Usage of functions in brunnermunzel package
Default and Formula class
Sample data
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
Analysis
analysis with Brunner-Munzel test
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)
#> 0.2839506analysis with permuted Brunner-Munzel test
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)
#> 0.2839506Because 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)
#> 0.6244444using force option
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 = 0.2341using alternative option
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 0When 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$group
#> [1] x x x x x x x x x y y y y y y y y y
#> Levels: x ybrunnermunzel.test(value ~ group, data = dat, alternative = "greater")$p.value
#> [1] 0.08137809
wilcox.test(value ~ group, data = dat, alternative = "greater")$p.value
#> Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
#> compute exact p-value with ties
#> [1] 0.06645973brunnermunzel.test(x, y, alternative = "less")$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] 0.9442044using est option
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)
#> -0.4320988Matrix and Table class
In some case, data is provided as aggregated table. Both
brunnermunzel.test and
brunnermunzel.permutation.test accept data of
matirix and table class.
| Normal | Moderate | Severe | |
|---|---|---|---|
| A | 5 | 3 | 2 |
| B | 1 | 3 | 6 |
Sample data
dat1 <- matrix(c(5, 3, 2, 1, 3, 6), nr = 2, byrow = TRUE)
dat2 <- as.table(dat1)
colnames(dat2) <- c("Normal", "Moderate", "Severe")dat1 # matrix class
#> [,1] [,2] [,3]
#> [1,] 5 3 2
#> [2,] 1 3 6
dat2 # table class
#> Normal Moderate Severe
#> A 5 3 2
#> B 1 3 6Analysis
analysis with Brunner-Munzel test
brunnermunzel.test(dat1)
#>
#> Brunner-Munzel Test
#>
#> data: Group1 and Group2
#> Brunner-Munzel Test Statistic = 2.4447, df = 17.394, p-value = 0.02542
#> 95 percent confidence interval:
#> 0.5359999 0.9840001
#> sample estimates:
#> P(X<Y)+.5*P(X=Y)
#> 0.76
brunnermunzel.test(dat2)
#>
#> Brunner-Munzel Test
#>
#> data: A and B
#> Brunner-Munzel Test Statistic = 2.4447, df = 17.394, p-value = 0.02542
#> 95 percent confidence interval:
#> 0.5359999 0.9840001
#> sample estimates:
#> P(X<Y)+.5*P(X=Y)
#> 0.76analysis with permuted Brunner-Munzel test
brunnermunzel.permutation.test(dat1)
#>
#> permuted Brunner-Munzel Test
#>
#> data: Group1 and Group2
#> p-value = 0.05116
#> sample estimates:
#> P(X<Y)+.5*P(X=Y)
#> 0.76
brunnermunzel.permutation.test(dat2)
#>
#> permuted Brunner-Munzel Test
#>
#> data: A and B
#> p-value = 0.05116
#> sample estimates:
#> P(X<Y)+.5*P(X=Y)
#> 0.76