The Mantel-Haenszel Test and Tests of Marginal Symmetry; Fixed-Effects and Mixed Models for a Categorical Response, Correspondent Paper

The Mantel-Haenszel test of treatment, response independence within strata in an s x t x r contingency table is reviewed. In the case of one individual per (stratum, treatment) the theory and application of this test have many links with the theory and application of tests of marginal symmetry in an r' contingency table. The latter theory is reviewed and developed and the links are explored. The two theories provide qualitative response analogues of the fixed-effects and mixed model theories of analysing a quantitative response in an s x t (block, treatment) experiment.