The effect of sample design on the comparison of associations
E. A. C. MOLINA, T. M. F. SMITH · Biometrika · 1986
A family of measures of association designed to compare the inherent association in two r×c contingency tables was proposed by Altham (1970). Under simple random sampling the measures are asymptotically distributed as noncentral chi-squared random variables. In this paper we show that under complex sampling this distribution changes to a mixture and that ignoring the design may lead to misleading results. We derive measures of the misestimation and measures of association that are adequate for most standard designs and which have a simple distribution theory. Also, simple corrections for the simple random sampling statistic are given. Two cases of stratified sampling and clustering are discussed.