For paired binary data, McNemar's test is widely used to test marginal homogeneity or symmetry for a 2 by 2 contingency table. In this article, we extend McNemar's test by considering a series of paired binary data in which the series is defined by a stratification factor. We provide a test for testing homogeneous stratum effects. For illustration, we apply our test to a cancer epidemiology study. Finally, we conduct simulations to show that our test preserves the nominal type I error level and evaluate the power of our test under various scenarios.
Keywords: Bowker’s test; Marginal homogeneity; McNemar’s test; Paired binary data; Stratified test; Stuart–Maxwell test; Symmetry.