Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H0 and for arbitrary scores asymptotically a X2-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.