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Last data update: 2014.03.03

R: The Brunner-Munzel Test for Stochastic Equality

brunner.munzel.test

R Documentation

The Brunner-Munzel Test for Stochastic Equality

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.

Usage

brunner.munzel.test(x, y, alternative = c("two.sided", "greater",
"less"), alpha=0.05)

Arguments

`x`	the numeric vector of data values from the sample 1.
`y`	the numeric vector of data values from the sample 2.
`alpha`	confidence level, default is 0.05 for 95 interval.
`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.

Value

A list containing the following components:

`statistic`	the Brunner-Munzel test statistic.
`parameter`	the degrees of freedom.
`conf.int`	the confidence interval.
`p.value`	the p-value of the test.
`data.name`	a character string giving the name of the data.
`estimate`	an estimate of the effect size, i.e. P(X<Y)+.5*P(X=Y)

Author(s)

Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth, Weiwen Miao This function was updated with the help of Dr. Ian Fellows

References

Brunner, E. and Munzel, U. (2000) The Nonparametric Behrens-Fisher Problem: Asymptotic Theory and a Small-Sample Approximation, Biometrical Journal 42, 17-25.

Neubert, K., Brunner, E. (2007) A Studentized Permutation Test for the Non-parametric Behrens-Fisher Problem, Computational Statistics and Data Analysis 51, 5192-5204.

Reiczigel, J., Zakarias, I. and Rozsa, L. (2005) A Bootstrap Test of Stochastic Equality of Two Populations, The American Statistician 59, 1-6.

Examples

## Pain score on the third day after surgery for 14 patients under
## the treatment emph{Y} and 11 patients under the treatment emph{N}
## (see Brunner and Munzel (2000))

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)

brunner.munzel.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