HP8uP8Dh OQEx9~Lwe>Y{-!_#jzDcS 4 0If7 clc,M _s<-%|I7TUpp'[('ae͏jKf Z 1< tj1"4d= ѩzg &(CfNa8Y  ' O3o82oAn+mwl7gDp ))6}ϨT2: ŢN{=uղkN͕ xԲUĬSrۀ'!TVQ=4J6-VQu*+KjKTZvIԴ/> ;"TԼ]V!V[{[>Ժ!V֍+(*]~C|"3YKAg!N8F sJsG}kJf%*,QuI3iJi[ɷ/sH K/idb MxOMg"s1mub|9 PKA [ڈZ?(c|6;*Q"և3gc+Z@ ̋PmZ =u`H _S<|;jJ8p)m:C;00F\i%C'fMmWn yH<Y 0 <0בFC4NA>l;]+Ugwi xa*ߕ'P\|i-#o*G7!6*sX>>o5_'Z?Yj&F[!K]+d%Z7pd|'Da'pde,c[ߛQj{!fx4v=ɺ pVOaMe K9:T됯kW x$6+h8 yVYA+TQqʞyU㿁]^|Mš>)o`J!뻮+oP kK,? |u_g`D` c!< th/ MrAdoBGk oaVWfB3,5vj@R=D&=vNx?ߣ}B Ky' !+}q>/L?a ,?=AxO, /AV@oߙOe-8%J?| R i'ժgQ삻ܨ96Ԙ޷})^OR;/"ekH?*6fV7J~c|KwS +@lKeWwrJlPB뵦[`D@k/Z8y\Y۫܍ -r'ѥ% xڠ D` To1%ݽ[fE n:$Mϻ̩X mp^,M B8yFXЩ ĖW ێZ/sbޡӵ%o7a)Ѻ M6Խ@& 9vx1M2aħa%T] N[;!lPj]w)k& z Ү*5buihdCG~xMo&nV0d=ڂhK4n!O+9Xߠ}B%'#(ҘW|vhшٵR61W+\-*G0ʴ}ghWsۋ!> )Eiݰ$>!R@VN4J5f ryKތ5 (TrE틲 =2ykf?"w{RѦbC4vAC[0!+k`7e,U͊mddfk6WKPSoRnCޛR{M4?/,d+qiOkҨXIW/`dYJ`L8Y#C@炊<8!duFD !<Ӂ]j UR8CZ3Jx F1#G Ѧ-}R)yۣ$䤲Z!)~e-]‹|%sS#g1^!RۿIx+% <Y6Yc,x0*z AR4prq0d(' Km^26^F]C:wa)RqvQBGF/㳜Y5+b߾IqܫM%[WDʏ* kHWH_)CBi[>&m}1^4+W2ۋ$e?>b[QMty70x4w߷cg+rV;L!Ș/Cr:iqϓ; ˄#EѦЗ5vs?wLBU5v݀R }U:b`l֤*>j5e&?Rֆnh{CݺEg6D+<];a5mwRp/ݡ亁}YÞܶlLR6e9Ӛbkhj-f/0QTt|%\8˒3s^/͊bgs 5,\clRזXn|d>'kRp[MhUցi3xi"7LQ Ϣ5?/0rit|(SQ ʽ, m_emb5% e M۝,il(0jr8˒;bUR˾F 1fW|YCL}^G{K^+"Ǿ#cԵVY7+^#¢cL̋go+-g|ݘJVu N4I4ߔ]"zcɬkU$&\>>{T`L5|+;WϺ ;Z,N٬VG'=VOIS:Yqinyeذw\Ġz=V!֤d-,zc*|Y.XJ^eBE3X R_VS#7fe˲qxϗ0}_k(M# |C/k#>[AűuuJŘw$(2aeb8e Ox3oz!o,7_2_[U [hN/ ?}8t8r Z |\HLGƴO?6pez̊gAM*7䱽at .ho@^0)<[i_ְ~YȤؔij|sMy.#<vRͷ_-ĮS/mLusqͩFUJ0PiT gyJڭ--(x|0{eґla"Ӿxf%aE"B̉%7}},gXv18%xؗ6{'N{5W+5Tץ Ka==|69_qfMf"P$cOFm @6\&Ίܰ$ OɷcHEsLH1`ޗ}XR̿cy /( \Z=7} >yrWSဘpuM7%jrFDKVq)Vs]oRd3V4KQ]r 5ƭ+U0 +ȂlkEVvݷFq|N;^t(/- 3(7BOq5U${З65sVCj`hu g%2_z x)c= <6NX>7Nī4|YngՅoǟ?5_/U :k{RLUc2WJ/}\u;11!aѱ}s}\6̎䆲\ɛOfbeh@}Gq驚E7ۻ!weXR.y'؊eLMjuɝ^xow<#kvG)ʺS"^o5W1Q0?$\} XZEz6} ߩ- VnpYUbֶV+&fD_jo]MGMuVd[[fɍ ;Vrm_+]O p&6)(~=Pc7IyUwKf1[M"{X/RTi c-$+rC %P":((9㍼~v8˝@6Po\0Ul]kTN:wZ="Fݰ9/ ^Ww|YkWFw}myV(vWqa5 utiaYn6Vn亁}PQmxt<f/+jsƘã˘ܭv zn7b;b=.:v 0pEr-mQ7iw饨 Q+p 9LI:kA#oɺujַe뛪q53em=tI?kcZcOE&N4nD_7}MT2J54ЁK r+EfÕ }y"|V"hbF0d٬Xt|!2l Iu_&֬(>/%h`hRox>e(@In0e ~sCt>7*^SɄ;QkqMn|l 5Ag<ۚ:.`җ m~ֱƻuݪ"^?gJwN/E9mZFNhHgU:U`[[eb>wݶ\ʹZ=bsڥYŏ,4\ڙ/NNp&O@i6 WVO]on\f4<l̏~QsjC e!‡ȐtU|gxvGAASF)$Y~ =|,,eV{|(n`Ηv2Z|PgpH%e_xcχ^e 7;&h:gk6 N΢b592?,gTa^ulޖsDZsC ]Ţog2f/kp粃^ZWQ~5sLH%G|YC&k.Q.x |zwAֱ޾b^k}Ϝe<u,icԊek0joɮn'LotrY/ݞ1F6]sΰI=2:(VvpFeΪV<,qdpQ1jnB2O)'Aol|^J80˄P./̰hB<#,-PrQ_N*kco2N#&uA3ƙ+Py Pyyh3t>wLQ溁|YIAĶ/ĺOzAQżΐ EA36Fi#'4_[$bAio ]hujV*gzi^6RE~b|C/,ȯL36Mg6 զ}y lFIUzy"|<=Rq\نYd[$|WA8(6XHOFE7\In&g}Yn]L IN|{)" qW5alK@sH#=6亁:c\:Alvߢ '72g4=>4:|~8=5}c,~;.V_*b}MuP/5?>USKQOUVT-icZ.tbIudwﺍmRӤM3ż5б+fېw~=(Օԥ&VLv '绝0Ij8.~Pw5Òi)E c9@'3l*g= ڄ9ΩlM[`B\/khӾ¢m}T37mT*5`oP 3(Ԍ,yJEGLXTS"]>c*jeSKڬʼ ]v6ӌM&o<>@Lj$:e4+QJ&߾9i\:_5lө&6D8,;OzDV^@Sf^ Is,25"\0˄AF+ ]Acxɗ i#f僒^eXFic4?,d+ܑswQs Psyh[M̏6BYeBy[\C2c瘗%p/]Vџ*z)XVƨ*E[$]1s ߩ X@*]Hy׭I1oV+&f`k]:ğUՍ:}Jm+25vF'LjMBS0Mg|Yak)>/P<46R }A&Oa=a=YOwnP2˄n)M]LNYX8Ħx— %Y`+`.nᚋ-A_?@ouXɰu؊bo.ψu,hcԊmS-ߝfҹ%[Ub`-VL̈$êHtx?uVdk8NzÙj<ힽ>A<=v*3D,4*W߷'G_}>rCl.q׀axti/#>=LjO % M-Tm]F+<5"!G|Y@1%xܗ%mݝq(9#0 js\qp&>eŶI2c\.\ y}׭oMgLD/EnmZ6FNhHfRY :UdkLjF&>y׭[>KMո՚=m=t>kcZcON™xxT4>C\S\Q1_@yn|tlbՌEm^|P\2rp\4GCg$f\M'><(E9OÚn0ḑ 0r, Fɝf|Y.歚h`hJ.!1ĨFmĸ(,p̗cFrȨȌ2")qPs Psy$nd6jM/eč$B[7 q#-Qh饨릍Q+n ͿIV,$!>y%_zDWK/':.ΐ訒xeV{u(;LMtWb󽓱tz|lD~-.NTݝҔZspv5:]>_&|:tiwP:-Qhw襨íQ+: MLoEӭZuVդ7XK#6k]::U5:?mKԻn'iN8O: @Mn=3*̹8yV-Z1"a+yfUcd20 /qC9xvG_M% 3J~_>K9 l3Jn?P3 62:N#m>} f\nM e-|wNۇ!8}B^3-0џ1u8L1jD9"C SˋL]oN}Ve뛪q5#uzth}ǎDzV[u4 p3gs~}Pkf|`TFPQrwtެZjTin 5iˢ* S3ԌrNB%*86fw/ib\aI/Kj2Z60x4ikdH(p̗厂h#F㾜WFix$΍@@d&|#!L\..i ᑘܭ鑣uO2xVe!LGNϘv^:KMո՚m=tx>kikɮ{7: g5MY1F$ZaG9?NlQ.ǻ .`(gOۯRK%oaV)fS1a~aP-a?ӯP~bͤ0=  KZe]ad.żSl$_>+!pi|9 Hl9Bũ-yY7 UK섗Br4ŭsdĉ@ƒeʵ|ϫS?/6.[E~Jڍy񒴑[ dPkV`ի̊_V+Ƽ|ZLR]KI@u ?E C7o:CIj[p~P*`Lv=m|H~C{FEUvA0RKꮂGUAD_ͫZ@a9 *3P>մ}gR3"| 7WJIeKb,iP] k'}B[FEffu)f}HW0 mcX-::<kt]稢a׌R-y\05 r@opw{WAQ&xi;Cޤmp؛FG}Q/[`{^hS΍ds{~fcDyF$f_`/xedkx($^ra 1 S1I/a |eDIK% Ko>V9rWJm/ ]8>7;0wKAofah//oBNo"'7s ]xuf"^{y] ԛwː»ȍz tqv{WdgoEnUk^ֱjb߆#nbfUg0y!HESooj6܎"ay w ;m WuF.D^S7ߪK4y M.J$d:P 22??44 e {)̛Gߤdõ?bʎe:lV, /- crhrO٦U}Ed/[(Aɟw0ٙ?W6JgeJR"S(YFĘ)nݚ&oLfީk%CPC 1ڠnh0bC4Dɟ!MzYC<~6B'G i~6B'G!m~6,<&k9ެ{8ʂ| |υiFZ17C+iV5N:iuZ[20 !RMTpˬT%Ӡ˦pͲiW]ҨX& O7I.FsI\aޟJN^2#rtKyѩF w>T7 sπC~nPvmZsCcVרlP W{ܗLsgՈ=b'HӐoW5EmI5]} r KّhE%MDz⡖lʵ22f+F*/4s0*}{$8$@/ˈQ?qOC?ķ5%/CZ%>۱M99eךiYM䫯k"Q.BR A+͹xGjlpB >;-iEt wɪ]l LmW.P}AV7Ta m.<8hwAo a3(3ZX{E${+*=:#{CGQggVVBgJvmtE`F(Fl4PQe'Xќ]5 +`Ydug>:Wh#4%O ׉pxM' /I1TEQ*s 3TêQRVx4[m`iq4Bs7hNFQZX{o”TnSUB=s`׻-̛8eV(kj Ŗ ݮYl[D bBַ, ,"y*_amȷil)d&ԷELA"BtB % d%ATǦs-}ӐOKhK_._G(b Rc;hKocR TbH^އ|_}h#<ХBVB9ХaJ7@N t(n NI[z]UiiWTڔhTBլf&\>_1JY`72/-er).^QsRBևv8"I'ut"EC<ݼ2*c+8El{0nA~]@Qoc/YckMQ-Fh},2&KԖp uO]YVQC":CK/ސ( 2dç5:0b dm縑,vpHo aƍy|^U kwvK0I4o$$pf'TG4f#ǎ.ZXĵkRx,h ,Es5BU?:_ds̪q9K]%TOGZm8h7Cƀ7!l}73.˝1,"r8Y}uB7<1\B 'H-l]!jLpH덉;<&&J˼5aT*G&MvaKnwAZҫP-mk4K@cG8Iv?,dbK&{8zMe+A 'uub{ 8 ,u[0ro0.oBW4n-ڜ[ǐ'Ijx[-~J)4Z\ტq tYnA$n !ޜ(POHMpϔ6)hy@VP|~ Bg>+ j{!KŬk(`)M#| @͛r{jhyþ #45g|8 yZwg [:Vu l܍ q=ahm4 m)QM`WqsΒ]<DЦ#m2P`,iN4W4YȳBwk7!ģ>#x8$00Y꛶P;yyeS`񴺝6%KE:vW>Wk uE71BUfG!`|BU7:l`-'{B(9~n/oƚɄ"M@@!Mm ˭GJIWα rF5ĬRvld)!ԚUUU-&=Y`a9B4ކ"da3r_v Ckޢ 21 YXL @B<4vdc 0^Ƚڌ]THm;uHxIeɬ< Yf?V. Kĵrg}QmQQW؍d;87S#(ZX஄1*#{BUDyKԛBUDy L4 55aliu[L]IUƗCHIE<g!*q,[Fn.{ÍBlvA*f)V~R˟%W.T-jX%QD d 98^~\Z"N@PBLoJB:Sb)Idwpbh8@8oF8ڦR7hNjaL@z=*:mOJqqZ& x5{]Cv:z;{=XDBbd7{·|+!"{%v%/:)D|Abf gڣ>MC8 Yj7Ή Y|DކNmBXxbrnIɰ}s6%%J Xc.aȇ[߂Pr[G V|JJ|*휒ReFRCة)CCU-~tʈƞꙒ(J˯*m옋VFaџ:I3?.>#+ׁ94RNi 17AV(z~ipHE'*D=poJ 0YjT}+ϗQ߉p6Q呯omߩuF)!T>Qš&"u-j=wJw={QXny{?R"ҞR sw揑ㄎ\x Bv<&QZIR"S}Jurz+) !&.֗Srm*6o-V Z] z ~~,eADUmį%!ٔ"Q!hX2P~E]=0p$QASXaԓw#)!PJv,V,Jp'z\=3X,е1.zBտڨ27R4ϭ?Xib%>"ɚϼaiTBa8-?[+=1:Zo B*f\r\k+Zf|+zW\lM]h>@>C ? 6ݙzz[W'.ہ{[߫Sr!@NamթMF? `z/俠UԾ"Twrj x/@<:Zſ%5]~lV˒ZCef-؎q"M7H5_M'&B& 2mx]_5TU|mA ׋UEtl}X;ƎSp?dcFO\7ʪ'OK `f(xk\L^-jYD pS4=^W2gy=9]b$٢7ax/#|( l'z̉V05@^H#z:NOWv}`yR27>>.9#҅7o5JE!\2*պ4y׵)dfV%SU;|i͓xV@ڄ^%5J N=@%QLfcBUV g#ũ-,2+T&3_}EFL(2a x&`&jzi!5"L0u̍AkQr!m mL%g)ȩ?MEz~[7bYyЂܘ,fwlɱQ1q 9,4xz>^O.9OmD$ @δ~pKɝ@POSQY`f)%@ְ(U 1cRPz{r8 yRYx&;hSx1B<]#`),YeBp{,.Q1XQI'[o,~ ̔^-4G5 dzJF,SY$Ӑ/y_QZW5?"8b.|rވo`iyg3}${ir}6S2Ūbff! /]{PfE> Pb3s`A.%_|ԸlA6/f'P慒YxLXuyɿBVH+:*Ö-TpTnU1ᝲ32 lI6R7,ƞ/ո;b.-DxoL1+cfF!d=٪83^}fðlb4&"ǀ!oyP ቄBXeY& M)SP !ddcI`r3mC D|M<.O;42FKqЅ]B5QeXtCdvBz߃,5WDaP)6JZ ȽZN@> {b*sowK9vAR2m~R/=:g1~(>mQr@|_ T2cX6&ATԠ eӌ/ D &Tr^)Q8< Y@;y->`r=9@(+ĊN$o _GGj.mvvX "2A(:Ƃ(Ð+kgw) ~ %S5!.8f $GӐGEǹqbL̾"< Y_sӇO҈O6#]f|8w)'}"J)u;9'"wM6ڣI}Uov`YȳdαXSC]Ǿ9|!V%w>affW[u"E O61؏'`0 2_׽'O=ː۰遒Y}î`+s\>1kOC&xA3ƇAurͭRvlV!j J H,;Q^C^FM-@X0,0ZybJhL|5t1bfXp`d ^+eL{x|)f"#3g3߲ TMƾ_;ufbyU-t}`U=/F.CW]_K6a.+zv)V̲-Bz{亁G U&>~3 UkYPC/A8y=fq8 wJ8p]jQN@9 HP |Yj&n)Rq-F"^?jѿT| WJ>/WmJkڷxBwd-ݨJ[-@i[>&m\#,{ѬX|CKm6hrt/#Eᦖ|Y_9s4)T=y -%Bv*oOgģX*nըƕdw稩Xp8_ZC7|BL{G FKC2t6ʆ7C3@QDDeWQck+9Yq&ͼD,4dxQֶ/IE+A^IS/>]^,UEϠBg)jMD&ݗ;a ]Ʋ?l,TC>zk亁' PVQwʒ^`ASF7dXGx؞>>X63?)+aTJbgGv$] *@QZw' Q,+ [FxItړ>/ *( d] Fڿ:᤿yBya8v1{}V`/^vȓ <YRF$JxPY1i^0#SOM3Zad٫4| h#ICt:Xc/D_kpp^BeЇdwCޭޫ%'x4 ںF$o6S*$xt`~?rtn$;&i7s97V6:׭b|Z\7p;dow'S,?n%Z?b%| Y}!ښŞ:WFE0A# ƃE1dC>^E?B<UEhջ"-KQHVx-uՁNX}m (U6&+z׍+L#6sk+R~"vWU8(~JLQn'iQ8S׆:g6[4.Ͱ\d@n:ierFaR> 1W F~yV|>T^L΢Mw\{aňQ8n}}OuJvӯX͏V"{:NQLfdprzwԋ)D{!jM^Q~}MWuh%G[_{ ^$,3^hkspw<Vg~7L#~}h6Vgv_zL''[Z߇eryg_sy v~hDwAP_tn^Mxg.+,S FσvHέ$Imi%<@>LUbA#q.]_L65\w  IoI1"@P ?n]!%ERw ;$< oCVw5,W+ƼCfIʌx$<2 $S̮py  M8Y} ??3s4\L~pL?gqh9POvn6mX0ڳB%*ygEZ at KD=iiieΓquemſwIȓ#o09;-8Kg42D 33Ӛ%~ѮWSSwSwVͥtyeKswF4L鯔EmmH't›{)①y*~eO'h Ҧ_˯JԶ{!_'?#WVd;!c.lGwopmCV4P-/ <#c Ox\nIll) t+}&(T`LPxj3b,r|rhnP?۴q|ٝ4΍l^e| %s5S?8[Q7 ˖ٙ?W6JgeeKܭ:f12-i[%sW{ 6QC~b_}SJ6 x$hDwk-6uE[!F2zw)jJB !MZSJJvCA;k?s͛8s%, !ڠ a]ZBGz_YZ}}| }|&\Vn3Bx6( OB>~BGNԑZ[!<\t #zKW|2x4j<dZg_[avvi {h&Hs=Gx 6hZ!ص. w'BG7kH| F\.MQBGگ)m*@4 e;TA,QI-{!ģI-{jlv@%!Kճ*!..:Ѥ#!5n;Sj Մ}Jj"<B<h3rb1mLd[`.Eb]FDh^(}!ģI/? f42iZS/t +&kznza WIO5jڇ'Hm7Ax>gZ }vC ^wOO}? =a{۶B'6J~_m@F1!e&[<Š ;*GU]@ÍVDmVP=膄'EI5T tC]GT3ntR 6FRO#ؙ*(i e|7gMQ9jf+$cl6Mn G ]kd;{ kvlƨx"bX*%B<z -@͒|(7r;b<==C%}#\nyЌIQA$mdoN16G!GOMIc &Ky zU_^|M$]qM;]:iI];k rV|B/sBF 5{ܗBU23T*% :Q@8yuw,P8XRwLLx([gy #dY;1Pߎ*ݽ&^|}ކ|ޅ|m`wLLP߲N^|}uυ|uLo@խӨO[R{ӨWױ6*[{Lqn_md3<|'jAf\c!jġ (o)4T!U4rEAXXqBn`GGQgG(PB]'#'MWˈ>0 Yi} N133*^-SF?ar(lXiNFW _Q.f^U\>P''\;rq]嵨!)f.\/ʪ9蛋zaI !.w!emڔ\xzDhpx)5тL}r d#\Sbx[ % xA̫eKKnƔQm$5|".# Rĵ^, 6sa$ZeC5 j*,6+|ǸQ:e mJ̚gN٪z_ oE5 ݶEM41*xVMlwiCB.Y-Jj ׋k5zy)I(D4k6)n^{"K,׊ݝ(?Q^|CʹLAjp k#rPMx=0QߢM&_ }r߲|qބc1亁XH[8/-Nᙃ=|pkQ" ?R4cM7*VsB>$vX(P2sE4 $<1F;KfsS*yyɧҼɒq70m&PwgZ*QF rW=ޭc-rA8Y} GmEfT̆r ~z<Mư,ںtu3TFiD!!vhdx )})^Bի/]@鎯^GHrGKP,f,\7p]*l>OFa?(r{ۤɴMԲ~/pefQk6]a(L09z!5MD!|7YnP ,5`8dGWJ~S3Yȳ<ഓ䞯ojWTBN/@r] %wxVۦduh;+?J\sh%Rt M\+9eRa=>2J%U0#D pz+ժ7ڢoK~?GupG<·O;LBv/*P lU}PO?p"Q.б !vF$h&&7 "N7{u K1녎-w݇H:@=~MݟS!'iǎ)#qTϤ&Mٿ reʦ+RHDw M~@~^>,uF\Ʊ(+S`آ|*ޮܢUUZ4]uiÕ{G|1dmƌ9)y#oT4?v鲤eJb&c'{-PƄ" C2BW:7l\8Kͅnx-eH7q9!M~f0b_v",U̲WT4KC6m>gs>F?5rV4r1>pH9J0p⻱p"Q?`!jݍ]߳'|gW[kdi[fGn*X:8sW4G_D..ŝ0ϑ6'Ld Kq1zj7rz7~ijhɽ.d65e1mG1n7~6_|a*' hSy-~bx8ym?%8 YQC%Dj8YzFLei7Jɡ FyOz% Vc}@lW_9iΛa)K5< PTJtX'(]q%[!j tvAo^ UR8'3Jx F"5$G 뻆qKor j9 LBVh >5{=b nR+^ _S1^!RÉٚ@C>z{亁G K&@]!<Y˾Ul56ՈiP~u;8p]xQ*]el⽌j61 s6q 8 Y+F"^~ҋ.9ߤ8BզϋᠮM)_EjV(⑬U-@i[>&ހaBc}{e Gho%.wQD=並Z+0( ih՚&{!9.Sr!W) 7C:Ϲ;I9hCK+j ^U: GLxKe7í޸ 55c K\aw/XIud~ҬЖAdӹ>Pt8}:,m_:o_),p򤲮lq8`)%`󊶇8/b Y9,c7چJ1:@δކ(r*- % j eYn3,71 H˰BWlS$n; 2k-}9 R ?ؓ2Ө,%.[4W>[kcRa adAJ3:jȌ*yJa{"=sϵޞ(nyR 2Mes8UXo~T;LKD+ zL)Ĕ),pdz#*pOAVo'~4dǍ˒`DGefjsФ*o.GT.FD4ح B,\"d{fV?ȱAMFI`_`;3`$"yjgc!dw@;6bOyvߺ#Sy186 09 QK !/ ΏYw?b3_G* VJptNٛXc ><>3DR;go{u.`6f~EqA,:Vt`ƚfrٱ@67 gy>fdžc2O'o>i8 yV4UecnEW,2 vYO&bN xGƩ, ?wK,.ŒAIILDFg (ga͂YUL g+!M(xA"p&)p-ȷ4m1.Wx6d(3•B<4W6_l wi3! >=m.s%Qr퐥0Vc)62e9v9 \fl0X63 { wx83W㗀;$d弟lfl͌  {3aΏ`&7"ooКqH;@=qπgl3ZE;h/o/wn^g5Wٲg+oVH &%C+V/.}/n j7%/+~vy)2"<YY-H;@=5'QsVlO2\MV$LCN+sK5iŽӷ2HosZ09dBSy0Y~;|Rg\uW Wb^E;wYhܗg5I'f gI_[Υx_2,-s={TlM¯mː['w!_w##-vp 4_/Ue OrX,..6lW,X#uD4gSdgpe~](%=-Bu_#ՠL#_%}{SIV̥k~QrMN%:_΄;`߃cn%n @>Gٶ-`?P_LܳP\&jbm|ׁ95הsqsՌv&9m2 Nx";5 H7h1<b+.Ky#":5o2lRq^yNu7'Z!pMLVk1 ~#hꛐe=x~Yovaѡ{feh&'^ T ʴՋy *L7!RWk܌X*.g)6=[@Afzh6~3cDp[Af ToZ I[Ks^ZCézHaP ;(Q~'ζ4j4fPZ~Vj鷞9 ~okijm>P}-TI~kifÆ24~4j?Z^HfA4C4emKiJvئO6/A@ZKs$IV? j4EG@hyHfУXFx )e]iZM X>/4dN1giqә}:|$|:}?Mf!Ӑ,+EOAq!(''8ax$PWoryTB0?Zocͫ5 ҵ5AP:iGӴ r֨Ybǩxdx%ʖJ xSca^\@ޣk(F*YMzRz[bٝ׳-S3i@eyGJr)gv%x]}˙UP67Jt  x͝w&@VYn+VJKcz^2_zBĦYYe;h~Z'L2R'݁ 罖5C&?qM_CBҺeg8,.rlTL?[tK7 $#R6>,n  9!<+:ȩPWkOmļX ),X.Ւb(o95הs(-W+ƼCS:\ʖN(YXrKˡFE='ԷQMܮ>P]HhAޘ {*MZAF껡$kT ]^{1JPz hf+Ln1~w432(ޱ0%b/#t'AP*z@G@eB}#QB)ٵD/p?$4'Ձ._#t}MG]vz aؒӎ]5MRr,߃- 2џF^~Ze8~А+TYGb&3Ԍ?!G_p:t|*02&էqg!D4Bթ Ud7=Tcug@P@z3Fz_@迴y ,l ӈћc I+ז(W)'@迵`HBVrC%Ge%*7|Py߹ݼmgx 6WCZP#'?ԫ ( ֫G| DTT:~WhT~Q™†)G\6F+֌jT P_"i5m3d+y xlѪ3ZsMy;zBa[AP5M6~T^'xG#̳<_SFfw5P12t6-R"Hiۀ 5)e+q Oq:mNv22??44 exsρ(3q7s0 ~^^zB#q(--qfsp09tAP䭥6jv'Ek}RY7+!r+TVݳ2!eT/m+u7T-A[%sWlzne3Foq㗵 ! WtҘ[=ۀ;!K1iN7ĉI^:p.P!ģI%R mw@2T7?7J5< F [i5 paDj$Ȯ5ہ$nj:nȻۯJ~OhR k&"cv_T?Y*8Nr˂l7|^6?ZRT $dEV^*L]!og7izBqK{e]+Lf'&~(2f fZ]s I6U!GCGj.kMË3opDo/0by\c.:j-phm@ |,*bA7(?~  (-_lVSj"S?,*䫭0Qrk)p?)%r8Y}1f}wJ"%\1[ }0DdЭ c^BL;%P+`_+ WJx NNģIG]! > f1ژsJQǻN TFor?GFQ-D",_I'8tFY'ϟ,VW*Ŕ[5+Xҗ>:lbbICzâc%N?؛fr@hedz1y'ӓ7x}XߍEȁƪZ(g{4 ءG|._|[V܉בֿSYXbdzVo;JqF*N1l{\4^KF8r18E"Ez: ЩJD~o}m} wa 3eJټv n^b7]+;J>訅mJ~Z-,2-ϭyFmxy7VqضC]+=m6XEn]Y)M#5,a6K pTCᵵWߞ).o*wx m O0h%fN%$ѻ~)@;p͒07; iSc(Z8QJoo*ӛ`-83~ s!:M@=ؐP (r43t=eK& d8f*xm 4JP)sL'ǤdwBV ow)IhF~d>GgGxV.C Jm.|8prftDn#":2d ؞JcctzY*KQPV -8_ͿSe"ؽU%"|ͪ d.֌FK?ٮw@idȽ t31x4;!*9[(udthtb,$(Qv>n8JNEy*9I(Wĭ-M9P$lu( ]./Ua0JRrn9>}D/|jҺ @up۔<ԣ7*\ VK<WP&\D7XT?t_GI~-$)6b\цJ8\nH;@=F{hW.V#6=qa}- KA,/I'Y'*](Ăٚ:u/7["YVy\+$~\ C"ﻱS|S̮m٩ U.-kMZ״jֺrܼu'YBSVʢW$ 7v͢~f'POGsko}s^\ =PE]p7XžyERbĕ2VE#V5Q~hƜt~v +_ͨT2^eٓo „A"SEs_J1¼ŊѼ39y7SOis<7_Rd Q4Va %B5ɪj+^?,DmzkcR yoBɿBEmK4\UN[[o]zi88SEz7:f,_PBm+(mZ(.޼˄JhN~K>z#[fg\(枕 3^V{_e[<[WֻbP[comSC ! hdD=6D~YqF1m~)-;/K~@C]vrM#X\7ٍ94*a(BuE'CGRW]t]!ģX*h#{4nW,q1}ct+|MwoJ4rV̐eT[|SRعг;]}+TAvBvYGT[u۠DЂ"u%iMC2I*XF4vb\ڕi廵/G/"= ۣCw@E?Y^(;T]"tev&+ԝm{◊C?1`x1 Uur.+pT #R(p 6ley9\ކ|=Jށ|GY)h"ھ>Pf}JڪU م!Yjt.f!^rY`-Z5]dVrHߑ\/Pi$˱i0 F\ݮ)[ ,]_Te[UQtezi#jzi;P}DMj蝣!|Fe#}uOpg@)ȩ%w V֘ hS̞"uIfٴJgx԰J\=Y]w#5# )STFs{}s?[e,؎k[ <x%4wnI4)ƒ8J$Af<@86%tj n~5ۼ@[+|<Yjd#!~1FI/JtfbC^,lJN&Qo oZV-#K,2)+v 8cbj6!vVX| J r6-`\Tv8nMQny>TFTD!`쒵. NģX*{ZYP#b3*tkzy":3,رPqjKu &| rkYtL:s-Z7Z0Fw}(i3fO5{{Vd_lj^ƒ{feؐ1p! ykѪUzl>JZVUAQ,̷ [q}M& ~nKf @~C,rקp0X"vլE{*^5+A٬\X$yYICR1˜ؽ 5p z;&\M(iPi@C8ܖXuU亁wI׿l|"g6"x+FF`}6qaO߼ߟˎsds^OLL޿;tht`&9s)ìAx2֨n]uJFXNo,G;^L#*륨#6F\t1oIW<[Y:Ue78bjmj_(pdx<4t478K%|oRDi;d)[Lu}7 %b#BM)m&6>Hx.8 ܝX5EjR(=!ģI)ϜV)9 V(i}]V {bh7f!g5VkCvkχV. ӡgW( c\V1]] J@WPfW&3%R5TlyB3g|'lh L3ƩEhCCbMᛡ!k!o.,$h'|rb]$۠V n ۖhm:80j¶8ģX*CQ7yzEay³w$s_bg"UP[U3Q,pOx'Y0TkEĕjD=6hIC/lf0a!BGdhRMjz;-h˻ -JLhO&ڳ]}z؃flmS6!hE luBlOczstdh!Ed{/̇0"ȶx[MrD/Bz))eI& i`!J5=jSJ3c됯G3y$Iԥ77!H7K/ZS[ƥpEf>PJ3T׌WDn&ܨ׈7EtȽKDڦa϶-Y*ӆU=˪M^}?/}콶Tq( 1oV>p#߇|_9;p(WfdNZlTZn)y8ϻs:c'];߬G 3V12/ f-{F-,0SeføxàKq'RrlH-ޡz~u;@zG {BiV&0 "dD)6#@*o*B~)hٜz5ıykT!,o^9l*E˭z]o/<WaD,QN  ٕSnXN٤ {!6 [AuA>ްȨxhROPNYg5j#&\ĉsh=$\y0d^O 5Q rԊk+ s j6ʅݸ?,7Y+IT»^=uJF[T-W;^PCe襨#T6F\t1 IWh-*Z[k5u+ a]on r8FIW͆)#fEo۵rH*юEsOF&Fw;azq™xT\ 7PR,\WӺB\v he|>_ 5{.<}ݷ/?E̒d6zTiJemU<)HɴYb[b|44YLw>;ND' mXƬ2P G R. ϖ2lht8RM1+%˞`Jnt8s•hG!j+5.QͤzC43~#jKY/@=%Ρ%t+t&;|fK? fEV`/dz9Z$V5S^ᄿNA|ʹ 1v@>l1)dŶgݓk.2?Y/2 8g<2o7105n o GށH۰$8q"*gt1&eAQR[XjGhLѫ+v+*S)QǐN %3k~! >!i~b-1 zmu0_jq׫ >+ZvF'™x4ENnB<Ժo]v!\qediRg꧂'fѢ@N3@~LV˄(TVvx4z;UeP42՝xïtG+ӏI?Yr}׈F}vґ&٪I1R(U͊K>.'P |TeWb*2o:H;@=54*,Oyz9F"GN՜`O5N͙ķPs"tҜe ND+]qTڼ;t`i]egd~KtFP||aWgvFpQʚhR\ѮFoDCu~ߚK4K_.Pk\!VcUi?1hȏw ּ?c_L A+d^cɮk@N 9dAqݣ?_/ZaWh\)p)}ʮ҈7mjeѱx$hD7X:n y }i쁼Z&48[5BXl#S]߭tۥJ~hRFeRF(0"yJ p.P;CbBVkf(j#H4|FX/jϗ^DB f+iE8yHcY&vJ~$x$*zvbl r _H 6w^Ƚ-[B*B Y)g3K-0a2I4nٓh]F2ܓ[вEy*ZU)/l [a{j-EY2+ʛoԖw8yJQ`FӐ*nX~0W)|ZnpsΓm,2lNCV/YʵRWT^)4*ϻ6(t7Δ~n_m),ctޜs)g d,Nma|u櫯my$n7qPFSE͍CcՎq9zsOC6&~18LAZLuGJl{J+x$s*ƞQ,yu9e{QwhCd%bR~^$~x i(@<4==9j6.λ27YQ1@aQ%:,=EIyh(ҸZib[/e%+a0d{FD@cF"4x {iPVee0H\Y+2vI\m*ˆRU90 9~QQ1=ӮXO]6y.f_7V.2Z5ʬYcT%:hvCGcE̾`Z%\fRx`7YLus3zR]؀{V-q XDSم <Ú槇oUsEg'y(vKt_; ,5fRrc՛)$2{8O4BB'txR/P<9i#{`V\sy=pm a.sc G / W(Dcu5r/<9* g@21ZA#^2KgY_"-BV߽#N^oSm/B^T$VYQvU{xSyv۝ː/vf24zrh+_w1kt#<*92L3ʙ:˘Vrb}&z)=MM ؍2l )-ȷZ_)sFs`%$Q!Y~XF|z oh1)nvRLSwALlvB>*J[C17>6fs^\nlh0NkCm vMl'B'dX't=uT):gM{kuƨN5&&"銱zA,>2ِyݽ^ib/1ZJTϪ|.:Z[dkğ~7::_!=tW{HbYhA_.!tdf3v?t:On*0 Lq;}Q0'J[%dGP!=D萗=UAvA8JB571$= z=5JHErFmx(ӐwIKn,4%mn4f^fc+5}F!deT 1ݺhU0ZH{R-ƨ"m䄦z$nxv]uSi_[ou c=6jʁ賊CYhi3QGͻp=DLL5v{PGm)v/Qb7[f8U\^:թ,fj!<^ o$>S^Ƚ }ӆWtG,HXn$۰}x/N(w'bVp!2&hB4O.!5w}U+Rt:?Yȳ J;/%KzCD+x$MvHf8=+.k3wGіK*|`j<[vj~4Bj?"u}( !f-]r"sZЈgqu(:r;ZMKQ*qLXuyd+/ff Էb3ۯyZ31n |չJ+3_Sna(" ^=" keZvb"Y{  :HfW$]nu1odCW*=oOK9_2>aw@0B6<_k9Tl>%J)7U[RjrLŚK~K!;EƗVX_H(/V%z| f ǡ n4Z1c ː[x)vh\ģּ5vpC) WO%/ oQa_:MZ\D{WL# g̅:'wџ@LEټP!؀SK9,u;uX]160}ՆbB 2gp'dP[%|ohR\ Cz;ZwB֧At'jVɱi/ aW]6k*{ZnrOC>QQqOnrCڭ(JlH*j>.B54B˃*]t%n1.Y ]V[_ݙ7᥈. -KUS Ye(~WXrvfXZf5|ZjŪT-=8C;5Վ7ś nh _\1kWBb%vBsUpߝ`u0T鄢7DS `RvF~l{)eΜkV^WVlT>Jcs% +%zPU;P)[d CE|5궝hSD5EbTKVK>d#"Khy0x-hٵY :bͽHW՚clŪlBO{z؍߭*V^lcB/m s0zZͭ -I.F?rGӷѤ"&-ִKl+sM mhZ3rMK9igBIm7-[T-:jmZ)A;9K|i\QC KRlZ" ND6ؾNp(ctowl~ہ!jTδr&!_nrW _QVNKNjcqx{ßÓ`v?M,Zn)9 ˢ|<LX 8Bz6mM H5 DY+Ay"<qWzo>T)UWSf@UoEzRހ,7h.<S7  p*Ti}iۉb8ħUkh%n>TpUV 8Ρ֙4nj*4#S$Ag`>gߺqER^m1ˡN/A± 䌾ҳ7eT2 ,WpCA?qu/W2k%FG)3;c|krY9zo@T18qe5eyk /y`r~  bf(v9ց[̝C۟SÖsR32Q,u@ARqÐz\cQ43X5{H?,Sk޺ĩqP~nfEBىb8@=ËyRpOg% \PoM\ECz%Sp&>;KJӲZ&Ž`o `Ugf\Ga6uenըTڮ/1{cJ&}$_XGĨ, bpx\֊8jldPB.|bm3fՌ Q^,ˌM}p_93cw "z |r^1.!z jE~_ᕭ@wf:v gV$ږj $Y 9LU!j{~ezNB>q)0;d,]SKCq8yB[+aUb\D14Rif}tr:hx[eyϺU|oY^1ϵkGύ7=_c8t8jZíU*1j~ !/+! X>yr|hx5*VɤØƚQ3+7NL1a:%+V؀W?뼭OsL3.h  /tuGƖxX"ƄxTIq,rY+/oE*БyxO.T]w?R8} PioaN*SqہÐ1/rS)LlOB --S^t_u)?7W(fRLuG5;,|\|vc ú_doswIƷVƧbg[&6FƧ\| 6I:~.m b l8~V6&K7.[3^'aђ'M;g||?vY]lCb$ o 2#_֣D.1yv\7"JiHPJ'#|Fmw?I,ڝd+0֦ ,2!,k^rf7oFdb6DsI Cw'Slq2yQ=7-aYU/.,%*,,:)n87/eV;\Rj8JjkAx1qKTQAcxm*j%ӟJN H;V4S CoW-/ β̆MoԹ<,X^ mU Ƣ~ Qa,xd*S׊⌹-TE7c/;bU,o'}:xKыD>U 7Sh$X>R&5#B*Y+gWlϳskq^bG,OdJD5ރ(nLGvΎ?"Ln @>Ln~E4z;`K-B)^lKU,fhRK]#μ7Eh4EqQ}<V?]?B3:WV^y.aZ|v}S)R]?3B}YJUbgmZZmVbO-ָCkwŚg׃_qmy]"#?uLT^6>.?$wV rFtRݯAP7K7G8%[᠖ߠo1~@զLF.kogzAۏw1$K]KQޘ];8!6|z V=TZlt/L%&2ց]3}] LRƤ-X /hL7ݿK7ꋗxDwlq*HYʼniimZR @Q_;GU4aZ.<#d<-SXO+K`{SZoT?Lqqqjy6*Kgb(1{UJ'\BڂU : Zl0׬%Jq>9un(z)Xj=a*r qGU^0(z'eo62x?ϖcO(cnͳ;agZAN[:.ʬd^1  .n5j|^beUZr:@ZgQW՗~7t@Us5ji8^AWcxM„T8[C& m/g$=>H:Rq!?VVW"[ %\1VȲb.7/ޑ˿?-r \qnP(L P^,L-.R'!O֓Ķ.Ȱn:;}ӊݢ&'Xz)ꈥQ/bj#_jBSMNHWTwu0FM42J+w?֋Tgm1{[zt F&cvjuv eLdi֣#OGƁRrD)!Jy/B=_02Fk#J9o~9LQxCs"=ipsXsDz&Ef!XyyH ;97IF+8ģk;#օx|J6\Taig[;?-̊kUrWrGRta~rjvzj~P.ZRxm.Zbı^a0hMuꯈvG^:_o$5~T̈ge\/ݪ kbĶz4ñcgq{o&TrCvL@pxYm=~K^19ȹ(WxmKO 慝,KP'"ʏbk6ҁxQ}bz䉽߂//rƠ{a9礗T͇h\PާqY=K"Կ>8`,7YfYx" f37$*prTp2v^B{fy^KkA AfD daGqCv*:@z$䍅hKKe앱Pq!>?< @֟|`>hpp8?9cE{-HSB Nΐ`ROp9mWUb Dg8Yʽ-f=T)W%# W')j^|?j)o@Wx*ooAVwLQ>N4DuXqXJr_*N(u;d%-e2DƋx6+UD5L w3l3yl(lJQ *Q$檨MĬ5Vlj?PmW>R!(1YDQhPK_5huͥQp-{s0Z:1wyAYwcY,~ .ʄ\>DʄbG_q͍k쉽^ s]boaU8,0G.OX&e(,?2!Os6$)*W,8sy4ZSf٣w\sD(,3_]L5S1}}^6jpKpϲ'dV (KttL@(=PLڧWp9X5D/ AcwiQIYBm9AFQBGWQ>èp[*~?x4-Ӣa:_2%BVNv03Eqn ta ޗ1CX#AԤkUsju vKu h} vKl8K2g|d\vA}mbUV/En1E[msI6wO*1mQa^QQy49eg}.fY$|V䕌9j’߯DR|K'kSD A~\bbm>zj|W3t&Ch@u %ҦnG2k2 Sɭ5߯㴌_ q#o[oЈ6,~fF!\nphD_w*.-%y]Rm_@ʯ?O/}J^pn|şƃsj8'`HbvDUץŸHۨ$3V6Y0_nGba*g7M{8eՀ_/:FB§/pDzc}KA\xQmLQkӨ%A>7?!M-5}3sSi6咉=h]8ڔC2{p+R Îb DTf/NS2疢}1=JﱯjT=Vp,=sq7"EM=EQf!H˷,|"ߟӸC1 HSj3J\HJѤAOqƖ[3Q>hL/{(jD%GBŏrGR>cվ["pkߵ)c~d/5ƞs=K|ҏ[oiS֒~DC*6x$uyHwVyN :UǮ2^A㘕pp^l>fU#34*%{>'yrj$Vh_di[Me2j[c7;vX $R@9X $%2p1@Pm1|uV!V1 # ,MOoa2ÄsZxȇ/նnUE&} CM-07Jp4ʐ1j|8*ux0jNhzAWqC<ߌLpio\ ;ެk*Q<2x}erZG`#2+mƱcFQ:Kk/B[Fƀ!ԦܔJN@>M5#D% x9*J$Bַ몒q`rNY%R-;y)ZusNJ+oG+[<^,;_oC=5hҤ&ʊHgIKĝVxNv a m?-uV?5d4J1u]*nxi͎6h0(rLq,%5Td06cf !K,,JAJTK(؃m;(A5Y)#!:cHaqOOBr9:;E4vNѯ}"A!ikHlBBGH~i/ZKH(za@Be- ҡ1y%[ cvݱ:~o}vrxwf- Nժú魛" 3-3V=Vz_ccUMׯ ¯;Zͨ6Unru2Է!/+K|)2ϭXChN9ˊ _W#J3e±o{ԩd:F<~>3!<"{(:B=#ݣ0Af v Lz ֍[sT~*[A`mw慪(EjYɷiVV,LɄ7B=oL c?;vA8 fT\=6{ dVȄwYROkyaS+C-iUqe*{hN=xST1WIx 63Eᕉ}:ՊIL.hkn 5~"wU!(cƂLYcAs'Shm;2C~\%ƭX; 8PZs9]n.׭_QޖjSޖj ӷ>w{Ͳߐ$)z2,p Q$13BUBdrC<^(H9 <Yk.!Hҧ!KiϚ":/rȜf!;4%'kzD6AۼJg":#s$um͢=ffv7>dW},Gk[\-%v3kH{{=Mp/x1 mS,ssZB'EEeC:L~kK{4|@|,XvՔY!`@Tv@T!5/f%q D[d%|1Oi{gR*'8P,䧦 SŅ]3ZP;V׌. zтo&^,RԑB^F.ax@o$-P~T,ge\,tjS'׊IX$kY&ŏ}Er?Pۊ-KJ/` sYzT4ra?hrZ<rWjN҉QԦzNtƁ1im{.JƤ4!mim)ԦvOV+C--qZHmJk+ٶ*im h!˜rR\GRH}xZ[qx$)mT`LZ[ImhHkKZE:%-)zOs;)g$K%։3y_ꯊv7^:܀ Fol^{֝粷%ֶ%ͪ $ 5zs1/k_fwdKbxtXj=GQŰ#4Q+67eНS95ZMAh-| Mjq.i4J+5si[">`rQȕ?ƁSԻVb] >׀!_ר 76BoD39?// `rZ6?NiM:_) 3Sf'u' 47}ox ̗R:poIw4K~,3'ϳ>/Xr43O_fᔏeǮ,,={s, f 2a[we4j kѨd#[곉Kt*CjU~_f'%tƪ ̻5{o۹ixB}a*.*0n?{îoE|kB jfs-a]zժ]a5w>Ч=a`#@#hy ĕI魿4M(yp?W Ca:ð( 7-y]@8HM/2{5QlXs0G{}TyAWUGYv A&N_I6 5-sHLq|X`].ǍE@>"Sl$Tmh͜{Gj< `9抚I'MtƱ53J͇; v6' T+&=wsqCݨ~IvDmh@~Lw6-Vxgxo0(@(s;QgN9;^.Ė:w+qv['ajޅGc FsE)h>´Sш*:Î rѡXup(#ȌsB[Q9[;30^k3wxeE&M%}XlIUy^JqƪcBcl4q; "im&0`rFŝN@PA|e5jea(o 7 &%c}+*E[:Z*2ZL?esժY55߼/&T*BK ~厈0en. ;a5jsQTcum•GEƵV4i¢OuB;}=T")ziE1j|f.2fW ۋzh:A)+l<ʀSfL_Qx$"~yKꆅU_&BϮl4u7NK~ZV7];KP(wyVӦ-tWLiւO?hu"uz\Z £QI7lSQW,S%Ƭ~G +inZSiSQiնCêth5!Vy؛Lg=M?1>2jKM?<7jknE zf-H.O덪rg&Ml%|r)Q~)s*jjSqQ"Z*ΑG[]y RM._B Ȩ2w^*xU)h8i)D!HȊFmٟ ӹx&.@8'mNSsBq:8=[Cb0Ib$dTk֓$d: ;NFߴ'tD =^:icԋcŗHo'+nwvgeiǾtk+LҊxڱ>(f[ke$,2pӝ+o?NW2ۍ%ڗ]0}cyJ\o=ZϵN)2a7hr/7|#JiHVUP(f/{d{S˲p%ޠ[ˬd<[ ]?7iYb&] {f٢CaxC "cU:BgT!=!jGTRդS5& ,k5 Y=4 f*>dCJ!E 0 Y~ش+H,MW38 yXY#,{2 < 4+mcAW.NOŅ$]wu4SN!/̫}u4kk2ϛVdYմ;R`ƨfm䄜z$ij7TŚ.LֹVͦsfִ^['kD=X_vAJ\k=D=4osl9^q OWKV}0愷!V;G؃; N"Ѝp ơ)CmrU!$,LE̫B,w)t$35es W؜_U9/ S I*L*w ߑL!w9weX'.Gq}(D]'+u׉6Fph#'$I{A5UDŽ}V%1ҭM1^+FlH:%?v̓@mK;e|@AE)T !ȽL!ʎPz E1aJ@˱HOר4ht˲zM 7f)Ϧbŵ2. O (y5'w{#cz'|=Zp,s >)O(\G!@/Pvz8+p9ި4ć`A8 Y݇U2z#ԣCmw0%Bw*hbȤ\ܲAaҩ"4ECPL&+%< L(MxMf"|mƭQJ-\LUfTijq{7KP ?Zx$$'܉bck&;Ёx4 VC }ixTjK#H5SmsC<6s2jՆQl'\nTf5%WNٖj ĪlON|ƁW Kmẋ; v= dm5:2 fRނ|K}+<S_o7g0p[~(vsXꙋ7CPlCpu N\Z6& Cצ#g8yJb6!*w> z>Ֆ^v x4i%=3#:Sބ,l? $E/.,r9 |FSfT]G2Tkhba.i#-+Ui;(䣢Uo5+=Ʊ>&úhd)+5Cҷ&^nM-U/G2]1EhWmKM©I -cM3koK6nUmZ1 z49"˄voHj[ _vAv+t%E -?$.oJNmN3aGXWɩr)g ˜[<ʎP?>˚s2U5<X-jLQ<2]3?aX\Y?" :,Rb< ssʜF3Ztqq\ڸ@DwҲ3SsL7L] u cb*oqw5.}[R?ڵsV}ny5sC]a9s}CG}H?>&zb} ʤ1r͕T Jo8q?ő,x UuA3[{6aGͼ:lYVkTM*G->qƱNjb ată1jk&l\fA|@;YBip()AqS0t(!:Z6 r\>Ihj`TLxႮ;cyf#˨/O],0%fi 2qY`5w$vEXt OsGқ%d$1=ԦHbd#9j _-TA~{$(;NJ"_t$1V]H'{ᔬ]5 e;ПhbGG4`k" }&uF t4~?!M*n>MLQ1ODST ? ,e)IKZ.섢GR9J[pT&c22L~t "x 1m J"<xCşvгC<؛w̳KY56VWMM mTs ngF=~LTB-C^V.YKEHNL*N[Jm6Î}u'Dh[j3xR3gp* j3raHx[%6N?uiVG&\PgؗJT谪B?"9۽+5ɆI>=ѱc)EQVizzcvr4xK᫅eƆ+@Kc- 5[N0(0rL~Y#gzT}SvaQ,:p; ANIc=1وI(ZƘl*0.&qqQ!*/rSK/)J*Q 6$)h% <`lTp@> XavN;ppp 쐪kIq;- ګNK 6F 8!=0oP…U2h2`=evDeI;7 Sm`ٛ2*NCJ&3}L~Xk^d\1h#efG~榓X `Ojߧ߾F؀9zo@T18qe5en:,הy"~.h&܉b;ځzs9arZF%܎c"K`j]"Ff84aZ{8숬+=ruT* dGv@La-6vANۚJ\09,{f-#áS ] /8| 20 }m5eJ@ި(xceͯEfPG%\,偉-[(@(*>J9"ҡx[k<{g)Z38@y9ϙ]nM'\,K :=`fj, Q-LIc$DrObլer,"~6?:ϥW3Ɖaҗ?܍Zmb<㐥)bxye5 /pGJй!mH L]f!g/ <;͉&*9"diOj P%VAO b87Y(.ff2DX(Oqw<>8N]#7!x(fV>1q<ݹ}%,Z]l]a7֣:T}yQI;E<\pU!|r^0.[YfOJ^}Mrj0\ݱKfnxۨ+t"y63s Ǫl"Aϙ}u FwM p,0YW¨' Owo\e讒xS4j#L]NC:j.Ld\a> ;ʤ=|44^+gjKUI:11։KpA~2=\-QhwꥨūQ/\ 6I.KƨnPϛJgzWK6|Zz1^#MpY7[$-QЗ]S|%"g$^bz37H&D)!1i* /B<3WqG|yo=$w\xWxg2H6`yσw)t3oF2kD(N_B~ܸLď=trŠerŨ5]*ȖO%b6[~gW௯$( /jAaR | tK8LXxRB'+[NqH_Oy?R`:RL!׸\IRϡ(7q|dZeb:k؛:0aoa#@~t( M܍ !Rէa*>͡48][ sؑUY?4JkQN.)$Dxerw+A"0 SQ %Ȳ (j3Q+xޅ|W&Wct7I )P`Iн/[]ߎuR ŬRR1cNPkmD&E͢hmr.H *> #NJbd(⢌L 4j&Wd!an&MmJ2|39"TAoHV CX>MeFW)~IbRtM2t,mXl!~\5\TBўiمE:jXn-i^x$hYП[h}BRI:5JdG:*e:YUl[,jBŏrGRϢ̰lʘɖ%E3˚YJcU=vyAUUG_#SLQlWInapyfoFv/ӡT8GAh o10eph>!9)-Y#Fͪ ao(k|*N%Pi;v=sCD؋I')41Cr6(*Qlٸd8¦l8s p8S.~@-7%5zHUDco%E&e)  CM5dv0F cBf+FARn 6zA q(ڌƼ-.d\}\)Ya}\Lp1wܜPֶ*Dm-"7 DzX$[`jk9UEql!D[NuƖhӪzFQʽMF}(Rq`H4sm9v/62QqHŝrH_~.E2 F(b|>.fFb6 \pφ*p=ʤↁJLm{Dbrx.L>eqGN;u@=8I5C6[ݞj%JoMECvɐ ]#LZ@o{#Cd`ټtLf~۔ ZWY9{ˮsF|׉A uz*4d#l_z*n*f0 쵽b:kr;f:Q~cl%sϕ؝kH.ׂ?#}%ʕZfnbuSE# nYNbЎu_\yw6H:6ԙs߬L*0M+G$%U,u7a,jJ5%(jm(8+GhLCjF9UoVgc xU_7wR-jrWz‹~u>)'iE>SOulI3r JPTn`!.#)go*nt ېQV4o^84QeJCcէhxN~[6=݆Qc+³s֘S 9f7Y(ὅMguVğ5i c Q e͑Yx0 B zU qRQiնxT*jCs7Ә#3.(FcT6Y+gWVUo< ofl%d&Q{ ~}PlxWnsf$[EzEzKhMx/xC3OX? ͛_\ ή~o3y CV00B] 1YYPyT%n/L7XW[Kc`A7dRAJh\ӝnZ nZhLOly*jewZLW*Zk=wn"I p${~-L- i_tNqNrml8e{,xo2uPw3zf]O0;c09uZPعDŧ9Ts.mzeCrY4 ,-u̍wPSX-TA5@vSѿ)ot@ww;?:Gֻ-~&WOo˟OL/ͭάɒm&Fm2Z?j6 d8Q-$ FEM=48~A}J gt?a]/mJQ%3P[%ThRd < Yj,T D*(x4PO8 *h'Bx>(h'eGbDş&^{JNU_A=!_샪ɘKW=9ģIU Ga$«AaꛐaoQ9h[9;3Sng lڍ޾uzn|ŭ | jlZJžhvj_ڢpG.sǹ!ywJrXY&<8ģYC쇆q΢AUaBU*닂9},0&WqtC#nvFr=1j׻Sm{,}qG ա#MQ艰3* E8+陧Ơ>l zƠlk}/=% OB?RC<"9#2+9ej*0x4))F4Ľ NNt뙢 |~+!3pk*{k;HEr"ԫ(8Ӗ)qwpJ}lC|{Vm-hlExBŏrGR);kW /LHօ3Gq˸;i .ؗ&M-ԓs)\pꁒs +ԧiA=y e#Y 7>OTsx]e U#:{'(9FYr*MYq0ܖj˳Jܱc\~ψT ^m ҡsGU1<"4} Ìr3\P4`C3^tL Vp̤]=8 CCݑz$Tsx̤]59wujM3O R&s4i32'öL[we-9VfJ< د隊OsGƋ˷Sapk)Q"jW* e".%5KSǡSv}q:%|E[!i~toMH![;V,:?s &Hp:j*t޽=ԷߛW}&qMrx2TaK+,dS{m#)ݽhqOܮ*. Q<ٿD3mRTEGI:S#zR_>yxkGO"<1^ETg!WZyAړ*"pxZo:t'j}f~R̤qj'Q#"YKDEAt&"0,B:Ѕt w$HN@(wf# tr> UʌƳă׫o!y.)(!ff=W?Ԉ|fUE6-I>@o_VَW gͪ/A!Ig@|wl5w>]&J2(f ˽#/ =/C]P5N)5wn ӷa_p5$O-@#nMkJ_NA_צbѵpӥ]IDx];CcpB:1M7ѱ-א|:Ut=X{nDowTs ֯D_YT| =\n6uBAwx<ՌD)U}0sX.L9I-:a[M+ΔMR6Lw,ΛcOyX,>b}AE^PO{3mvܝi +(AfPO~|gE0Nq"%V@k+ uEbj Vt+U{]l_kZ崳0*|OsG !^KIQ.!X~ C59>@Y5w Csϕ\ayvZ YWL6— `{O\k=akyf5a܎b~ Z ZCڊhPrJbFtR6XQa΍6o2* < )}4fZl6N' OvLYBAWI)hO+pn ~h'-B͔QW\T⺏G|!^Ro֣j #83AJYLDg8꛳ ,jT5ߋ1pjv5ĻZZJFdެj4J1ջM"dwJ^3*2d9e$TNBַ%m&EARCDCwwN0g#3g^0N, c%4el͟jSguexW/{ڪhNouEh+RN,Qi?2B:X5>ZFUVPeʵg̥Kg\{$+8hZl;d+_0!߫?#ԳxzxWU`~9h7jy3Q`l;ٚؕo7 :|d7uA :dl}n\2+o泑5 ExK;>wƁ!_8zB KX0k^5!fC8 Y%OxT^d[oF)] V9z EyHe@/!ݝ?bX5jn8叫b4I4'h3;9s5wnP6arZ^_؉w(qO)nhX0a5\+F*,-r]Aڵ\+󲤄>,3i#yñ\go>i5e,APnƊkzn=P6$e Y7\QV0ە^\>G̷ nֲ8ezLr3O}=\۩ߍ,*Y09B}'\8=?Ow}aq6v0»U:8 _ê43%r+ڸ8lOciݨƊ%1p R*2;Z˭D튘nW:{[6kI=NvElL~IZrT5_Hhn#(eopo {@,p#2.(%?s8Yw+g1E[oG?SDiݨX_'v .J?# ?.*m/p,e3hA+穠Y /@_Io%tC<}PEU".cr^ /I>1_B~TT ӐڦF!`/M t)]ަnQB+#hW+@N/Aw(r/CV?CbE 28d FS& j# Kn!/ٌ[5B8Yn-m aM(^,3!* "d׹0t,Z ú E4\nZ+ߟrHabv.>ِ&wQq3O|vla(jPg LU.`Q%Em{!,,J|1xJW&"}w?vn?D͊x>zeR!L#4' pS_/Y?}HD2c2%(>N5sJ @V_UZ;qx \F+ %F,EXʺ @']=q\%*E dQl\g!kZ\5-i9rJWhq 3!LCN;u&JCC)HbCm|XY32bpxq mĆ/AÆ; Yas@j -)O_zzW!vA. B7Z=oy^[ľ@vAާ{po>}H4+`?dCY6Ob}׆Nvi%QZg>=l1yl/xf·іY@t{ɯIJʒ1 [Ne!| r:vBJS -|#le~Kgu^⫑ IǛݪX?o~aU\m8e7t 2eZ g8}>G ѷo8ALNdqp; <Y2DGZԦ8 d#/{JC]tY6e:;q> .X#R/~`/ ﹟2Ieu4Ÿ ӥʚBlPCHiw$f֮ʘ K{oM\N. 愷!Vťòx;G xFLrB3*2SY>.1>\d/G_D6oxu.V,ϡ<1Ek.tMJEOhm]_`'YN^]P'Է(:B=}}S=>r;ܿ(B<=Ri K9ڝYƶ#r.IB['[AGMOjmZṊFO!K%BiC 5T3sP Dm4 S/{SS:u^Dc9RN9MŝCVx|":Y$̉p21&i4\Or8yl}O}㐏++i'@,"{qdtnxV4K.#Z ,PeCSc~T]a<5 );Up)I4jm4!\5GR:}OյwG_rvg:#ZZEVdQ88y$Ƚ\! (}C=_@VR\(Ytwuշ,y; vlz!sw.wSؕK,i~@1%UzNd*>!IVwJ?p&/A+)ɧL: Lްfevd?8dvOs 3]Abq\m#:yA5ɔm;osKLvSB g՗#`ձV7//B.8%zQ)RN*17 < Y}`/[kTM*~sjxQx1Eo@֗w\M2pjK)*>͡R* g(ʞp)%1_h3:WxR҆b xg":g9RJ;d)]Kl|\h:Ufպg{VIsgէM@Ǝx3?%WPqXK/+u1^\Ό0d\Y <+y# Gxym˔%%  Y"D.*Fs*j$Bxbl&(Gwk OB>XY1_uXժ.))|Lt8J.B^TaRK/N_@V!~? -!<қE) Y_/Q))ͧmblQiہG 9Y2*q: ̢UX) )!F*-цQE[T ժ-*HY_N:hP8 aUk]0[چD(ؿ hm)5BFU]2U4*zd5\^2І| P}4[o8&|);Wmej+}0 |Y_(]][Rہ!+s7+7Ly UJW40(U(E0 гQtO' O ΃DgC<=+䂲X}n]r^Į\q^8p@/4x$ vI? DGU^1{˲ٷY//;v$Kcyb˨6 _AV'e3^LG޴R,[%&:!g4DŽTvYgx4i(]\s2w+vP9dyt,S,LdYq;2:_ ZG wȍu6*{)g]X3o4JvŽv{*Vf|q| b05ybaq>W]taxXAvmܛg ݗקrϗ~ہO o o^u ?~9q΂tSS։_c`o^?=^jv&BwVǁRicA1/nWέ%~[pW\®nx=otaպA: q;b tO>+ݤ%Rht׾>EvTgmA)#a|osaj\5j#- wx1-楺`8mo.7Y-.,\2 /9/eX'6_G4rw 1}qb_襨Ł6FxqWCo$m/o ;>+#}[id5V}?$}tV\AzǍgp*KpCbxt;xzT43ah cw>N-CߚjT*Y:$CRl g Ϩ h7U;b^1]Z7˵kYuK:fo NÐ5Q -, Y2j[;m]2kókwٲc͉>%ȗHz2c,V=w7ܓ7ާ徽e9ub!ok˜#AԄpr.aIF>lŢF%P"^|Y*^Qޅ3EB'2{P9ģHCE? LCN |{ KJg98 YjFr0O7\8;-ޑ^iȧyisCV5?3P/N'TjvyQfW9Ʊ&:q'~{H~E[o6Fk#_jLo$yi.m b L|omLYMlIpN灔Ǯ4-~[l/]0}cYZOw=Mz}BO[6k劙eOS] OPJN |uhUœP0fnZs`5;]5='n85"A(p+Cō@dsC<-gpFm$[,pKY:83 ω,.d)Kj644>] 3s m|Ffjχ؞XaEO{eQji襨磍Q/|> m6oKR[Lϧ6&ҍt֌ۉմϏ]>?֖&z χo%M[jՂ ¯or'-Z*A3ڳ{}kB8yLR8]G] 5{D8Y;~QWp;K2l_?2 ĕZĶJDA6Fi#'e$I¼XgTu ->+[ }FzDxz']^M8|j[dP-OmeAV=ىD;Mtm}Yop>M|p7a` t4 8RjDwD'%7brkﮱ'zM{W_)G.bnK 9EY05)iX2ݘiH) }} _4u׃(~]P)HUV ?+:2UYtA>Lk}OMeFNvWf(XvYmMs081xOG?Dy(_ʃ?I!VTDP#dz)5ѿ:>z%XE)\+fiϊ2K)H^~+P@xJmο-5g C8Ur@7nR$>ZUóޛ,'Pvp*[i),wtr˖W5jr%hހ~&f:cJ7fՌxk?QBWTg eGGG}S3mfY^ 8chP!@eG8(ƿ [l kG V ."Y<3eV/P&\L?G]3C bnޱF-S6#'>/ LKem`$K*?p'\Vk̨TXݰkFԻ6H$w@PZe&9w>x#%THM:Ğ/G#JGߴWmpTU g0΍m|gnKx qdư5#=SlKSm{3*,lVԃPi܋-v蝉S1wjUt m렳+T+Hgp$ 5e;`;1Gkkahu)NC'Rg]u :!<Nvߋ0z rȦAFS)Ay.~~##~d/[\MknNzka2Jqژ,ܤ |Ԭn}\;?4|9$$KI|@m |W֢6'Gn꛷r ~a*.*0n?{t)Dv-|%/GC̉6{:-vdл|^*flBͨ ำ|?L458 dD+=}0JvF=N%~*IC UC+&ԯkk#nي1qtߋ&{mS$Juhx`t <FxW-xk?!IͤUDpl?i1 e ǨLYUL07ʳGQw6TiB&GX4?>@e}W6ݒcZ_tlXe_Bhbdžqso7b8nZ\6w{TNU:CbPn }~W\>ł+S0I,\<w0/Bw*hb h BnƕnmZӼ":Q! ;ߕrP!< Yj|Id1( ^FtL,ٵ;!# !bKͰj5~O`;}`v+TCb# 7 <Yjk4.U!9ģh3'_d%vUF|O8 |OB>m<47+C_^|C_: v$4 ifxsL##yWx>ރ|o 1 f;Q3JRrYQ^1 ~kb vݪTXChTM**z$thCC<"gCRlW+Ze1K&F&GWcTXvϧJ&?T6Dy4H鄿*j-U:QXFp"<g1[s4b5wUVؑ ߢ|;rU3kWm"jL)Y}% [ wk67<{v>!.#H ѫ^1J4>žv ޺pTN"~(ə䏥AXy3%m[WQjX:$\\El,`jnY64j|*gP`p ׏2"/YAZ>Ы/%/Sn(=\,ys`89 R!WS,: K\d5ͷVdkFvjƪ;VxR=BܥSO+tgcʛm$//OYg ʻ}gXQ3ZMWQiՖCtH8ģ*qlZœB`fs l_UͲLc3(9UwI:TE=ݯ s`GxD x4ѤTTsi^ADQY&k.BVwPu࿄K*V,a3JvM:nHx %њ7^X_a<(!k[[o5k41jvST*V;iʤbƨXK؆g$tŭV=o9X{kkXt#?="f5-~[l_vAb+U\ZbI8 RC<#֞Iܾ͡isnWR!VQȣ%2]P6?!_+o*3ENXd ~DS&nsLnխD|vFl)HG[if;bӍ0?ާq>Ŧ:_:6]TB&H6|tR[֢qo6R*jl² q4i_Jv٪% 8#պL*lJkQc/7$+۝:YYmJK%z#6ƔѳC.sag9 P2'-s"~ZְY7KK"<13?ϩpCjډb8ܜ 7hqU=li]62`CF h. 7 Wl)( -+Gi#*~AņRN;BnnaUZ[͋x[m({ц,5qQMvM t\g:Ɩ*V16 D% >GNmApVܠ+bQ%[Ja8%u$V %[p{1[svƠN8I[ co,9(7 TD$z&29W9 i*g4&ہnw9}nvR6%b`C Zy:1 6;Tmh@ %Leݍ)iْI9Dk2sI*|/ kH>X⇂'As25W^Pb(Uz' Z@=Ō"Z0 9M ]nG[O5QECvɞ;wӲ'Ś!}| :PbaBUˬ?wA:F uQ?Th~9S& L!w1׬0`v|N1cH7fmݴY >i85"kjP)[L3b9e8\ ?g?fÙ_'ɦ ,kE&J6`LBUoFͳ*۬j>GGsyn9쑘-bFg{F%Dk"\NZL %XXz؉S.||VˍfX8$nd/ ZM 3Z>+=,j"&<>ʨkC<Ե8%&ކ|[:RQq @NVTǁDMs\<ƝP-5F2T9 ?Ka~-gr?ӳلuG<h%}Gl92Z/[⚹[껸O rݚ_*^/eicԋw%,m[[jT{h~Vf&KO~c~Q:vh>>}l2z )ΧeL2NfN}+N%]0}c)8JM7阵RlZa?HJ{oOI|)(Tx&)Ž4q]ΟgKTuMS”CܡlEw}D*PeNʸrOAfvU&gwkbqϯ.&TKY!@!r0q>6 |fg!6$ux=N) HPmvHGS*HȽ/P9#2EM/&Ob溮O$t[n3?Ɩ7 ԺQƘ7QkigE;lX}-OiٖjO;GF79(aؗ/P8ģI%r ދKm:z%JC UI/*jD%A`BŏrGR~S3k?q 3;VRlj#*qGRGiU:P~?~5`:ذ/ѹ;VM0gfP[MذˬvĎ kOD?bL6= :Gg8T#h1џ!7]qBM ۦEwB IE>oFnUE㮈dZmH~v85%qC8 <8ZqdJ ;K8zͲWnOsGnN63~¡b7+9p.6Y#~LC(FDƁȅw X\T2SSiڔIWts f# Ie_=[ˁPF寴ɾtIL>Ts>赙Pq' K^⚄vNB>??ȏDp#<ދR d]~'Du]"vIQگHFU5|Zޫ~KDyJ6E-hj:~y= "jXHmy=M[^o u"0,7 `}MAZ+g,SOyȭfi}Mqk*npkp٭O^q}M1 ׈`ׇB&eV&;SZ_@=kqaYKS0k݂Qg9+\VfYkA 3ן̜=n(P_S)v_%<&Aw hiRrGQ@>T|Cϰ* 'EG}NYDQ,3́Aj+cɮ r355o=Xk,tes) V0`IDU'BnY=Nxu +ںgbD*$*}SF+YhJz g8YjnJFBD*.*Z5F_c&cc2׳ף|&GJ51h">6r {pPzd3OX*ֲvge\QtjS'׊IX%~kY&؏}Er?Pۊ-Kt/` Ê8zk7R\SR-bD)!1*_xg',9ZnSB+zuFx_Ϫsr 3|06X_l-^.W={8jv6'xS,d9R[oJC<pMmD>R}%:8ƀW[ 2\uf'Ϻ#~}he@2ksڱd#V bĽWa _S ]ߴr[nm.z>7VCqXO pIO=ȴyqxHSqG!]9*Ndta~!.,2:jGR*C6/HmjҵBB:׳!ߖYչNl8K2g\Vvͻ+]URJƨtm\8zd;'Pmx}V%ͪ >e.֌Fv.楜?vl ZWl]k FE6=3xv[魿fr>rDh÷or|\Lj룑gv)/|[yZ:rѪb;֋N/=z_}oJFțzoT:~ ֏}}Q-aUMk*5?u5롵eW?n*_+.*97S6~ߧRj85Ilsop䔬Z_fk9=2W .suӬ[ugǩx`Pcoin/tests/0000755000176200001440000000000013527753030012351 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 0.0039062 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] 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [57] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 [64] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [71] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [78] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [85] 0.0019531 0.0039062 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 0.0039062 0.0039062 [106] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0039062 [113] 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 [120] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0039062 [127] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [134] 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 [141] 0.0039062 0.0039062 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [169] 0.0019531 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0019531 0.0019531 [190] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [197] 0.0039062 0.0039062 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 [204] 0.0039062 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0039062 [211] 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0039062 [218] 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 [225] 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 [232] 0.0039062 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 [239] 0.0039062 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0039062 [246] 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 0.0039062 0.0039062 [253] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [260] 0.0019531 0.0019531 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0019531 [281] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0039062 0.0039062 [309] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 [316] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [323] 0.0039062 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [330] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 [337] 0.0039062 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 [344] 0.0039062 0.0039062 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 0.0039062 0.0019531 [365] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [372] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [379] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [386] 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [393] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 [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 0.0039062 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] 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [57] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 [64] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [71] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [78] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [85] 0.0019531 0.0039062 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 0.0039062 0.0039062 [106] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0039062 [113] 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 [120] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0039062 [127] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [134] 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 [141] 0.0039062 0.0039062 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [169] 0.0019531 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0019531 0.0019531 [190] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [197] 0.0039062 0.0039062 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 [204] 0.0039062 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0039062 [211] 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0039062 [218] 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 [225] 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 0.0019531 [232] 0.0039062 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 [239] 0.0039062 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0039062 [246] 0.0039062 0.0019531 0.0039062 0.0019531 0.0039062 0.0039062 0.0039062 [253] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [260] 0.0019531 0.0019531 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0019531 [281] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 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 0.0039062 0.0019531 0.0039062 0.0039062 [309] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 [316] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [323] 0.0039062 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [330] 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 [337] 0.0039062 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 [344] 0.0039062 0.0039062 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 0.0039062 0.0019531 [365] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [372] 0.0019531 0.0019531 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 [379] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [386] 0.0019531 0.0039062 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 [393] 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0019531 0.0039062 [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 4.12 0.56 4.68 coin/tests/regtest_Ksample.R0000644000176200001440000002327213437154626015641 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 = "Fleming-Harrington", rho = 1) stopifnot(identical(lt@method, "K-Sample Fleming-Harrington 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/0000755000176200001440000000000013527753030014127 5ustar liggesuserscoin/tests/Examples/coin-Ex.Rout.save0000644000176200001440000026665413527753030017264 0ustar liggesusers R Under development (unstable) (2019-07-02 r76766) -- "Unsuffered Consequences" Copyright (C) 2019 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) > 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 > > ## 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 > > > > 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 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,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... > (l <- statistic(ct, type = "linear")) 1 2 3 1 1 0 1 2 0 2 0 3 1 0 1 > > ## ...and its expectation... > (El <- expectation(ct)) 1:1 2:1 3:1 1:2 2:2 3:2 1:3 2:3 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 0.6666667 3:3 0.6666667 > > ## ...and covariance > (Vl <- 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 > > ## The standardized contingency table... > (l - El) / sqrt(variance(ct)) 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 > > > > 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 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 > > > > ### *