Multiple Regression Approach to Analyzing Contingency Tables: Post Hoc and Planned Comparison Procedures

Abstract

Post hoc and planned comparison procedures for interpreting chi-square contingency-table test results, not currently discussed in most standard textbooks, are presented. A planned comparison procedure that simplifies the tedious process of partitioning a contingency table by creating single-degree-of-freedom contrasts through a regression-based approach is proposed. Importantly, these post hoc methods supplement the analysis of standardized residuals by reporting the percentage contribution for each cell to the overall chi-square statistic (relative contribution) and to the percentage of variance shared by the two factors (absolute contribution). Both methods can be readily incorporated into existing statistical packages such as SAS or SPSS. The equivalence of the percentage contribution method to the more common standardized residual method is also presented along with an example of a typical application.