Nonparametric Statistics Notes - Wald-Wolfowitz Runs Test

The Wald-Wolfowitz runs test is a nonparametric alternative to the t-test for independent samples. The procedure expects the data to be arranged in the same way as for the t-test for independent samples (Basic Statistics). Specifically, the data file should contain a coding variable (independent variable) with at least two distinct codes that uniquely identify the group membership of each case in the data file. Select Comparing two independent samples (groups) from the Nonparametric Statistics Startup Panel - Quick tab to display the Comparing Two Groups dialog box, in which you select the coding variable and a dependent variable list (variables in which the two groups are to be compared), and the codes used in the coding variable for identifying the two groups.

Assumptions and interpretation

The Wald-Wolfowitz runs test works as follows: Imagine you want to compare male and female subjects on some variable. You can sort the data by that variable and look for cases when, in the sorted data, same-gender subjects are adjacent to each other. If there are no differences between male and female subjects, then the number and "lengths" of such adjacent "runs" of subjects of the same gender will be more or less random. If not, the two groups (genders in our example) are somehow different from each other. This test assumes that the variable under consideration is continuous, and that it was measured on at least an ordinal scale (i.e., rank order). The Wald-Wolfowitz runs test assesses the hypothesis that two independent samples were drawn from two populations that differ in some respect, i.e., not just with respect to the mean, but also with respect to the general shape of the distribution. The null hypothesis is that the two samples were drawn from the same population. In this respect, this test is different from the parametric t-test which strictly tests for differences in locations (means) of two samples.

Siegel (1956) recommends a continuity correction when the combined sample sizes is not very large. This adjusted z-score, along with its adjusted p-value, is given on the Wald-Wolfowitz Runs Test Results spreadsheet.

See Comparing Two Groups - Quick tab for further details.