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Friedman's two way ANOVA

The Friedman test was developed for the nonparametric analysis of data collected using a randomized block design. The original test employed rank-transformed values to obtain a test statistic.

More recent work has shown that the preferred statistic is the 2-way ANOVA F-ratio computed on the ranks of Y. For k treatments and b blocks the F-ratio has k-1 and (b-1)(k-1) degrees of freedom. Nonparametric multiple comparison tests are given in several texts, including Conover (1999).