A multivariate perspective on the analysis of categorical data

Abstract

Psychological research often involves analysis of an I x J contingency table consisting of the responses of J groups of individuals on a criterion variable with I nominal categories. The conventional statistical approach for comparing responses across groups is the Pearson chi-square test. Alternatively, this analysis can be viewed as a multivariate analysis of variance with binary dependent variables, a canonical correlation analysis with two sets of binary variables, or a form of correspondence analysis. Although these analysis approaches stem from different traditions, they produce equivalent results when applied to an I x J table.