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Showing content from http://cran.rstudio.com/web/packages/rJava/../Deducer/../brunnermunzel/vignettes/usage.html below:

Usage of brunnermunzel package

In this section, we will use sample data from 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)

For formula interface, data was converted to data.frame.

dat <- data.frame(
    value = c(x, y),
    group = factor(rep(c("x", "y"), c(length(x), length(y))),
                   levels = c("x", "y")))

library(dplyr)
dat %>%
    group_by(group) %>%
    summarize_all(list(mean = mean, median = median))
#> # A tibble: 2 x 3
#>   group  mean median
#>   <fct> <dbl>  <dbl>
#> 1 x      1.77   1.68
#> 2 y      1.33   1.06

library(brunnermunzel)

brunnermunzel.test(x, y)
#> 
#>  Brunner-Munzel Test
#> 
#> data:  x and y
#> Brunner-Munzel Test Statistic = -1.4673, df = 15.147, p-value = 0.1628
#> 95 percent confidence interval:
#>  -0.02962941  0.59753064
#> sample estimates:
#> P(X<Y)+.5*P(X=Y) 
#>        0.2839506

brunnermunzel.test(value ~ group, data = dat)
#> 
#>  Brunner-Munzel Test
#> 
#> data:  value by group
#> Brunner-Munzel Test Statistic = -1.4673, df = 15.147, p-value = 0.1628
#> 95 percent confidence interval:
#>  -0.02962941  0.59753064
#> sample estimates:
#> P(X<Y)+.5*P(X=Y) 
#>        0.2839506

To perform permuted Brunner-Munzel test, use brunnermunzel.test with “perm = TRUE” option, or brunnermunzel.permutation.test function. This “perm” option is used in also formula interface, matrix, and table.

When perm is TRUE, brunnermunzel.test calls brunnermunzel.permutation.test in internal.

brunnermunzel.test(x, y, perm = TRUE)
#> 
#>  permuted Brunner-Munzel Test
#> 
#> data:  x and y
#> p-value = 0.1581
#> sample estimates:
#> P(X<Y)+.5*P(X=Y) 
#>        0.2839506

brunnermunzel.permutation.test(x, y)
#> 
#>  permuted Brunner-Munzel Test
#> 
#> data:  x and y
#> p-value = 0.1581
#> sample estimates:
#> P(X<Y)+.5*P(X=Y) 
#>        0.2839506

Because statistics in all combinations are calculated in permuted Brunner-Munzel test (\({}_{n_{x}+n_{y}}C_{n_{x}}\) where \(n_{x}\) and \(n_{y}\) are sample size of \(x\) and \(y\), respectively), it takes a long time to obtain results.

Therefore, when sample size is too large [the number of combination is more than 40116600 (\(=\) choose(28, 14))], it switches to Brunner-Munzel test automatically.

# sample size is 30
brunnermunzel.permutation.test(1:15, 3:17)
#> Warning in brunnermunzel.permutation.test.default(1:15, 3:17): Sample number is too large. Using 'brunnermunzel.test'
#> 
#>  Brunner-Munzel Test
#> 
#> data:  x and y
#> Brunner-Munzel Test Statistic = 1.1973, df = 28, p-value = 0.2412
#> 95 percent confidence interval:
#>  0.4115330 0.8373559
#> sample estimates:
#> P(X<Y)+.5*P(X=Y) 
#>        0.6244444

When you want to perform permuted Brunner-Munzel test regardless sample size, you add “force = TRUE” option to brunnermunzel.permutation test.

brunnermunzel.permutation.test(1:15, 3:17, force = TRUE)
#>
#>  permuted Brunner-Munzel Test
#>
#> data:  1:15 and 3:17
#> p-value = 0.2341

brunnermunzel.test also can use “alternative” option as well as t.test and wilcox.test functions.

To test whether the average rank of group \(x\) is greater than that of group \(y\), alternative = "greater" option is added. In contrast, to test whether the average rank of group \(x\) is lesser than that of group \(y\), alternative = "less" option is added.

The results of Brunner-Munzel test and Wilcoxon sum-rank test (Mann-Whitney test) with alternative = "greater" option are shown. In this case, median of \(x\) is 1.68, and median of \(y\) is 1.06.

brunnermunzel.test(x, y, alternative = "greater")
#> 
#>  Brunner-Munzel Test
#> 
#> data:  x and y
#> Brunner-Munzel Test Statistic = -1.4673, df = 15.147, p-value = 0.08138
#> 95 percent confidence interval:
#>  -0.02962941  0.59753064
#> sample estimates:
#> P(X<Y)+.5*P(X=Y) 
#>        0.2839506

wilcox.test(x, y, alternative = "greater")
#> Warning in wilcox.test.default(x, y, alternative = "greater"): cannot compute
#> exact p-value with ties
#> 
#>  Wilcoxon rank sum test with continuity correction
#> 
#> data:  x and y
#> W = 58, p-value = 0.06646
#> alternative hypothesis: true location shift is greater than 0

When using formula, brunnermunzel.test with alternative = "greater" option tests an alternative hypothesis “1st level is greater than 2nd level”.

In contrast, brunnermunzel.test with alternative = "less" option tests an alternative hypothesis “1st level is lesser than 2nd level”.

dat$group
#>  [1] x x x x x x x x x y y y y y y y y y
#> Levels: x y

brunnermunzel.test(value ~ group, data = dat, alternative = "greater")$p.value
#> [1] 0.08137809

wilcox.test(value ~ group, data = dat, alternative = "greater")$p.value
#> Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
#> compute exact p-value with ties
#> [1] 0.06645973

brunnermunzel.test(x, y, alternative = "less")$p.value
#> [1] 0.9186219

wilcox.test(x, y, alternative = "less")$p.value
#> Warning in wilcox.test.default(x, y, alternative = "less"): cannot compute exact
#> p-value with ties
#> [1] 0.9442044

Normally, brunnermunzel.test and brunnermunzel.permutation test return the estimate \(P(X<Y) + 0.5 \times P(X=Y)\). When ‘est = "difference"’ option is used, these functions return mean difference [\(P(X<Y) - P(X>Y)\)] in estimate and confidence interval.

Note that \(P(X<Y) - P(X>Y) = 2p - 1\) when \(p = P(X<Y) + 0.5 \times P(X=Y)\).

This change is proposed by Dr. Julian D. Karch.

brunnermunzel.test(x, y, est = "difference")
#> 
#>  Brunner-Munzel Test
#> 
#> data:  x and y
#> Brunner-Munzel Test Statistic = -1.4673, df = 15.147, p-value = 0.1628
#> 95 percent confidence interval:
#>  -1.0592588  0.1950613
#> sample estimates:
#> P(X<Y)-P(X>Y) 
#>    -0.4320988

brunnermunzel.permutation.test(x, y, est = "difference")
#> 
#>  permuted Brunner-Munzel Test
#> 
#> data:  x and y
#> p-value = 0.1581
#> sample estimates:
#> P(X<Y)-P(X>Y) 
#>    -0.4320988

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