Search

A general computer program which generates either the Wilcoxon, Kruskal-Wallis, Friedman, or extended Friedman statistic (where the numbers of cell observations nij may be any positive integer or zero) can be formulated simply by using the computational algorithm for the Benard-Van Elteren statistic. It is shown that the Benard-Van Elteren statistic can be computed using matrix algebra subroutines including multiplication and inverse or g-inverse computational algorithms in the case where the rank of the matrix V of the variances and covariances of the column totals is k-1. For the case where the rank of V is less than k-1 the use of the g-inverse is shown to greatly reduce the labors of calculation. In addition, the use of the Benard-Van Elteren statistic in testing against ordered alternatives is indicated.

A study of the small sample properties of linear models analyses of contingency tables with ordered response categories is presented. Analytical and empirical study of the linear models approach of Williams and Grizzle suggests that modification would improve its performance in small sample situations. Subsequent simulation studies of the modified procedure show that for small samples it has acceptable performance with respect to Type I errors and is robust with respect to response distribution form and inequality among the sample sizes in the contingency table.