On Two Tests for Comparing Matched Proportions

The power functions of McNemar's and Gart's tests are derived by using an extension of the logistic model. This permits us to investigate the validity and power performance of two tests for comparing the response proportions of drugs A and B in the matched sample case with respect to the effect of the order of drug administration. This investigation shows that the P-value of McNemar's test is distorted by the order effect and Gart's test is, on the average, less powerful than McNemar's test when the order effect is zero. It is suggested that Gart's test is preferable if the sample size is small. If the sample size is large and the order effect is unknown, the experimenter may use a preliminary test for order effect before choosing a test for treatment effect.