THE VALIDITY AND POWER OF TESTS FOR EQUALITY OF 2 CORRELATED PROPORTIONS

With measurements taken on subjects over time, on matched pairs of sub jects or on clusters of subjects, the data often contain pairs of corr elated dichotomous responses. McNemar's test is perhaps the best known test to compare two correlated binomial proportions. The salient feat ure of McNemar's test is that we compute the variance of the contrast estimator under the restriction that the null hypothesis is true. Wald 's test, on the other hand, does not require that restriction. As a co nsequence, Wald's statistic is always greater in magnitude than McNema r's statistic when the marginal proportions are unequal, but there is a problem with the validity of both McNemar's test and WaId's test wit h small to moderate samples. There have been various modifications sug gested for McNemar's test to improve its performance. We propose a mod ified Wald's test that is valid in small to moderate samples and maint ains good power. We also evaluate the performance of McNemar's test an d Wald's test with and without modifications to enhance validity as we ll as the performance of the large sample likelihood ratio test and an exact test of the equality of correlated binomial proportions. In a s maller study, we compare the behaviour of a test based on the James-St ein estimator of the common odds ratio proposed by Liang and Zeger to McNemar's test and Wald's test. (C) 1997 by John Wiley & Sons, Ltd.