Abstract
The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data. The inference is conditional on the treatment and outcome totals on each stratum being known before sighting the data. The CMH tests are important for analysing randomised blocks data when the responses are categorical rather than continuous. This overview of some recent extensions to CMH testing first describes the traditional CMH tests and then explores new alternative presentations of the ordinal CMH tests. Next, the ordinal CMH tests will be extended so they can be used to test for higher moment effects. Finally, unconditional analogues of the extended CMH tests will be developed.
Highlights
The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data
We suggest that readers interested in CMH testing more broadly use their preferred search engines
In consumer studies with just about right (JAR) responses such as in the Jams Example following, when c is small the randomised block F test will often be invalid in spite of the well-known ANOVA robustness
Summary
The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to particular tables of count data. We suggest that readers interested in CMH testing more broadly use their preferred search engines. This overview will first describe the traditional CMH tests and explore new alternative presentations of the ordinal CMH tests. One rationale for developing these extensions was to enable a comparison with the nonparametric ANOVA tests introduced in References [1,2,3]. These tests permit univariate moment assessments beyond the mean and bivariate assessments beyond the (order (1, 1)) correlation.
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