On the null distribution of the Kruskal–Wallis statistic

This article extends existing tables of null probability points for the Kruskal–Wallis statistic and compares various methods for approximating these probability points. Van de Wiel's technique of partitioning the combined ranking into the upper and lower ranks is combined with Iman, Quade, and Alexander's recursive formula to find the joint distribution of the rank totals for each sample. The Kruskal–Wallis statistic's distribution is then accumulated. It is shown that the well-known chi-square approximation of Kruskal–Wallis probability points is overly conservative. Four other methods are shown to provide better approximations than the chi-square approximation.