Abstract
Abstract The limit distribution of Cochran's Q statistic for testing the equality of k proportions in matched samples is obtained for sequences of Pitman alternatives. Comparison of the asymptotic power of the test based on the Q statistic with that of the test based on Wald's statistic for the same asymptotic level shows that neither test is uniformly better than the other. We study by simulation a modified Q test using an estimated critical value obtained from a Satterthwaite-type approximation for cases when the proportions to be compared are near one-half and k = 4. The operating characteristics agree closely with estimated values in samples of 50 and 100, while the agreement with the Wald statistics was occasionally poor.
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