Distribution of Q When Testing Equality of Matched Proportions

Abstract

The asymptotic distribution of Cochran's Q statistic is obtained under the null hypothesis H ₀ for comparing proportions in matched samples under the multinomial model. Simulation studies show that a Satterthwaithe-type approximation provides a better approximation to the limiting distribution than does the chi-square distribution. Also, if by the nature of the problem, H ₀ implies the side condition H, which is necessary for Q to have a limiting chi-square distribution, then Q has the same Pitman efficiency as a Wald statistic that is known to have some optimal asymptotic properties and that has the χ² distribution in the limit under H ₀ whether or not H holds.

Key Words:

• Matched samples
• Asymptotic distribution
• Multinomial model
• Satterthwaithe-type approximation
• Cochran's Q statistic