Simultaneous Test Procedures for Multiple Comparisons on Categorical Data

Abstract

Comparisons of several populations with regard to their distributions on a qualitative attribute must often be based on sample data. An overall large sample test of homogeneity of all the populations is extended to provide multiple comparison tests on homogeneity of subsets of populations, and tests of partial homogeneity, i.e., homogeneity only on certain categories of the qualitative distributions. Grouping of populations into several homogeneous subsets can also be achieved by this procedure, and so can a similar grouping of categories. Probabilities of errors on various hypotheses and partial hypotheses are defined and computed. An alternative procedure is proposed which has some advantages.