R Under development (unstable) (2026-03-10 r89593 ucrt) -- "Unsuffered Consequences"
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> ### 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")
Loading required package: survival
> 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)$p.value
> 
> stopifnot(isequal(pvalue(kruskal_test(y ~ x, data = dat)), ptwo))
> 
> stopifnot(isequal(pvalue(oneway_test(y ~ x, data = dat, distribution = "asympt",
+     ytrafo = function(data) trafo(data, numeric_trafo = rank_trafo))), ptwo))
> 
> ### approximated distribution
> rtwo <- pvalue(kruskal_test(y ~ x, data = dat, distribution = "approx")) / ptwo
> stopifnot(all(rtwo > 0.9 &
+               rtwo < 1.1))
> 
> ### <FIXME> add block examples </FIXME>
> 
> ### sanity checks
> try(kruskal_test(x ~ y, data = dat))
Error in check(object) : 
  'object' does not represent a K-sample problem (maybe the grouping variable is not a factor?)
> try(kruskal_test(x ~ y | y, data = dat))
Error in .local(.Object, ...) : 'block' is not a factor
> 
> 
> ### Fligner-Killeen Test
> 
> ### asymptotic distribution
> ptwo <- fligner.test(y ~ x, data = dat)$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))
> 
> ### <FIXME> add block examples </FIXME>
> 
> ### sanity checks
> try(fligner_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(fligner_test(x ~ y | y, data = dat))
Error in .local(.Object, ...) : 'block' is not a factor
> 
> 
> ### One-way Test
> oneway_test(y ~ x, data = dat)

	Asymptotic K-Sample Fisher-Pitman Permutation Test

data:  y by x (1, 2, 3, 4)
chi-squared = 3.2735, df = 3, p-value = 0.3513

> 
> oneway_test(y ~ ordered(x), data = dat)

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.1278, p-value = 0.8983
alternative hypothesis: two.sided

> oneway_test(y ~ ordered(x), data = dat,
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.1278, p-value = 0.4492
alternative hypothesis: less

> oneway_test(y ~ ordered(x), data = dat,
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.1278, p-value = 0.5508
alternative hypothesis: greater

> 
> oneway_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.1278, p-value = 0.8983
alternative hypothesis: two.sided

> oneway_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.1278, p-value = 0.4492
alternative hypothesis: less

> oneway_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.1278, p-value = 0.5508
alternative hypothesis: greater

> 
> 
> ### Normal Scores Test
> normal_test(y ~ x, data = dat)

	Asymptotic K-Sample van der Waerden (Normal Quantile) Test

data:  y by x (1, 2, 3, 4)
chi-squared = 3.3466, df = 3, p-value = 0.3412

> 
> normal_test(y ~ ordered(x), data = dat)

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.3135, p-value = 0.7539
alternative hypothesis: two.sided

> normal_test(y ~ ordered(x), data = dat,
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.3135, p-value = 0.377
alternative hypothesis: less

> normal_test(y ~ ordered(x), data = dat,
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.3135, p-value = 0.623
alternative hypothesis: greater

> 
> normal_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.3135, p-value = 0.7539
alternative hypothesis: two.sided

> normal_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.3135, p-value = 0.377
alternative hypothesis: less

> normal_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.3135, p-value = 0.623
alternative hypothesis: greater

> 
> 
> ### Median Test
> median_test(y ~ x, data = dat)

	Asymptotic K-Sample Brown-Mood Median Test

data:  y by x (1, 2, 3, 4)
chi-squared = 0.85938, df = 3, p-value = 0.8352

> 
> median_test(y ~ ordered(x), data = dat)

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.65897, p-value = 0.5099
alternative hypothesis: two.sided

> median_test(y ~ ordered(x), data = dat,
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.65897, p-value = 0.255
alternative hypothesis: less

> median_test(y ~ ordered(x), data = dat,
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = -0.65897, p-value = 0.745
alternative hypothesis: greater

> 
> median_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.65897, p-value = 0.5099
alternative hypothesis: two.sided

> median_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.65897, p-value = 0.255
alternative hypothesis: less

> median_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = -0.65897, p-value = 0.745
alternative hypothesis: greater

> 
> 
> ### Savage Test
> savage_test(y ~ x, data = dat)

	Asymptotic K-Sample Savage Test

data:  y by x (1, 2, 3, 4)
chi-squared = 2.3638, df = 3, p-value = 0.5004

> 
> savage_test(y ~ ordered(x), data = dat)

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.7774
alternative hypothesis: two.sided

> savage_test(y ~ ordered(x), data = dat,
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.6113
alternative hypothesis: less

> savage_test(y ~ ordered(x), data = dat,
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by ordered(x) (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.3887
alternative hypothesis: greater

> 
> savage_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.7774
alternative hypothesis: two.sided

> savage_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.6113
alternative hypothesis: less

> savage_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+             alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  y by x (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.3887
alternative hypothesis: greater

> 
> 
> ### Taha Test
> taha_test(y ~ x, data = dat)

	Asymptotic K-Sample Taha Test

data:  y by x (1, 2, 3, 4)
chi-squared = 2.8264, df = 3, p-value = 0.4192

> 
> try(taha_test(y ~ ordered(x), data = dat))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(taha_test(y ~ ordered(x), data = dat,
+               alternative = "less"))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(taha_test(y ~ ordered(x), data = dat,
+               alternative = "greater"))
Error in check(object) : 'ordered(x)' is an ordered factor
> 
> try(taha_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))))
Error in check(object) : 'x' is an ordered factor
> try(taha_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+               alternative = "less"))
Error in check(object) : 'x' is an ordered factor
> try(taha_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+               alternative = "greater"))
Error in check(object) : 'x' is an ordered factor
> 
> 
> ### Klotz Test
> klotz_test(y ~ x, data = dat)

	Asymptotic K-Sample Klotz Test

data:  y by x (1, 2, 3, 4)
chi-squared = 7.0047, df = 3, p-value = 0.07175

> 
> try(klotz_test(y ~ ordered(x), data = dat))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(klotz_test(y ~ ordered(x), data = dat,
+                alternative = "less"))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(klotz_test(y ~ ordered(x), data = dat,
+                alternative = "greater"))
Error in check(object) : 'ordered(x)' is an ordered factor
> 
> try(klotz_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))))
Error in check(object) : 'x' is an ordered factor
> try(klotz_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+                alternative = "less"))
Error in check(object) : 'x' is an ordered factor
> try(klotz_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+                alternative = "greater"))
Error in check(object) : 'x' is an ordered factor
> 
> 
> ### Mood Test
> mood_test(y ~ x, data = dat)

	Asymptotic K-Sample Mood Test

data:  y by x (1, 2, 3, 4)
chi-squared = 7.3257, df = 3, p-value = 0.06221

> 
> try(mood_test(y ~ ordered(x), data = dat))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(mood_test(y ~ ordered(x), data = dat,
+               alternative = "less"))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(mood_test(y ~ ordered(x), data = dat,
+               alternative = "greater"))
Error in check(object) : 'ordered(x)' is an ordered factor
> 
> try(mood_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))))
Error in check(object) : 'x' is an ordered factor
> try(mood_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+               alternative = "less"))
Error in check(object) : 'x' is an ordered factor
> try(mood_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+               alternative = "greater"))
Error in check(object) : 'x' is an ordered factor
> 
> 
> ### Ansari-Bradley Test
> ansari_test(y ~ x, data = dat)

	Asymptotic K-Sample Ansari-Bradley Test

data:  y by x (1, 2, 3, 4)
chi-squared = 6.9382, df = 3, p-value = 0.07389

> 
> try(ansari_test(y ~ ordered(x), data = dat))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(ansari_test(y ~ ordered(x), data = dat,
+                 alternative = "less"))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(ansari_test(y ~ ordered(x), data = dat,
+                 alternative = "greater"))
Error in check(object) : 'ordered(x)' is an ordered factor
> 
> try(ansari_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))))
Error in check(object) : 'x' is an ordered factor
> try(ansari_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+                 alternative = "less"))
Error in check(object) : 'x' is an ordered factor
> try(ansari_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+                 alternative = "greater"))
Error in check(object) : 'x' is an ordered factor
> 
> 
> ### Conover-Iman Test
> conover_test(y ~ x, data = dat)

	Asymptotic K-Sample Conover-Iman Test

data:  y by x (1, 2, 3, 4)
chi-squared = 4.8413, df = 3, p-value = 0.1838

> 
> try(conover_test(y ~ ordered(x), data = dat))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(conover_test(y ~ ordered(x), data = dat,
+                  alternative = "less"))
Error in check(object) : 'ordered(x)' is an ordered factor
> try(conover_test(y ~ ordered(x), data = dat,
+                  alternative = "greater"))
Error in check(object) : 'ordered(x)' is an ordered factor
> 
> try(conover_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8))))
Error in check(object) : 'x' is an ordered factor
> try(conover_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+                  alternative = "less"))
Error in check(object) : 'x' is an ordered factor
> try(conover_test(y ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+                  alternative = "greater"))
Error in check(object) : 'x' is an ordered factor
> 
> 
> ### Logrank Test
> logrank_test(Surv(y) ~ x, data = dat)

	Asymptotic K-Sample Logrank Test

data:  Surv(y) by x (1, 2, 3, 4)
chi-squared = 2.3638, df = 3, p-value = 0.5004

> 
> logrank_test(Surv(y) ~ ordered(x), data = dat)

	Asymptotic Linear-by-Linear Association Test

data:  Surv(y) by ordered(x) (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.7774
alternative hypothesis: two.sided

> logrank_test(Surv(y) ~ ordered(x), data = dat,
+              alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  Surv(y) by ordered(x) (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.6113
alternative hypothesis: less

> logrank_test(Surv(y) ~ ordered(x), data = dat,
+              alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  Surv(y) by ordered(x) (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.3887
alternative hypothesis: greater

> 
> logrank_test(Surv(y) ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)))

	Asymptotic Linear-by-Linear Association Test

data:  Surv(y) by x (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.7774
alternative hypothesis: two.sided

> logrank_test(Surv(y) ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+              alternative = "less")

	Asymptotic Linear-by-Linear Association Test

data:  Surv(y) by x (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.6113
alternative hypothesis: less

> logrank_test(Surv(y) ~ x, data = dat, scores = list(x = c(2, 4, 6, 8)),
+              alternative = "greater")

	Asymptotic Linear-by-Linear Association Test

data:  Surv(y) by x (1 < 2 < 3 < 4)
Z = 0.28273, p-value = 0.3887
alternative hypothesis: 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)
[1] TRUE
> isequal(round(pvalue(lt), 4), 0.1643)
[1] TRUE
> 
> ### Peto-Peto, X^2_SPP
> lt <- logrank_test(Surv(time, event) ~ group, data = leukemia,
+                    type = "Peto-Peto")
> stopifnot(identical(lt@method, "K-Sample Peto-Peto Test"))
> stopifnot(all(round(-statistic(lt, "linear"), 3) == c(4.171, -2.582, -1.589)))
> isequal(round(statistic(lt), 3), 3.527)
[1] TRUE
> isequal(round(pvalue(lt), 4), 0.1715)
[1] TRUE
> 
> ### 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)
[1] TRUE
> isequal(round(pvalue(lt), 4), 0.1621)
[1] TRUE
> 
> ### 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)
[1] TRUE
> isequal(round(pvalue(lt), 4), 0.1485)
[1] TRUE
> 
> ### 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)
[1] TRUE
> isequal(round(pvalue(lt), 4), 0.1285)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
   2.23    0.40    2.56