Methods for analyzing multidimensional contingency tables

Many problems investigated by researchers in higher education involve simple frequency counts and their analysis. Not too infrequently, these frequency counts arise from the cross-classification of a sample of observations on a number of qualitative variables. In this case, the investigator is usually interested in examining the multiplicative interactions among the classification variables. When the number of classification variables exceeds two, however, the investigator is faced with rather severe problems in undertaking his analysis. All too often, the researcher is reduced to breaking up his multidimensional contingency table into smaller, typically two-way tables, and analyzing each separately. This article describes a unified approach, developed by L.A. Goodman, to the analysis of the p-way contingency table which enriches our understanding of the relationships existing among the classification variables. Two examples from research in higher education are used to demonstrate the usefulness of the method.