Friedman test

The Friedman test is a non-parametric statistical test developed by Milton Friedman.^[1]^[2]^[3] 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:

${\textstyle n}$ wine judges each rate ${\textstyle k}$ different wines. Are any of the ${\textstyle k}$ wines ranked consistently higher or lower than the others?
${\textstyle n}$ welders each use ${\textstyle k}$ welding torches, and the ensuing welds were rated on quality. Do any of the ${\textstyle k}$ torches produce consistently better or worse welds?

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.

^ Friedman, Milton (December 1937). "The use of ranks to avoid the assumption of normality implicit in the analysis of variance". Journal of the American Statistical Association. 32 (200): 675–701. doi:10.1080/01621459.1937.10503522. JSTOR 2279372.
^ Friedman, Milton (March 1939). "A correction: The use of ranks to avoid the assumption of normality implicit in the analysis of variance". Journal of the American Statistical Association. 34 (205): 109. doi:10.1080/01621459.1939.10502372. JSTOR 2279169.
^ Friedman, Milton (March 1940). "A comparison of alternative tests of significance for the problem of m rankings". The Annals of Mathematical Statistics. 11 (1): 86–92. doi:10.1214/aoms/1177731944. JSTOR 2235971.

[1] Friedman, Milton (December 1937). "The use of ranks to avoid the assumption of normality implicit in the analysis of variance". Journal of the American Statistical Association. 32 (200): 675–701. doi:10.1080/01621459.1937.10503522. JSTOR 2279372.

[2] Friedman, Milton (March 1939). "A correction: The use of ranks to avoid the assumption of normality implicit in the analysis of variance". Journal of the American Statistical Association. 34 (205): 109. doi:10.1080/01621459.1939.10502372. JSTOR 2279169.

[3] Friedman, Milton (March 1940). "A comparison of alternative tests of significance for the problem of m rankings". The Annals of Mathematical Statistics. 11 (1): 86–92. doi:10.1214/aoms/1177731944. JSTOR 2235971.

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