On Asymptotic Power and Efficiency of Tests of Independence in Contingency Tables with Ordered Classifications

Abstract

Asymptotic power formulas for tests of independence against simple association models in I × J contingency tables with ordered categories are presented. Yates's score correlation test and Spearman's tied rank correlation test are compared with a likelihood ratio test proposed by S. J. Haberman for testing independence in log-linear models with ordered classifications. Asymptotic power and relative efficiencies are derived under local alternatives that need not be included in the likelihood model assumed by Haberman's procedure. Some computations for real and fictitious data are presented.