A computer program for testing average partial association in three-way contingency tables (PARCAT)

Abstract

PARCAT is a computer program which implements alternative tests for average partial association in three-way contingency tables within the framework of the product multiple hypergeometric probability model. Primary attention is directed at the relationship between two of the variables, controlling for the effects of a covariable. This approach is essentially a multivariate extension of the Cochran/Mantel-Haenszel test to sets of (s x r) tables. A set of scores such as uniform, ridits, or probits can be assigned to categories which are ordinally scaled. In particular, if ridit scores with midranks assigned for ties are utilized, this procedure is equivalent to a partial Kruskal-Wallis test when one variable is ordinally scaled, and is equivalent to a partial Spearman rank correlation test when both variables are ordinally scaled.