Tests for Several Related Samples Test Types

Three tests are available to compare the distributions of several related variables.

The Friedman test is the nonparametric equivalent of a one-sample repeated measures design or a two-way analysis of variance with one observation per cell. Friedman tests the null hypothesis that k related variables come from the same population. For each case, the k variables are ranked from 1 to k. The test statistic is based on these ranks.

Kendall's W is a normalization of the Friedman statistic. Kendall's W is interpretable as the coefficient of concordance, which is a measure of agreement among raters. Each case is a judge or rater, and each variable is an item or person being judged. For each variable, the sum of ranks is computed. Kendall's W ranges between 0 (no agreement) and 1 (complete agreement).

Cochran's Q is identical to the Friedman test but is applicable when all responses are binary. This test is an extension of the McNemar test to the k-sample situation. Cochran's Q tests the hypothesis that several related dichotomous variables have the same mean. The variables are measured on the same individual or on matched individuals.