Two-way contingency tables for complex sampling schemes

Abstract

SUMMARY Methods for testing independence, quasiindependence, and marginal symmetry in contingency tables are derived for a wide variety of sampling schemes including stratified multistage cluster sampling. The null hypothesis is a vector of linear and quadratic contrasts involving the probabilities. The asymptotic null distribution of the test statistic is chi-squared. The theory can also be used to test equality of failure distributions in a stratified prospective multiclinio trial, jointly for all strata or merely population-wide.