brunnermunzel (version 2.0)

brunnermunzel.test: brunnermunzel.test

Description

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, ...)
# S3 method for default
brunnermunzel.test(
  x,
  y,
  alternative = c("two.sided", "greater", "less"),
  alpha = 0.05,
  perm = FALSE,
  est = c("original", "difference"),
  ...
)
# S3 method for formula
brunnermunzel.test(formula, data, subset = NULL, na.action, ...)
# S3 method for matrix
brunnermunzel.test(x, ...)
# S3 method for table
brunnermunzel.test(x, ...)

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

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 NAs. Defaults to getOption("na.action").

See Also

The R script of brunnermunzel.test.default is derived from that of brunner.munzel.test in lawstat package, and is rewritten with FORTRAN. Thanks to authors of lawstat package.

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