# 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.