Package 'brunnermunzel' reference manual

Title:	(Permuted) Brunner-Munzel Test
Description:	Provides the functions for Brunner-Munzel test and permuted Brunner-Munzel test, which enable to use formula, matrix, and table as argument. These functions are based on Brunner and Munzel (2000) <doi:10.1002/(SICI)1521-4036(200001)42:1%3C17::AID-BIMJ17%3E3.0.CO;2-U> and Neubert and Brunner (2007) <doi:10.1016/j.csda.2006.05.024>, and are written with FORTRAN.
Authors:	Toshiaki Ara [aut, cre]
Maintainer:	Toshiaki Ara <[email protected]>
License:	GPL-2 \| GPL-3
Version:	2.0
Built:	2025-02-05 04:11:05 UTC
Source:	https://github.com/toshi-ara/brunnermunzel

permuted Brunner-Munzel test

Description

This function performs the permuted Brunner-Munzel test.

Usage

brunnermunzel.permutation.test(x, ...)

## Default S3 method:
brunnermunzel.permutation.test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  force = FALSE,
  est = c("original", "difference"),
  ...
)

## S3 method for class 'formula'
brunnermunzel.permutation.test(formula, data, subset = NULL, na.action, ...)

## S3 method for class 'matrix'
brunnermunzel.permutation.test(x, ...)

## S3 method for class 'table'
brunnermunzel.permutation.test(x, ...)
brunnermunzel.permutation.test(x, ...)

## Default S3 method:
brunnermunzel.permutation.test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  force = FALSE,
  est = c("original", "difference"),
  ...
)

## S3 method for class 'formula'
brunnermunzel.permutation.test(formula, data, subset = NULL, na.action, ...)

## S3 method for class 'matrix'
brunnermunzel.permutation.test(x, ...)

## S3 method for class 'table'
brunnermunzel.permutation.test(x, ...)

Arguments

`x`	the numeric vector of data values from the sample 1, or 2 x n matrix of table (number of row must be 2 and column is ordinal variables).
`...`	further arguments to be passed to or from methods (This argument is for only formula).
`y`	the numeric vector of data values from the sample 2. If x is matrix or table, y must be missing.
`alternative`	a character string specifying the alternative hypothesis, must be one of `two.sided` (default), `greater` or `less`. User can specify just the initial letter.
`force`	FALSE (default): If sample size is too large [number of combinations > 40116600 = choose(28, 14)], use `brunnermunzel.test`. TRUE : perform permuted Brunner-Munzel test regardless sample size.
`est`	a method to calculate estimate and confidence interval, must be either `original` (default) or `difference`. original (default): return $p = P(X < Y) + 0.5 * P(X = Y)$ difference : return mean difference. i.e. $P(X < Y) - P(X > Y)$ = 2 * p - 1 This change is proposed by Dr. Julian D. Karch.
`formula`	a formula of the form `lhs ~ rhs` where `lhs` is a numeric variable giving the data values and `rhs` a factor with two levels giving the corresponding groups.
`data`	an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset`	an optional vector specifying a subset of observations to be used.
`na.action`	a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.

Value

A list containing the following components:

`method`	the characters “permuted Brunner-Munzel Test”
`data.name`	a character string giving the name of the data.
`p.value`	the $p$ -value of the test.
`estimate`	an estimate of the effect size

Note

FORTRAN subroutine 'combination' in combination.f is derived from the program by shikino (http://slpr.sakura.ne.jp/qp/combination) (CC-BY-4.0). Thanks to shikono for your useful subroutine.

References

Karin Neubert and Edgar Brunner, “A studentized permutation test for the non-parametric Behrens-Fisher problem”, Computational Statistics and Data Analysis, Vol. 51, pp. 5192-5204 (2007).

Examples

## 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)

brunnermunzel.permutation.test(x, y)
##
##       permuted Brunner-Munzel Test
##
## data:  x and y
## p-value = 0.158
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##        0.2839506

## 'est' option
## if 'est = "difference"' return P(X<Y) - P(X>Y)
brunnermunzel.permutation.test(x, y, est = "difference")
##
##       permuted Brunner-Munzel Test
##
## data:  x and y
## p-value = 0.158
## sample estimates:
## P(X<Y)-P(X>Y)
##    -0.4320988


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

brunnermunzel.permutation.test(value ~ group, data = dat)
##
##       permuted Brunner-Munzel Test
##
## data:  value by group
## p-value = 0.158
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##        0.2839506


## Pain score on the third day after surgery for 14 patients under
## the treatment Y and 11 patients under the treatment N
## (see Brunner and Munzel, 2000; Neubert and Brunner, 2007).

Y <- c(1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1)
N <- c(3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4)


brunnermunzel.permutation.test(Y, N)

##
##       permuted Brunner-Munzel Test
##
## data:  Y and N
## p-value = 0.008038
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##         0.788961

## Formula interface.
dat <- data.frame(
    value = c(Y, N),
    group = factor(rep(c("Y", "N"), c(length(Y), length(N))),
                   levels = c("Y", "N"))
)


brunnermunzel.permutation.test(value ~ group, data = dat)

##
##       permuted Brunner-Munzel Test
##
## data:  value by group
## p-value = 0.008038
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##         0.788961


## Matrix or Table interface.
##
dat1 <- matrix(c(4, 4, 2, 1, 5, 4), nr = 2, byrow = TRUE)
dat2 <- as.table(dat1)

brunnermunzel.permutation.test(dat1)  # matrix
##
##       permuted Brunner-Munzel Test
##
## data:  Group1 and Group2
## p-value = 0.1593
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

brunnermunzel.permutation.test(dat2)  # table
##
##       Brunner-Munzel Test
##
##       permuted Brunner-Munzel Test
##
## data:  A and B
## p-value = 0.1593
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

## 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)

brunnermunzel.permutation.test(x, y)
##
##       permuted Brunner-Munzel Test
##
## data:  x and y
## p-value = 0.158
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##        0.2839506

## 'est' option
## if 'est = "difference"' return P(X<Y) - P(X>Y)
brunnermunzel.permutation.test(x, y, est = "difference")
##
##       permuted Brunner-Munzel Test
##
## data:  x and y
## p-value = 0.158
## sample estimates:
## P(X<Y)-P(X>Y)
##    -0.4320988


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

brunnermunzel.permutation.test(value ~ group, data = dat)
##
##       permuted Brunner-Munzel Test
##
## data:  value by group
## p-value = 0.158
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##        0.2839506


## Pain score on the third day after surgery for 14 patients under
## the treatment Y and 11 patients under the treatment N
## (see Brunner and Munzel, 2000; Neubert and Brunner, 2007).

Y <- c(1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1)
N <- c(3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4)


brunnermunzel.permutation.test(Y, N)

##
##       permuted Brunner-Munzel Test
##
## data:  Y and N
## p-value = 0.008038
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##         0.788961

## Formula interface.
dat <- data.frame(
    value = c(Y, N),
    group = factor(rep(c("Y", "N"), c(length(Y), length(N))),
                   levels = c("Y", "N"))
)


brunnermunzel.permutation.test(value ~ group, data = dat)

##
##       permuted Brunner-Munzel Test
##
## data:  value by group
## p-value = 0.008038
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##         0.788961


## Matrix or Table interface.
##
dat1 <- matrix(c(4, 4, 2, 1, 5, 4), nr = 2, byrow = TRUE)
dat2 <- as.table(dat1)

brunnermunzel.permutation.test(dat1)  # matrix
##
##       permuted Brunner-Munzel Test
##
## data:  Group1 and Group2
## p-value = 0.1593
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

brunnermunzel.permutation.test(dat2)  # table
##
##       Brunner-Munzel Test
##
##       permuted Brunner-Munzel Test
##
## data:  A and B
## p-value = 0.1593
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

This function performs the Brunner–Munzel test for stochastic equality of two samples, which is also known as the Generalized Wilcoxon Test. NAs from the data are omitted. This function enables to use formula as argument.

Usage

brunnermunzel.test(x, ...)

## Default S3 method:
brunnermunzel.test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  alpha = 0.05,
  perm = FALSE,
  est = c("original", "difference"),
  ...
)

## S3 method for class 'formula'
brunnermunzel.test(formula, data, subset = NULL, na.action, ...)

## S3 method for class 'matrix'
brunnermunzel.test(x, ...)

## S3 method for class 'table'
brunnermunzel.test(x, ...)
brunnermunzel.test(x, ...)

## Default S3 method:
brunnermunzel.test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  alpha = 0.05,
  perm = FALSE,
  est = c("original", "difference"),
  ...
)

## S3 method for class 'formula'
brunnermunzel.test(formula, data, subset = NULL, na.action, ...)

## S3 method for class 'matrix'
brunnermunzel.test(x, ...)

## S3 method for class 'table'
brunnermunzel.test(x, ...)

Arguments

`x`	the numeric vector of data values from the sample 1, or 2 x n matrix of table (number of row must be 2 and column is ordinal variables).
`...`	further arguments to be passed to or from methods (This argument is for only formula).
`y`	the numeric vector of data values from the sample 2. If x is matrix or table, y must be missing.
`alternative`	a character string specifying the alternative hypothesis, must be one of `two.sided` (default), `greater` or `less`. User can specify just the initial letter.
`alpha`	significance level, default is 0.05 for 95% confidence interval.
`perm`	logical FALSE (default): perform Brunner-Munzel test. TRUE : perform permuted Brunner-Munzel test.
`est`	a method to calculate estimate and confidence interval, must be either `original` (default) or `difference`. original (default): return $p = P(X < Y) + 0.5 * P(X = Y)$ difference : return mean difference. i.e. $P(X < Y) - P(X > Y) = 2 * p - 1$ This change is proposed by Dr. Julian D. Karch.
`formula`	a formula of the form `lhs ~ rhs` where `lhs` is a numeric variable giving the data values and `rhs` a factor with two levels giving the corresponding groups.
`data`	an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset`	an optional vector specifying a subset of observations to be used.
`na.action`	a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.

Value

A list containing the following components:

`data.name`	a character string giving the name of the data.
`statistic`	the Brunner–Munzel test statistic.
`parameter`	the degrees of freedom.
`p.value`	the $p$ -value of the test.
`conf.int`	the confidence interval.
`estimate`	an estimate of the effect size

Note

There exist discrepancies with Brunner and Munzel (2000) because there is a typo in the paper. The corrected version is in Neubert and Brunner (2007) (e.g., compare the estimates for the case study on pain scores). The current R function follows Neubert and Brunner (2007).

Examples

## 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)

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

## 'est' option
## if 'est = "difference"' return P(X<Y) - P(X>Y)
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


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

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 


## Pain score on the third day after surgery for 14 patients under
## the treatment Y and 11 patients under the treatment N
## (see Brunner and Munzel, 2000; Neubert and Brunner, 2007).

Y <- c(1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1)
N <- c(3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4)

brunnermunzel.test(Y, N)
##
##       Brunner-Munzel Test
##
## data: Y and N
## Brunner-Munzel Test Statistic = 3.1375,  df = 17.683, p-value = 0.005786
## 95 percent confidence interval:
##  0.5952169 0.9827052
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##        0.788961

## Formula interface.
dat <- data.frame(
    value = c(Y, N),
    group = factor(rep(c("Y", "N"), c(length(Y), length(N))),
                   levels = c("Y", "N"))
)

brunnermunzel.test(value ~ group, data = dat)
##
##       Brunner-Munzel Test
##
## data:  value by group
## Brunner-Munzel Test Statistic = 3.1375, df = 17.683, p-value =
## 0.005786
## 95 percent confidence interval:
##  0.5952169 0.9827052
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##         0.788961


## Matrix or Table interface.
##
dat1 <- matrix(c(4, 4, 2, 1, 5, 4), nr = 2, byrow = TRUE)
dat2 <- as.table(dat1)

brunnermunzel.test(dat1)  # matrix
##
##       Brunner-Munzel Test
##
## data:  Group1 and Group2
## Brunner-Munzel Test Statistic = 1.5511, df = 16.961, p-value =
## 0.1393
## 95 percent confidence interval:
##  0.4351213 0.9248787
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

brunnermunzel.test(dat2)  # table
##
##       Brunner-Munzel Test
##
## data:  A and B
## Brunner-Munzel Test Statistic = 1.5511, df = 16.961, p-value =
## 0.1393
## 95 percent confidence interval:
##  0.4351213 0.9248787
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

## 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)

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

## 'est' option
## if 'est = "difference"' return P(X<Y) - P(X>Y)
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


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

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 


## Pain score on the third day after surgery for 14 patients under
## the treatment Y and 11 patients under the treatment N
## (see Brunner and Munzel, 2000; Neubert and Brunner, 2007).

Y <- c(1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1)
N <- c(3, 3, 4, 3, 1, 2, 3, 1, 1, 5, 4)

brunnermunzel.test(Y, N)
##
##       Brunner-Munzel Test
##
## data: Y and N
## Brunner-Munzel Test Statistic = 3.1375,  df = 17.683, p-value = 0.005786
## 95 percent confidence interval:
##  0.5952169 0.9827052
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##        0.788961

## Formula interface.
dat <- data.frame(
    value = c(Y, N),
    group = factor(rep(c("Y", "N"), c(length(Y), length(N))),
                   levels = c("Y", "N"))
)

brunnermunzel.test(value ~ group, data = dat)
##
##       Brunner-Munzel Test
##
## data:  value by group
## Brunner-Munzel Test Statistic = 3.1375, df = 17.683, p-value =
## 0.005786
## 95 percent confidence interval:
##  0.5952169 0.9827052
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##         0.788961


## Matrix or Table interface.
##
dat1 <- matrix(c(4, 4, 2, 1, 5, 4), nr = 2, byrow = TRUE)
dat2 <- as.table(dat1)

brunnermunzel.test(dat1)  # matrix
##
##       Brunner-Munzel Test
##
## data:  Group1 and Group2
## Brunner-Munzel Test Statistic = 1.5511, df = 16.961, p-value =
## 0.1393
## 95 percent confidence interval:
##  0.4351213 0.9248787
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

brunnermunzel.test(dat2)  # table
##
##       Brunner-Munzel Test
##
## data:  A and B
## Brunner-Munzel Test Statistic = 1.5511, df = 16.961, p-value =
## 0.1393
## 95 percent confidence interval:
##  0.4351213 0.9248787
## sample estimates:
## P(X<Y)+.5*P(X=Y)
##             0.68

Package 'brunnermunzel'

Help Index

permuted Brunner-Munzel test

Description

Usage

Arguments

Value

Note

References

See Also

Examples

brunnermunzel.test

Description

Usage

Arguments

Value

Note

See Also

Examples