One-Way Layout for Counts and the Exact Enumeration of the Kruskal-WallisHDistribution with Ties

Abstract In a one-way layout situation in which the observations are counts corresponding to ordered categories, the attractive H test of Kruskal and Wallis is recommended. Because of the large number of ties, the variance-covariance correction factor for the chi-squared approximation is inaccurate in small samples, with approximate significance levels varying between overly conservative and overly optimistic values depending upon the tie configuration and the outcome. To overcome this problem, a computer algorithm and program are developed which calculate the exact small sample distribution. In addition, an exact Scheffé-type method of multiple comparisons is given.