The sizes of the three popular asymptotic tests for testing homogeneity of two binomial proportions

摘要

In statistical hypothesis testing it is important to ensure that the type I error rate is preserved under the nominal level. This paper addresses the sizes and the type I errors rates of the three popular asymptotic tests for testing homogeneity of two binomial proportions: the chi-square test with and without continuity correction, the likelihood ratio test. Although it has been recognized that, based on limited simulation studies, the sizes of the tests are inflated in small samples, it has been thought that the sizes are well preserved under the nominal level when the sample size is sufficiently large. But, Loh [1989. Bounds on the size of the χ2 test of independence in a contingency table.