brunner.munzel.test {lawstat}

Brunner–Munzel Test for Stochastic Equality

Description

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.

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.

Details

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 function follows Neubert and Brunner (2007).

Value

A list of class "htest" with 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) + 0.5 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, Munzel U (2000). “The nonparametric Behrens–Fisher problem: asymptotic theory and a small-sample approximation.” Biometrical Journal, 42(1), 17–25.

Neubert K, Brunner E (2007). “A studentized permutation test for the non-parametric Behrens–Fisher problem.” Computational Statistics & Data Analysis, 51(10), 5192–5204. doi:10.1016/j.csda.2006.05.024.

See Also

wilcox.test, pwilcox

Examples

## 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)

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