Two-sample Wilcoxon Test

The Wilcoxon rank sum test is used to test whether two sets of observations come from the same distribution. The alternative hypothesis is that the observations come from distributions with identical shape but different locations. Unlike the two-sampled t-test, this test does not assume that the observations come from normal (Gaussian) distributions.

This test is equivalent to the Mann-Whitney test. For paired data, specify Signed Rank as the Type of Rank Test.

To perform a two-sample Wilcoxon test

Choose Statistics __image\ebd_ebd23.gif Compare Samples __image\ebd_ebd24.gif Two Samples __image\ebd_ebd25.gif Wilcoxon Rank Test. The dialog shown below appears.

__image\wilcox2.gif

The two-sample Wilcoxon test has the following options:

Data

Data Set

Select a data set from the dropdown list or type the name of a data set. You can also type into the Data Set edit field any expression that evaluates to a data set.

Variable 1

Specify a column as the first sample, when the data set does not have a grouping indicator.

Variable 2

Specify another column as the second sample, when the data set does not have a grouping indicator.

Variable 2 is a Grouping Variable

Select if one column in the data set is a grouping indicator that categorizes cases into two groups. In this case, select the response from Variable 1 and the indicator from Variable 2.

Test

Type of Test

Choose between Rank Sum and Signed Rank. The Signed Rank test is not available when Variable 2 is a Grouping Variable is selected.

Hypotheses

Mean Under Null Hypothesis

Enter the difference between the assumed population means of Variable x and Variable y.

Alternative Hypothesis

Specify the alternative hypothesis. For example, to perform a one-sided test against the alternative hypothesis that the mean of Variable 1 is greater than the mean of Variable 2, select greater from the list box.

Options

Use Exact Distribution

Select this to use the exact distribution of the test statistic to compute the p-value.

Continuity Correction

Select this to use a continuity correction in the normal approximation to the distribution of the test statistics.

Results

Save As

Enter the name for the object in which to save the results of the analysis.

Print Results

Select this to print out the results of the analysis in the designated output window.

Related S-PLUS language functions

wilcox.test, t.test