Homogeneity tests for 2 × 2 contingency tables

Abstract

Using the likelihood ratio statistic, we develop a significance index, called P-value, to test the hypothesis of homogeneity in 2 × 2 contingency tables. The Pvalue does not depend on asymptotic distributions, and is based on the elimination of the nuisance parameter. Therefore, we obtain the exact distribution of the likelihood ratio statistic in a way that is, moreover, compatible with the likelihood principle. For a better understanding of significance indices to test homogeneity, we perform a study comparing the P-value with some indices (likelihood ratio test (LRT), chisquare test) and with the full Bayesian significance test (FBST). This comparative study shows an interesting relation between all the analyzed indices, Bayesian and frequentist.