THE TEST OF HOMOGENEITY FOR 2X2 CONTINGENCY-TABLES - A REVIEW OF AND SOME PERSONAL OPINIONS ON THE CONTROVERSY

The 2 × 2 table has received an enormous amount of attention in the research literature. Most studies have focused on Type I error rates and the power of the chi-square statistic, but some have been more concerned with the theoretical justification behind methods of analysis. Little consensus has been achieved in either area. The reason for this is that 2 basic inferential paradigms that underlie much of the work in 2 × 2 tables are incompatible. Thus, empirical studies of Type I error rates of the chi-square test within the Neyman-Pearson framework are considered irrelevant by advocates of Fisher's exact test. Both approaches are described in this article. Barnard's 1947 test is shown to be theoretically superior to the chi-square test and all of its corrected cousins. However, Fisher's exact test is advocated as the most rational choice.