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Type 'q()' to quit R. > ### Regression tests for the 2 sample problem, i.e., > ### testing the independence of a numeric variable > ### 'y' and a binary factor 'x' (possibly blocked) > > suppressWarnings(RNGversion("3.5.2")) > set.seed(290875) > library("coin") Loading required package: survival > isequal <- coin:::isequal > options(useFancyQuotes = FALSE) > > ### generate data > dat <- data.frame(x = gl(2, 50), y = rnorm(100), block = gl(5, 20))[sample(1:100, 75), ] > > > ### Wilcoxon Mann-Whitney Rank Sum Test > > ### asymptotic distribution > ptwo <- wilcox.test(y ~ x, data = dat, correct = FALSE, exact = FALSE)$p.value > pless <- wilcox.test(y ~ x, data = dat, alternative = "less", + correct = FALSE, exact = FALSE)$p.value > pgreater <- wilcox.test(y ~ x, data = dat, alternative = "greater", + correct = FALSE, exact = FALSE)$p.value > > stopifnot(isequal(pvalue(wilcox_test(y ~ x, data = dat)), ptwo)) > stopifnot(isequal(pvalue(wilcox_test(y ~ x, data = dat, alternative = "less")), + pless)) > stopifnot(isequal(pvalue(wilcox_test(y ~ x, data = dat, alternative = "greater")), + pgreater)) > > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo))), ptwo)) > ### check direct supply of a function via ytrafo > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = rank_trafo)), ptwo)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), + alternative = "less")), pless)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), + alternative = "greater")), pgreater)) > > ### exact distribution > ptwo <- wilcox.test(y ~ x, data = dat, exact = TRUE)$p.value > pless <- wilcox.test(y ~ x, data = dat, alternative = "less", exact = TRUE)$p.value > pgreater <- wilcox.test(y ~ x, data = dat, alternative = "greater", + exact = TRUE)$p.value > > stopifnot(isequal(pvalue(wilcox_test(y ~ x, data = dat, distribution = "exact")), + ptwo)) > stopifnot(isequal(pvalue(wilcox_test(y ~ x, data = dat, alternative = "less", + distribution = "exact")), pless)) > stopifnot(isequal(pvalue(wilcox_test(y ~ x, data = dat, alternative = "greater", + distribution = "exact")), pgreater)) > > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "exact", + ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo))), ptwo)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "exact", + ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), + alternative = "less")), pless)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "exact", + ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo), + alternative = "greater")), pgreater)) > > ### approximated distribution > rtwo <- pvalue(wilcox_test(y ~ x, data = dat, distribution = "approx")) / ptwo > rless <- pvalue(wilcox_test(y ~ x, data = dat, alternative = "less", + distribution = "approx")) / pless > rgreater <- pvalue(wilcox_test(y ~ x, data = dat, alternative = "greater", + distribution = "approx")) / pgreater > stopifnot(all(c(rtwo, rless, rgreater) > 0.9 & + c(rtwo, rless, rgreater) < 1.1)) > > ### add block examples > > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "asympt")) [1] 0.1794892 > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "approx")) [1] 0.1956 99 percent confidence interval: 0.1854798 0.2060117 > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "exact")) [1] 0.1847028 > > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "asympt", + alternative = "less")) [1] 0.08974461 > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "approx", + alternative = "less")) [1] 0.0885 99 percent confidence interval: 0.08133160 0.09606348 > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "exact", + alternative = "less")) [1] 0.09335664 > > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "asympt", + alternative = "greater")) [1] 0.9102554 > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "approx", + alternative = "greater")) [1] 0.9158 99 percent confidence interval: 0.9083975 0.9228033 > pvalue(wilcox_test(y ~ x | block, data = dat, distribution = "exact", + alternative = "greater")) [1] 0.9098776 > > ### sanity checks > try(wilcox_test(x ~ y, data = dat)) Error in check(object) : 'object' does not represent a two-sample problem (maybe the grouping variable is not a factor?) > try(wilcox_test(x ~ y | y, data = dat)) Error in .local(.Object, ...) : 'block' is not a factor > > > ### Ansari-Bradley Test > > ### asymptotic distribution > ptwo <- ansari.test(y ~ x, data = dat, correct = FALSE, exact = FALSE)$p.value > pless <- ansari.test(y ~ x, data = dat, alternative = "less", + correct = FALSE, exact = FALSE)$p.value > pgreater <- ansari.test(y ~ x, data = dat, alternative = "greater", + correct = FALSE, exact = FALSE)$p.value > > stopifnot(isequal(pvalue(ansari_test(y ~ x, data = dat)), ptwo)) > stopifnot(isequal(pvalue(ansari_test(y ~ x, data = dat, alternative = "less")), + pless)) > stopifnot(isequal(pvalue(ansari_test(y ~ x, data = dat, alternative = "greater")), + pgreater)) > > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = function(data) trafo(data, numeric_trafo = ansari_trafo))), ptwo)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = function(data) trafo(data, numeric_trafo = ansari_trafo), + alternative = "greater")), pless)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt", + ytrafo = function(data) trafo(data, numeric_trafo = ansari_trafo), + alternative = "less")), pgreater)) > > ### exact distribution > ptwo <- ansari.test(y ~ x, data = dat, exact = TRUE)$p.value > pless <- ansari.test(y ~ x, data = dat, alternative = "less", exact = TRUE)$p.value > pgreater <- ansari.test(y ~ x, data = dat, alternative = "greater", + exact = TRUE)$p.value > > ### : Definition of two-sided P-values! > (isequal(pvalue(ansari_test(y ~ x, data = dat, distribution = "exact")), + ptwo)) [1] 0.2125862712 [1] 0.213574129 [1] FALSE > stopifnot(isequal(pvalue(ansari_test(y ~ x, data = dat, alternative = "less", + distribution = "exact")), pless)) > stopifnot(isequal(pvalue(ansari_test(y ~ x, data = dat, alternative = "greater", + distribution = "exact")), pgreater)) > > ### : Definition of two-sided P-values! > (isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "exact", + ytrafo = function(data) trafo(data, numeric_trafo = ansari_trafo))), ptwo)) [1] 0.2125862712 [1] 0.213574129 [1] FALSE > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "exact", + ytrafo = function(data) trafo(data, numeric_trafo = ansari_trafo), + alternative = "greater")), pless)) > stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "exact", + ytrafo = function(data) trafo(data, numeric_trafo = ansari_trafo), + alternative = "less")), pgreater)) > > ### approximated distribution > rtwo <- pvalue(ansari_test(y ~ x, data = dat, distribution = "approx")) / ptwo > rless <- pvalue(ansari_test(y ~ x, data = dat, alternative = "less", + distribution = "approx")) / pless > rgreater <- pvalue(ansari_test(y ~ x, data = dat, alternative = "greater", + distribution = "approx")) / pgreater > ### ??? > (all(c(rtwo, rless, rgreater) > 0.9 & + c(rtwo, rless, rgreater) < 1.1)) [1] TRUE > > ### add block examples > > ### sanity checks > try(ansari_test(x ~ y, data = dat)) Error in check(object) : 'object' does not represent a K-sample problem (maybe the grouping variable is not a factor?) > try(ansari_test(x ~ y | y, data = dat)) Error in .local(.Object, ...) : 'block' is not a factor > > > ### One-way Test > oneway_test(y ~ x, dat = dat) Asymptotic Two-Sample Fisher-Pitman Permutation Test data: y by x (1, 2) Z = -0.77735, p-value = 0.4369 alternative hypothesis: true mu is not equal to 0 > oneway_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Fisher-Pitman Permutation Test data: y by x (1, 2) Z = -0.77735, p-value = 0.2185 alternative hypothesis: true mu is less than 0 > oneway_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Fisher-Pitman Permutation Test data: y by x (1, 2) Z = -0.77735, p-value = 0.7815 alternative hypothesis: true mu is greater than 0 > > > ### Normal Scores Test > normal_test(y ~ x, dat = dat) Asymptotic Two-Sample van der Waerden (Normal Quantile) Test data: y by x (1, 2) Z = -0.85965, p-value = 0.39 alternative hypothesis: true mu is not equal to 0 > normal_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample van der Waerden (Normal Quantile) Test data: y by x (1, 2) Z = -0.85965, p-value = 0.195 alternative hypothesis: true mu is less than 0 > normal_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample van der Waerden (Normal Quantile) Test data: y by x (1, 2) Z = -0.85965, p-value = 0.805 alternative hypothesis: true mu is greater than 0 > > > ### Median Test > median_test(y ~ x, dat = dat) Asymptotic Two-Sample Brown-Mood Median Test data: y by x (1, 2) Z = -0.8015, p-value = 0.4228 alternative hypothesis: true mu is not equal to 0 > median_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Brown-Mood Median Test data: y by x (1, 2) Z = -0.8015, p-value = 0.2114 alternative hypothesis: true mu is less than 0 > median_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Brown-Mood Median Test data: y by x (1, 2) Z = -0.8015, p-value = 0.7886 alternative hypothesis: true mu is greater than 0 > > > ### Savage Test > savage_test(y ~ x, dat = dat) Asymptotic Two-Sample Savage Test data: y by x (1, 2) Z = -1.0738, p-value = 0.2829 alternative hypothesis: true mu is not equal to 0 > savage_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Savage Test data: y by x (1, 2) Z = -1.0738, p-value = 0.1414 alternative hypothesis: true mu is less than 0 > savage_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Savage Test data: y by x (1, 2) Z = -1.0738, p-value = 0.8586 alternative hypothesis: true mu is greater than 0 > > > ### Taha Test > taha_test(y ~ x, dat = dat) Asymptotic Two-Sample Taha Test data: y by x (1, 2) Z = -1.0835, p-value = 0.2786 alternative hypothesis: true ratio of scales is not equal to 1 > taha_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Taha Test data: y by x (1, 2) Z = -1.0835, p-value = 0.1393 alternative hypothesis: true ratio of scales is less than 1 > taha_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Taha Test data: y by x (1, 2) Z = -1.0835, p-value = 0.8607 alternative hypothesis: true ratio of scales is greater than 1 > > > ### Klotz Test > klotz_test(y ~ x, dat = dat) Asymptotic Two-Sample Klotz Test data: y by x (1, 2) Z = -0.83541, p-value = 0.4035 alternative hypothesis: true ratio of scales is not equal to 1 > klotz_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Klotz Test data: y by x (1, 2) Z = -0.83541, p-value = 0.2017 alternative hypothesis: true ratio of scales is less than 1 > klotz_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Klotz Test data: y by x (1, 2) Z = -0.83541, p-value = 0.7983 alternative hypothesis: true ratio of scales is greater than 1 > > > ### Mood Test > mood_test(y ~ x, dat = dat) Asymptotic Two-Sample Mood Test data: y by x (1, 2) Z = -1.1859, p-value = 0.2357 alternative hypothesis: true ratio of scales is not equal to 1 > mood_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Mood Test data: y by x (1, 2) Z = -1.1859, p-value = 0.1178 alternative hypothesis: true ratio of scales is less than 1 > mood_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Mood Test data: y by x (1, 2) Z = -1.1859, p-value = 0.8822 alternative hypothesis: true ratio of scales is greater than 1 > > > ### Fligner-Killeen Test > fligner_test(y ~ x, dat = dat) Asymptotic Two-Sample Fligner-Killeen Test data: y by x (1, 2) Z = -0.94847, p-value = 0.3429 alternative hypothesis: true ratio of scales is not equal to 1 > fligner_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Fligner-Killeen Test data: y by x (1, 2) Z = -0.94847, p-value = 0.1714 alternative hypothesis: true ratio of scales is less than 1 > fligner_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Fligner-Killeen Test data: y by x (1, 2) Z = -0.94847, p-value = 0.8286 alternative hypothesis: true ratio of scales is greater than 1 > > > ### Conover-Iman Test > conover_test(y ~ x, dat = dat) Asymptotic Two-Sample Conover-Iman Test data: y by x (1, 2) Z = -0.80308, p-value = 0.4219 alternative hypothesis: true ratio of scales is not equal to 1 > conover_test(y ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Conover-Iman Test data: y by x (1, 2) Z = -0.80308, p-value = 0.211 alternative hypothesis: true ratio of scales is less than 1 > conover_test(y ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Conover-Iman Test data: y by x (1, 2) Z = -0.80308, p-value = 0.789 alternative hypothesis: true ratio of scales is greater than 1 > > > ### Logrank Test > logrank_test(Surv(y) ~ x, dat = dat) Asymptotic Two-Sample Logrank Test data: Surv(y) by x (1, 2) Z = -1.0738, p-value = 0.2829 alternative hypothesis: true theta is not equal to 1 > logrank_test(Surv(y) ~ x, dat = dat, alternative = "less") Asymptotic Two-Sample Logrank Test data: Surv(y) by x (1, 2) Z = -1.0738, p-value = 0.1414 alternative hypothesis: true theta is less than 1 > logrank_test(Surv(y) ~ x, dat = dat, alternative = "greater") Asymptotic Two-Sample Logrank Test data: Surv(y) by x (1, 2) Z = -1.0738, p-value = 0.8586 alternative hypothesis: true theta is greater than 1 > > > ### confidence intervals, cf Bauer 1972 > > ### Location Tests > location <- data.frame(y = c(6, 20, 27, 38, 46, 51, 54, 57, + 10, 12, 15, 21, 32, 40, 41, 45), + x = gl(2, 8)) > > ### Wilcoxon Rank-Sum Test > wt <- wilcox_test(y ~ x, data = location, conf.int = TRUE, + distribution = "exact") > wt Exact Wilcoxon-Mann-Whitney Test data: y by x (1, 2) Z = 1.2603, p-value = 0.2345 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -7 31 sample estimates: difference in location 11.5 > ci <- confint(wt) > wt0 <- wilcox.test(y ~ x, data = location, conf.int = TRUE) > stopifnot(isequal(wt0$confint, ci$confint)) > stopifnot(isequal(wt0$estimate, ci$estimate)) > > wtx <- wilcox_test(y ~ x, data = location, conf.int = TRUE, + distribution = "approximate") > confint(wtx) 95 percent confidence interval: -9 33 sample estimates: difference in location 11.5 > > wta <- wilcox_test(y ~ x, data = location, conf.int = TRUE) > confint(wta) 95 percent confidence interval: -7 31 sample estimates: difference in location 11.20138 > > ### Normal Scores Test > nt <- normal_test(y ~ x, data = location, conf.int = TRUE, + distribution = "exact") > nt Exact Two-Sample van der Waerden (Normal Quantile) Test data: y by x (1, 2) Z = 1.2278, p-value = 0.2275 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -6 30 sample estimates: difference in location 11 > ci <- confint(nt) > stopifnot(isequal(ci$conf.int, c(-6, 30))) > stopifnot(isequal(ci$estimate, 11)) > > ntx <- normal_test(y ~ x, data = location, conf.int = TRUE, + distribution = "approximate") > confint(ntx) 95 percent confidence interval: -7 30 sample estimates: difference in location 11 > > nta <- normal_test(y ~ x, data = location, conf.int = TRUE) > confint(nta) 95 percent confidence interval: -7 30 sample estimates: difference in location 11 > > ### Median Test > mt <- median_test(y ~ x, data = location, conf.int = TRUE, + distribution = "exact") > mt Exact Two-Sample Brown-Mood Median Test data: y by x (1, 2) Z = 0.96825, p-value = 0.6193 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -21 42 sample estimates: difference in location 15.5 > confint(mt) 95 percent confidence interval: -21 42 sample estimates: difference in location 15.5 > > mtx <- median_test(y ~ x, data = location, conf.int = TRUE, + distribution = "approximate") > confint(mtx) 95 percent confidence interval: -21 42 sample estimates: difference in location 15.5 > > mta <- median_test(y ~ x, data = location, conf.int = TRUE) > confint(mta) 95 percent confidence interval: -21 42 sample estimates: difference in location 12.6 > > ### Savage Test > st <- savage_test(y ~ x, data = location, conf.int = TRUE, + distribution = "exact") > st Exact Two-Sample Savage Test data: y by x (1, 2) Z = 1.6095, p-value = 0.1091 alternative hypothesis: true mu is not equal to 0 95 percent confidence interval: -5 30 sample estimates: difference in location 12 > confint(st) 95 percent confidence interval: -5 30 sample estimates: difference in location 12 > > stx <- savage_test(y ~ x, data = location, conf.int = TRUE, + distribution = "approximate") > confint(stx) 95 percent confidence interval: -5 30 sample estimates: difference in location 12 > > sta <- savage_test(y ~ x, data = location, conf.int = TRUE) > confint(sta) 95 percent confidence interval: -6 31 sample estimates: difference in location 12 > > > ### Scale Tests > scale <- data.frame(y = c(-101, -35, -13, 10, 130, 236, 370, 556, + -145, -140, -40, -30, 2, 27, 68, 290), + x = gl(2, 8)) > > ### Ansari-Bradley Test > at <- ansari_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "exact") > at Exact Two-Sample Ansari-Bradley Test data: y by x (1, 2) Z = -0.21129, p-value = 0.9173 alternative hypothesis: true ratio of scales is not equal to 1 98.8 percent confidence interval: 0.1470588 20.5925926 sample estimates: ratio of scales 1.221264 > ci <- confint(at) > stopifnot(isequal(ci$conf.int, c(10, 556) / c(68, 27))) > stopifnot(isequal(ci$estimate, mean(c(35 / 30, 370 / 290)))) > > atx <- ansari_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "approximate") > confint(atx) 98.8 percent confidence interval: 0.09285714 20.59259259 sample estimates: ratio of scales 1.221264 > > ata <- ansari_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988) > confint(ata) # wrong in < 1.3-0 98.8 percent confidence interval: 0.1470588 20.5925926 sample estimates: ratio of scales 1.236009 > > ### Taha Test > tt <- taha_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.51, + distribution = "exact") > tt Exact Two-Sample Taha Test data: y by x (1, 2) Z = 1.2612, p-value = 0.2157 alternative hypothesis: true ratio of scales is not equal to 1 51 percent confidence interval: 4.814815 278.000000 sample estimates: ratio of scales 13.7037 > confint(tt) 51 percent confidence interval: 4.814815 278.000000 sample estimates: ratio of scales 13.7037 > > ttx <- taha_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.51, + distribution = "approximate") > confint(ttx) 51 percent confidence interval: 4.814815 278.000000 sample estimates: ratio of scales 13.7037 > > tta <- taha_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.51) > confint(tta) # wrong in < 1.3-0 51 percent confidence interval: 4.814815 278.000000 sample estimates: ratio of scales 13.7037 > > ### Klotz Test > kt <- klotz_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "exact") > kt Exact Two-Sample Klotz Test data: y by x (1, 2) Z = 0.092301, p-value = 0.9243 alternative hypothesis: true ratio of scales is not equal to 1 98.8 percent confidence interval: 0.1470588 13.7037037 sample estimates: ratio of scales 1.221264 > confint(kt) 98.8 percent confidence interval: 0.1470588 13.7037037 sample estimates: ratio of scales 1.221264 > > ktx <- klotz_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "approximate") > confint(ktx) 98.8 percent confidence interval: 0.1470588 13.7037037 sample estimates: ratio of scales 1.221264 > > kta <- klotz_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988) > ## confint(kta) # Mac M1 issue # wrong in < 1.3-0 > > ### Mood Test > mt <- mood_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "exact") > mt Exact Two-Sample Mood Test data: y by x (1, 2) Z = 0.15374, p-value = 0.9021 alternative hypothesis: true ratio of scales is not equal to 1 98.8 percent confidence interval: 0.1470588 13.7037037 sample estimates: ratio of scales 1.221264 > confint(mt) 98.8 percent confidence interval: 0.1470588 13.7037037 sample estimates: ratio of scales 1.221264 > > mtx <- mood_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "approximate") > confint(mtx) 98.8 percent confidence interval: 0.09285714 13.70370370 sample estimates: ratio of scales 1.221264 > > mta <- mood_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988) > confint(mta) # wrong in < 1.3-0 98.8 percent confidence interval: 0.09285714 20.59259259 sample estimates: ratio of scales 1.267119 > > ### Fligner-Killeen Test > ft <- fligner_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "exact") > ft Exact Two-Sample Fligner-Killeen Test data: y by x (1, 2) Z = 1.4442, p-value = 0.1545 alternative hypothesis: true ratio of scales is not equal to 1 98.8 percent confidence interval: 0.6965517 13.7037037 sample estimates: ratio of scales 2.525 > confint(ft) 98.8 percent confidence interval: 0.6965517 13.7037037 sample estimates: ratio of scales 2.525 > > ftx <- fligner_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "approximate") > confint(ftx) 98.8 percent confidence interval: 0.6965517 13.7037037 sample estimates: ratio of scales 2.525 > > fta <- fligner_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988) > confint(fta) # wrong in < 1.3-0 98.8 percent confidence interval: 0.4761905 10.6875000 sample estimates: ratio of scales 2.290076 > > ### Conover-Iman Test > ct <- conover_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "exact") > ct Exact Two-Sample Conover-Iman Test data: y by x (1, 2) Z = 1.5314, p-value = 0.1304 alternative hypothesis: true ratio of scales is not equal to 1 98.8 percent confidence interval: 0.6965517 13.7037037 sample estimates: ratio of scales 2.525 > confint(ct) 98.8 percent confidence interval: 0.6965517 13.7037037 sample estimates: ratio of scales 2.525 > > ctx <- conover_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988, + distribution = "approximate") > confint(ctx) 98.8 percent confidence interval: 0.6965517 13.7037037 sample estimates: ratio of scales 2.525 > > cta <- conover_test(y ~ x, data = scale, conf.int = TRUE, conf.level = 0.988) > confint(cta) # wrong in < 1.3-0 98.8 percent confidence interval: 0.5493881 10.6576087 sample estimates: ratio of scales 2.455078 > > > ### ties handling > y1 <- c(14, 18, 2, 4, -5, 14, -3, -1, 1, 6, 3, 3) > x1 <- c(8, 26, -7, -1, 2, 9, 0, -4, 13, 3, 3, 4) > pvalue(wilcoxsign_test(y1 ~ x1, alternative = "greater", + distribution = "exact", zero.method = "Wilcoxon")) [1] 0.4741211 > pvalue(wilcoxsign_test(y1 ~ x1, alternative = "greater", + distribution = "exact")) [1] 0.4609375 > > > ### Weighted logrank tests > > ### Collett (2003, p. 9, Table 1.3) > prostatic <- data.frame( + time = c(13, 52, 6, 40, 10, 7, 66, 10, 10, 14, + 16, 4, 65, 5, 11, 10, 15, 5, 76, 56, + 88, 24, 51, 4, 40, 8, 18, 5, 16, 50, + 40, 1, 36, 5, 10, 91, 18, 1, 18, 6, + 1, 23, 15, 18, 12, 12, 17, 3), + event = c(1, 0, 1, 1, 1, 0, 1, 0, 1, 1, + 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, + 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, + 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, + 1, 1, 1, 1, 0, 1, 1, 0), + Hb = c(14.6, 12.0, 11.4, 10.2, 13.2, 9.9, 12.8, 14.0, 7.5, 10.6, + 11.2, 10.1, 6.6, 9.7, 8.8, 9.6, 13.0, 10.4, 14.0, 12.5, + 14.0, 12.4, 10.1, 6.5, 12.8, 8.2, 14.4, 10.2, 10.0, 7.7, + 5.0, 9.4, 11.0, 9.0, 14.0, 11.0, 10.8, 5.1, 13.0, 5.1, + 11.3, 14.6, 8.8, 7.5, 4.9, 5.5, 7.5, 10.2)) > prostatic <- within(prostatic, + group <- factor(Hb > 11.0, labels = as.roman(1:2))) > > ### Leton and Zuluaga (2005, p. 384, Table 9) > > ### Gehan > lt <- logrank_test(Surv(time, event) ~ group, data = prostatic, + type = "Gehan") > stopifnot(identical(lt@method, "Two-Sample Gehan-Breslow Test")) > isequal(round(statistic(lt)^2, 4), 3.8400) [1] TRUE > isequal(round(pvalue(lt), 4), 0.0500) [1] TRUE > > ### Peto-Peto > lt <- logrank_test(Surv(time, event) ~ group, data = prostatic, + type = "Peto-Peto") > stopifnot(identical(lt@method, "Two-Sample Peto-Peto Test")) > isequal(round(statistic(lt)^2, 4), 4.0657) [1] TRUE > isequal(round(pvalue(lt), 4), 0.0438) [1] TRUE > > ### Prentice > lt <- logrank_test(Surv(time, event) ~ group, data = prostatic, + type = "Prentice") > stopifnot(identical(lt@method, "Two-Sample Prentice Test")) > isequal(round(statistic(lt)^2, 4), 4.1229) [1] TRUE > isequal(round(pvalue(lt), 4), 0.0423) [1] TRUE > > ### LR Altshuler > lt <- logrank_test(Surv(time, event) ~ group, data = prostatic) > stopifnot(identical(lt@method, "Two-Sample Logrank Test")) > isequal(round(statistic(lt)^2, 4), 4.4343) [1] TRUE > isequal(round(pvalue(lt), 4), 0.0352) [1] TRUE > > ### Tarone-Ware > lt <- logrank_test(Surv(time, event) ~ group, data = prostatic, + type = "Tarone-Ware") > stopifnot(identical(lt@method, "Two-Sample Tarone-Ware Test")) > isequal(round(statistic(lt)^2, 4), 4.3443) [1] TRUE > isequal(round(pvalue(lt), 4), 0.0371) [1] TRUE > > > ### Paired tests > > ### sanity check > set.seed(123) > x <- factor(rep(1:2, 15)) > y <- as.integer(round((rnorm(30) + as.numeric(x)) * 1000)) > id <- gl(15, 2) > try(symmetry_test(y ~ x | id, distribution = "exact", paired = TRUE)) Error in SR_shift_1sample(object, fact = attr(int, "fact")) : cannot compute exact distribution with negative scores > > proc.time() user system elapsed 4.46 0.29 4.73