Simplified Beta-Approximations to the Kruskal-Wallis H Test

Abstract

A Beta-approximation, commonly used to approximate permutation test distributions in the analysis of variance, is proposed for the null distribution of the Kruskal-Wallis H-statistic for one-way analysis of variance of ranks. The approximation seems slightly simpler and better than the Beta-approximation given by Kruskal and Wallis, particularly in bringing the H-test into closer relation to ordinary analysis of variance tests. Simple conditions on the group sizes allow further substantial simplifications in the approximations. Numerical comparisons for very small samples illustrate the various approximations.