An Algorithm for Computing the Exact Distribution of the Kruskal-Wallis Test

The Kruskal-Wallis test is a popular nonparametric test for comparing k independent samples. In this article we propose a new algorithm to compute the exact null distribution of the Kruskal-Wallis test. Generating the exact null distribution of the Kruskal-Wallis test is needed to compare several approximation methods. The 5% cut-off points of the exact null distribution which StatXact cannot produce are obtained as by-products. We also investigate graphically a reason that the exact and approximate distributions differ, and hope that it will be a useful tutorial tool to teach about the Kruskal-Wallis test in undergraduate course.