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> ### > attach(NULL, name = "CheckExEnv") > assign(".CheckExEnv", as.environment(2), pos = length(search())) # base > ## add some hooks to label plot pages for base and grid graphics > setHook("plot.new", ".newplot.hook") > setHook("persp", ".newplot.hook") > setHook("grid.newpage", ".gridplot.hook") > > assign("cleanEx", + function(env = .GlobalEnv) { + rm(list = ls(envir = env, all.names = TRUE), envir = env) + RNGkind("default", "default") + set.seed(1) + options(warn = 1) + delayedAssign("T", stop("T used instead of TRUE"), + assign.env = .CheckExEnv) + delayedAssign("F", stop("F used instead of FALSE"), + assign.env = .CheckExEnv) + sch <- search() + newitems <- sch[! sch %in% .oldSearch] + for(item in rev(newitems)) + eval(substitute(detach(item), list(item=item))) + missitems <- .oldSearch[! .oldSearch %in% sch] + if(length(missitems)) + warning("items ", paste(missitems, collapse=", "), + " have been removed from the search path") + }, + env = .CheckExEnv) > assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now > assign("ptime", proc.time(), env = .CheckExEnv) > grDevices::postscript("exactRankTests-Examples.ps") > assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv) > options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly")) > options(warn = 1) > library('exactRankTests') > > assign(".oldSearch", search(), env = .CheckExEnv) > assign(".oldNS", loadedNamespaces(), env = .CheckExEnv) > cleanEx(); ..nameEx <- "ASAT" > > ### * ASAT > > flush(stderr()); flush(stdout()) > > ### Name: ASAT > ### Title: Toxicological Study on Female Wistar Rats > ### Aliases: ASAT > ### Keywords: datasets > > ### ** Examples > > > data(ASAT) > # does not really look symmetric > > plot(asat ~ group, data=ASAT) > > # proof-of-safety based on ration of medians > pos <- wilcox.exact(I(log(asat)) ~ group, data = ASAT, alternative = "less", + conf.int=TRUE) > > # one-sided confidence set. Safety cannot be concluded since the effect of > # the compound exceeds 20% of the control median > exp(pos$conf.int) [1] 0.000000 1.337778 attr(,"conf.level") [1] 0.95 > > > > cleanEx(); ..nameEx <- "ansari.exact" > > ### * ansari.exact > > flush(stderr()); flush(stdout()) > > ### Name: ansari.exact > ### Title: Ansari-Bradley Test > ### Aliases: ansari.exact ansari.exact.default ansari.exact.formula > ### Keywords: htest > > ### ** Examples > > ## Hollander & Wolfe (1973, p. 86f): > ## Serum iron determination using Hyland control sera > ramsay <- c(111, 107, 100, 99, 102, 106, 109, 108, 104, 99, + 101, 96, 97, 102, 107, 113, 116, 113, 110, 98) > jung.parekh <- c(107, 108, 106, 98, 105, 103, 110, 105, 104, + 100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99) > ansari.test(ramsay, jung.parekh) Warning in ansari.test.default(ramsay, jung.parekh) : cannot compute exact p-value with ties Ansari-Bradley test data: ramsay and jung.parekh AB = 185.5, p-value = 0.1815 alternative hypothesis: true ratio of scales is not equal to 1 > ansari.exact(ramsay, jung.parekh) Ansari-Bradley test data: ramsay and jung.parekh AB = 185.5, p-value = 0.1881 alternative hypothesis: true ratio of scales is not equal to 1 > > ansari.exact(rnorm(20), rnorm(20, 0, 2), conf.int = TRUE) Ansari-Bradley test data: rnorm(20) and rnorm(20, 0, 2) AB = 250, p-value = 0.03133 alternative hypothesis: true ratio of scales is not equal to 1 95 percent confidence interval: 0.2979059 0.9800937 sample estimates: ratio of scales 0.5315074 > > > > cleanEx(); ..nameEx <- "bloodp" > > ### * bloodp > > flush(stderr()); flush(stdout()) > > ### Name: bloodp > ### Title: Diastolic Blood Pressure > ### Aliases: bloodp > ### Keywords: datasets > > ### ** Examples > > data(bloodp) > > # Permutation test > > perm.test(bp ~ group, data=bloodp) 2-sample Permutation Test data: bp by group T = 402, p-value = 0.1040 alternative hypothesis: true mu is not equal to 0 > perm.test(bp ~ group, data=bloodp, alternative="greater") 2-sample Permutation Test data: bp by group T = 402, p-value = 0.05641 alternative hypothesis: true mu is greater than 0 > perm.test(bp ~ group, data=bloodp, exact=FALSE) Asymptotic 2-sample Permutation Test data: bp by group T = 402, p-value = 0.1070 alternative hypothesis: true mu is not equal to 0 > > # Wilcoxon-Mann-Whitney test > > wilcox.exact(bp ~ group, data=bloodp, conf.int=TRUE, alternative="l") Exact Wilcoxon rank sum test data: bp by group W = 35, p-value = 0.9648 alternative hypothesis: true mu is less than 0 95 percent confidence interval: -Inf 20 sample estimates: difference in location 9.5 > wilcox.exact(bp ~ group, data=bloodp, conf.int=TRUE) Exact Wilcoxon rank sum test data: bp by group W = 35, p-value = 0.0989 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -4 22 sample estimates: difference in location 9.5 > > # compute the v.d. Waerden test > > sc <- cscores(bloodp$bp, type="NormalQuantile") > X <- sum(sc[bloodp$group == "group2"]) > round(pperm(X, sc, 11), 4) [1] 0.0462 > round(pperm(X, sc, 11, simulate=TRUE), 4) [1] 0.0469 > round(pperm(X, sc, 11, alternative="two.sided"), 4) [1] 0.0799 > round(pperm(X, sc, 11, alternative="two.sided", simulate=TRUE), 4) [1] 0.0798 > > # use scores mapped into integers (cf. dperm) > > sc <- cscores(bloodp$bp, type="NormalQuantile", int=TRUE) > X <- sum(sc[bloodp$group == "group2"]) > round(pperm(X, sc, 11), 4) [1] 0.0462 > round(pperm(X, sc, 11, alternative="two.sided"), 4) [1] 0.0799 > > > > > cleanEx(); ..nameEx <- "cscores" > > ### * cscores > > flush(stderr()); flush(stdout()) > > ### Name: cscores > ### Title: Computation of Scores > ### Aliases: cscores cscores.default cscores.Surv cscores.factor > ### Keywords: misc > > ### ** Examples > > > y <- rnorm(50) > # v.d. Waerden scores > nq <- cscores(y, type="Normal", int=TRUE) > # quantile for m=20 observations in the first group > qperm(0.1, nq, 20) [1] -102 > > > > > cleanEx(); ..nameEx <- "dperm" > > ### * dperm > > flush(stderr()); flush(stdout()) > > ### Name: dperm > ### Title: Distribution of One and Two Sample Permutation Tests > ### Aliases: dperm pperm qperm rperm > ### Keywords: distribution > > ### ** Examples > > > # exact one-sided p-value of the Wilcoxon test for a tied sample > > x <- c(0.5, 0.5, 0.6, 0.6, 0.7, 0.8, 0.9) > y <- c(0.5, 1.0, 1.2, 1.2, 1.4, 1.5, 1.9, 2.0) > r <- cscores(c(x,y), type="Wilcoxon") > pperm(sum(r[seq(along=x)]), r, 7) [1] 0.004351204 > > # Compare the exact algorithm as implemented in ctest and the > # Shift-Algorithm by Streitberg & Roehmel for untied samples > > # Wilcoxon: > > n <- 10 > x <- rnorm(n, 2) > y <- rnorm(n, 3) > r <- cscores(c(x,y), type="Wilcoxon") > > # exact distribution using the Shift-Algorithm > > dwexac <- dperm((n*(n+1)/2):(n^2 + n*(n+1)/2), r, n) > sum(dwexac) # should be something near 1 :-) [1] 1 > > # exact distribution using dwilcox > > dw <- dwilcox(0:(n^2), n, n) > > # compare the two distributions: > > plot(dw, dwexac, main="Wilcoxon", xlab="dwilcox", ylab="dperm") > # should give a "perfect" line > > # Wilcoxon signed rank test > > n <- 10 > x <- rnorm(n, 5) > y <- rnorm(n, 5) > r <- cscores(abs(x - y), type="Wilcoxon") > pperm(sum(r[x - y > 0]), r, length(r)) [1] 0.2783203 > wilcox.test(x,y, paired=TRUE, alternative="less") Wilcoxon signed rank test data: x and y V = 21, p-value = 0.2783 alternative hypothesis: true mu is less than 0 > psignrank(sum(r[x - y > 0]), length(r)) [1] 0.2783203 > > # Ansari-Bradley > > n <- 10 > x <- rnorm(n, 2, 1) > y <- rnorm(n, 2, 2) > > # exact distribution using the Shift-Algorithm > > sc <- cscores(c(x,y), type="Ansari") > dabexac <- dperm(0:(n*(2*n+1)/2), sc, n) > sum(dabexac) [1] 1 > > # real scores are allowed (but only result in an approximation) > # e.g. v.d. Waerden test > > n <- 10 > x <- rnorm(n) > y <- rnorm(n) > scores <- cscores(c(x,y), type="NormalQuantile") > X <- sum(scores[seq(along=x)]) # <- v.d. Waerden normal quantile statistic > > # critical value, two-sided test > > abs(qperm(0.025, scores, length(x))) Warning in findfact(scores - min(scores) + 1, m, tol) : cannot hold tol, tolerance: 0.010292 [1] 3.871345 > > # p-values > > p1 <- pperm(X, scores, length(x), alternative="two.sided") Warning in findfact(scores - min(scores) + 1, m, tol) : cannot hold tol, tolerance: 0.010292 > > # generate integer valued scores with the same shape as normal quantile > # scores, this no longer v.d.Waerden, but something very similar > > scores <- cscores(c(x,y), type="NormalQuantile", int=TRUE) > > X <- sum(scores[seq(along=x)]) > p2 <- pperm(X, scores, length(x), alternative="two.sided") > > # compare p1 and p2 > > p1 - p2 [1] -0.01441902 > > > > > cleanEx(); ..nameEx <- "ears" > > ### * ears > > flush(stderr()); flush(stdout()) > > ### Name: ears > ### Title: Survival of Ventilating Tubes > ### Aliases: ears > ### Keywords: datasets > > ### ** Examples > > data(ears) > if (require(survival, quietly=TRUE)) { + ls <- cscores(Surv(ears$left, ears$lcens), int=TRUE) + perm.test(ls ~ group, data=ears) + } Loading required package: splines 2-sample Permutation Test data: ls by group T = 748, p-value = 0.01222 alternative hypothesis: true mu is not equal to 0 > > > > > cleanEx(); ..nameEx <- "glioma" > > ### * glioma > > flush(stderr()); flush(stdout()) > > ### Name: glioma > ### Title: Malignant Glioma Pilot Study > ### Aliases: glioma > ### Keywords: datasets > > ### ** Examples > > data(glioma) > > if(require(survival, quietly = TRUE)) { + + par(mfrow=c(1,2)) + + # Grade III glioma + g3 <- glioma[glioma$Histology == "Grade3",] + + # Plot Kaplan-Meier curves + plot(survfit(Surv(Survival, Cens) ~ Group, data=g3), + main="Grade III Glioma", lty=c(2,1), + legend.text=c("Control", "Treated"), + legend.bty=1, ylab="Probability", + xlab="Survival Time in Month") + + # log-rank test + survdiff(Surv(Survival, Cens) ~ Group, data=g3) + + # permutation test with integer valued log-rank scores + lsc <- cscores(Surv(g3$Survival, g3$Cens), int=TRUE) + perm.test(lsc ~ Group, data=g3) + + # permutation test with real valued log-rank scores + lsc <- cscores(Surv(g3$Survival, g3$Cens), int=FALSE) + tr <- (g3$Group == "RIT") + T <- sum(lsc[tr]) + pperm(T, lsc, sum(tr), alternative="tw") + pperm(T, lsc, sum(tr), alternative="tw", simulate=TRUE) + + # Grade IV glioma + gbm <- glioma[glioma$Histology == "GBM",] + + # Plot Kaplan-Meier curves + plot(survfit(Surv(Survival, Cens) ~ Group, data=gbm), + main="Grade IV Glioma", lty=c(2,1), + legend.text=c("Control", "Treated"), + legend.bty=1, legend.pos=1, ylab="Probability", + xlab="Survival Time in Month") + + # log-rank test + survdiff(Surv(Survival, Cens) ~ Group, data=gbm) + + # permutation test with integer valued log-rank scores + lsc <- cscores(Surv(gbm$Survival, gbm$Cens), int=TRUE) + perm.test(lsc ~ Group, data=gbm) + + # permutation test with real valued log-rank scores + lsc <- cscores(Surv(gbm$Survival, gbm$Cens), int=FALSE) + tr <- (gbm$Group == "RIT") + T <- sum(lsc[tr]) + pperm(T, lsc, sum(tr), alternative="tw") + pperm(T, lsc, sum(tr), alternative="tw", simulate=TRUE) + } Loading required package: splines Warning in findfact(scores - min(scores) + 1, m, tol) : cannot hold tol, tolerance: 0.010019 Warning in findfact(scores - min(scores) + 1, m, tol) : cannot hold tol, tolerance: 0.010067 [1] 1e-04 > > > > graphics::par(get("par.postscript", env = .CheckExEnv)) > cleanEx(); ..nameEx <- "globulin" > > ### * globulin > > flush(stderr()); flush(stdout()) > > ### Name: globulin > ### Title: Differences in Globulin Fraction in Two Groups > ### Aliases: globulin > ### Keywords: datasets > > ### ** Examples > > data(globulin) > perm.test(gfrac ~ group, data=globulin, conf.int=TRUE) 2-sample Permutation Test data: gfrac by group T = 331, p-value = 0.1475 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -8.50 1.25 > > > > cleanEx(); ..nameEx <- "irank" > > ### * irank > > flush(stderr()); flush(stdout()) > > ### Name: irank > ### Title: Integer Ranks > ### Aliases: irank > ### Keywords: univar > > ### ** Examples > > x <- rnorm(10) > irank(x) [1] 3 5 1 10 6 2 7 9 8 4 > rank(x) [1] 3 5 1 10 6 2 7 9 8 4 > x <- c(1,2,3,3,0) > irank(x) [1] 2 3 5 5 1 > rank(x) [1] 2.0 3.0 4.5 4.5 1.0 > > > > cleanEx(); ..nameEx <- "lungcancer" > > ### * lungcancer > > flush(stderr()); flush(stdout()) > > ### Name: lungcancer > ### Title: Lung Cancer Clinical Trial > ### Aliases: lungcancer > ### Keywords: datasets > > ### ** Examples > > data(lungcancer) > attach(lungcancer) > > # round logrank scores > scores <- cscores.Surv(cbind(time, cens)) > T <- sum(scores[group=="newdrug"]) > mobs <- sum(group=="newdrug") > system.time(prob <- pperm(T, scores, m=mobs, al="le")) [1] 0.02 0.00 0.02 0.00 0.00 > prob [1] 0.000999001 > pperm(T, scores, m=mobs, al="tw") [1] 0.000999001 > pperm(T, scores, m=mobs, al="tw", simulate=TRUE) [1] 0.0011 > > # map into integers, faster > scores <- cscores.Surv(cbind(time, cens), int=TRUE) > T <- sum(scores[group=="newdrug"]) > mobs <- sum(group=="newdrug") > system.time(prob <- pperm(T, scores, m=mobs, al="le")) [1] 0 0 0 0 0 > prob [1] 0.000999001 > pperm(T, scores, m=mobs, al="tw") [1] 0.000999001 > pperm(T, scores, m=mobs, al="tw", simulate=TRUE) [1] 9e-04 > > detach(lungcancer) > > > > > cleanEx(); ..nameEx <- "neuropathy" > > ### * neuropathy > > flush(stderr()); flush(stdout()) > > ### Name: neuropathy > ### Title: Acute Painful Diabetic Neuropathy > ### Aliases: neuropathy > ### Keywords: datasets > > ### ** Examples > > data(neuropathy) > # compare with Table 2 of Conover & Salsburg (1988) > wilcox.exact(pain ~ group, data=neuropathy, alternative="less") Exact Wilcoxon rank sum test data: pain by group W = 357, p-value = 0.1654 alternative hypothesis: true mu is less than 0 > css <- cscores(neuropathy$pain, type="ConSal") > pperm(sum(css[neuropathy$group=="control"]),css, + m=sum(neuropathy$group=="control")) Warning in findfact(scores - min(scores) + 1, m, tol) : cannot hold tol, tolerance: 0.047123 [1] 0.03075730 > > > > > cleanEx(); ..nameEx <- "ocarcinoma" > > ### * ocarcinoma > > flush(stderr()); flush(stdout()) > > ### Name: ocarcinoma > ### Title: Ovarian Carcinoma > ### Aliases: ocarcinoma > ### Keywords: datasets > > ### ** Examples > > > data(ocarcinoma) > attach(ocarcinoma) > # compute integer valued logrank scores > logrsc <- cscores.Surv(cbind(time, cens), int=TRUE) > # the test statistic > lgT <- sum(logrsc[stadium == "II"]) > # p-value > round(pperm(lgT, logrsc, m=sum(stadium=="II"), al="tw"), 4) [1] 0.0191 > > # compute logrank scores and simulate p-value > logrsc <- cscores.Surv(cbind(time, cens), int=FALSE) > # the test statistic > lgT <- sum(logrsc[stadium == "II"]) > # p-value > round(pperm(lgT, logrsc, m=sum(stadium=="II"), al="tw", simulate=TRUE), 4) [1] 0.0179 > > > > > cleanEx(); ..nameEx <- "perm.test" > > ### * perm.test > > flush(stderr()); flush(stdout()) > > ### Name: perm.test > ### Title: One and Two Sample Permutation Test > ### Aliases: perm.test perm.test.default perm.test.formula > ### Keywords: htest > > ### ** Examples > > > # Example from Gardner & Altman (1989), p. 30 > # two treatments A and B, 1 means improvement, 0 means no improvement > # confidence sets cf. R\"ohmel (1996) > > A <- c(rep(1, 61), rep(0, 19)) > B <- c(rep(1, 45), rep(0, 35)) > perm.test(A, B, conf.int=TRUE, exact=TRUE) 2-sample Permutation Test data: A and B T = 61, p-value = 0.01180 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: 0.05263158 0.34285714 > > # one-sample AIDS data (differences only), Methta and Patel (2001), > # Table 8.1 page 181 > > data(sal) > attach(sal) > ppdiff <- pre - post > detach(sal) > > # p-values in StatXact == 0.0011 one-sided, 0.0021 two.sided, page 183 > > perm.test(ppdiff) 1-sample Permutation Test data: ppdiff T = 4831, p-value = 0.002136 alternative hypothesis: true mu is not equal to 0 > perm.test(ppdiff, alternative="less") 1-sample Permutation Test data: ppdiff T = 4831, p-value = 0.999 alternative hypothesis: true mu is less than 0 > perm.test(ppdiff, exact=FALSE) Asymptotic 1-sample Permutation Test data: ppdiff T = 4831, p-value = 0.08779 alternative hypothesis: true mu is not equal to 0 > > > > > cleanEx(); ..nameEx <- "rotarod" > > ### * rotarod > > flush(stderr()); flush(stdout()) > > ### Name: rotarod > ### Title: Rotating Rats Data > ### Aliases: rotarod > ### Keywords: datasets > > ### ** Examples > > data(rotarod) > wilcox.exact(time ~ group, data=rotarod, alternative="g") Exact Wilcoxon rank sum test data: time by group W = 102, p-value = 0.01863 alternative hypothesis: true mu is greater than 0 > wilcox.exact(time ~ group, data=rotarod, conf.int=TRUE) Exact Wilcoxon rank sum test data: time by group W = 102, p-value = 0.03727 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: 0 137 sample estimates: difference in location 14.5 > wilcox.exact(time ~ group, data=rotarod, exact=FALSE) Asymptotic Wilcoxon rank sum test data: time by group W = 102, p-value = 0.01473 alternative hypothesis: true mu is not equal to 0 > # the permutation test > perm.test(time ~ group, data=rotarod) 2-sample Permutation Test data: time by group T = 3600, p-value = 0.03727 alternative hypothesis: true mu is not equal to 0 > perm.test(time ~ group, data=rotarod, exact=FALSE) Asymptotic 2-sample Permutation Test data: time by group T = 3600, p-value = 0.0324 alternative hypothesis: true mu is not equal to 0 > > > > cleanEx(); ..nameEx <- "sal" > > ### * sal > > flush(stderr()); flush(stdout()) > > ### Name: sal > ### Title: Serum Antigen Level > ### Aliases: sal > ### Keywords: datasets > > ### ** Examples > > data(sal) > attach(sal) > > wilcox.exact(pre, post, paired=TRUE, conf.int=TRUE) Exact Wilcoxon signed rank test data: pre and post V = 124, p-value = 0.002136 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: 54 292 sample estimates: (pseudo)median 137.75 > wilcox.exact(pre,post, paired=TRUE, conf.int=TRUE, exact=FALSE) Asymptotic Wilcoxon signed rank test data: pre and post V = 124, p-value = 0.003783 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: 54.49998 281.50005 sample estimates: (pseudo)median 137.2646 > > detach(sal) > > > > > cleanEx(); ..nameEx <- "wilcox.exact" > > ### * wilcox.exact > > flush(stderr()); flush(stdout()) > > ### Name: wilcox.exact > ### Title: Wilcoxon Rank Sum and Signed Rank Tests > ### Aliases: wilcox.exact wilcox.exact.default wilcox.exact.formula > ### Keywords: htest > > ### ** Examples > > ## One-sample test. > ## Hollander & Wolfe (1973), 29f. > ## Hamilton depression scale factor measurements in 9 patients with > ## mixed anxiety and depression, taken at the first (x) and second > ## (y) visit after initiation of a therapy (administration of a > ## tranquilizer). > x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) > y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) > wilcox.exact(x, y, paired = TRUE, alternative = "greater") Exact Wilcoxon signed rank test data: x and y V = 40, p-value = 0.01953 alternative hypothesis: true mu is greater than 0 > wilcox.exact(y - x, alternative = "less") # The same. Exact Wilcoxon signed rank test data: y - x V = 5, p-value = 0.01953 alternative hypothesis: true mu is less than 0 > > ## Two-sample test. > ## Hollander & Wolfe (1973), 69f. > ## Permeability constants of the human chorioamnion (a placental > ## membrane) at term (x) and between 12 to 26 weeks gestational > ## age (y). The alternative of interest is greater permeability > ## of the human chorioamnion for the term pregnancy. > x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46) > y <- c(1.15, 0.88, 0.90, 0.74, 1.21) > wilcox.exact(x, y, alternative = "g") # greater Exact Wilcoxon rank sum test data: x and y W = 35, p-value = 0.1272 alternative hypothesis: true mu is greater than 0 > > ## Formula interface. > data(airquality) > boxplot(Ozone ~ Month, data = airquality) > wilcox.exact(Ozone ~ Month, data = airquality, + subset = Month %in% c(5, 8)) Exact Wilcoxon rank sum test data: Ozone by Month W = 127.5, p-value = 6.109e-05 alternative hypothesis: true mu is not equal to 0 > > # Hollander & Wolfe, p. 39, results p. 40 and p. 53 > > x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30) > y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29) > > wilcox.exact(y,x, paired=TRUE, conf.int=TRUE) Exact Wilcoxon signed rank test data: y and x V = 5, p-value = 0.03906 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -0.786 -0.010 sample estimates: (pseudo)median -0.46 > > # Hollander & Wolfe, p. 110, results p. 111 and p. 126 > > x <- c(0.8, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46) > y <- c(1.15, 0.88, 0.90, 0.74, 1.21) > > wilcox.exact(y,x, conf.int=TRUE) Exact Wilcoxon rank sum test data: y and x W = 15, 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 > > > > > ### *