Power Analysis for Contingency Tables and The Cochran-Mantel-Haenszel Test

Abstract

Fisher's exact test for testing independence in a 2x2 contingency table has been criticized as conservative by the discrete nature of the null distribution. A calibration study establishes that the conditional distributions of the likelihood ratio test, the Pearson chi-square and the Fisher exact are closely comparable, and are also invariant under the alternative hypotheses, establishing the asymptotic power based upon a mutual information identity. Thereby, the distinctive nature between the conditional tests and the exact unconditional tests manifests the flaw of the criticism against Fisher's exact test. As an application of the information identity, tests for homogeneity of odds ratios and for conditional independence across strata in a series of 2x2 tables are analyzed. The Cochran-Mantel-Haenszel test is examined for a flaw in its basic logic which yields a case of invalid application. This is joint work with Michelle Liou and John A. D. Aston, Institute of Statistical Science, Academia Sinica.