The Kruskal–Wallis tests are Cochran–Mantel–Haenszel mean score tests

The Kruskal–Wallis tests are appropriate tests for the completely randomised design, both for when the data are untied ranks, and, with adjustment, for when there are ties and mid-ranks are used. Both these tests are shown to be Cochran–Mantel–Haenszel mean score tests. The relationship between the Kruskal–Wallis test statistic and the ANOVA F test statistic when there are no ties generalises to the same relationship between the Cochran–Mantel–Haenszel mean score test statistic and the ANOVA F test statistic. It thus also relates both Kruskal–Wallis test statistics to the ANOVA F test statistic. A small simulation study finds that p-values may be more accurately found using the F test.