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Journal of the American Statistical Association Volume 76, 1981 - Issue 373
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Theory and Method

On the Asymptotic Power of Tests for Comparing K Correlated Proportions

Sylvan Wallenstein Division of Biostatistics, School of Public Health, College of Physicians and Surgeons, Faculty of Medicine, Columbia University, 600 W. 168 Street, New York, NY, 10032, USA
&
Agnes Berger Division of Biostatistics, School of Public Health, College of Physicians and Surgeons, Faculty of Medicine, Columbia University, 600 W. 168 Street, New York, NY, 10032, USA
Pages 114-118 | Received 01 Sep 1978, Published online: 12 Mar 2012
 
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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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