The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple test attempts. The procedure involves ranking each row (or block) together, then considering the values of ranks by columns. Applicable to complete block designs, it is thus a special case of the Durbin test.
Classic examples of use are:
The Friedman test is used for one-way repeated measures analysis of variance by ranks. In its use of ranks it is similar to the Kruskal–Wallis one-way analysis of variance by ranks.
The Friedman test is widely supported by many statistical software packages.
Post-hoc tests were proposed by Schaich and Hamerle (1984) as well as Conover (1971, 1980) in order to decide which groups are significantly different from each other, based upon the mean rank differences of the groups. These procedures are detailed in Bortz, Lienert and Boehnke (2000, p. 275). Eisinga, Heskes, Pelzer and Te Grotenhuis (2017) provide an exact test for pairwise comparison of Friedman rank sums, implemented in R. The Eisinga c.s. exact test offers a substantial improvement over available approximate tests, especially if the number of groups () is large and the number of blocks () is small.
Not all statistical packages support post-hoc analysis for Friedman's test, but user-contributed code exists that provides these facilities (for example in SPSS, and in R.). Also, there is a specialized package available in R containing numerous non-parametric methods for post-hoc analysis after Friedman.