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Ordinal Cochran-Mantel-Haenszel Testing and Nonparametric Analysis of Variance: Competing Methodologies

Author

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  • J. C. W. Rayner

    (National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia
    Centre for Computer-Assisted Research Mathematics and its Applications, School of Information and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia)

  • G. C. Livingston

    (Centre for Computer-Assisted Research Mathematics and its Applications, School of Information and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia)

Abstract

The Cochran-Mantel-Haenszel (CMH) and nonparametric analysis of variance (NP ANOVA) methodologies are both sets of tests for categorical response data. The latter are competitor tests for the ordinal CMH tests in which the response variable is necessarily ordinal; the treatment variable may be either ordinal or nominal. The CMH mean score test seeks to detect mean treatment differences, while the CMH correlation test assesses ordinary or (1, 1) generalized correlation. Since the corresponding nonparametric ANOVA tests assess arbitrary univariate and bivariate moments, the ordinal CMH tests have been extended to enable a fuller comparison. The CMH tests are conditional tests, assuming that certain marginal totals in the data table are known. They have been extended to have unconditional analogues. The NP ANOVA tests are unconditional. Here, we give a brief overview of both methodologies to address the question “which methodology is preferable?”.

Suggested Citation

  • J. C. W. Rayner & G. C. Livingston, 2022. "Ordinal Cochran-Mantel-Haenszel Testing and Nonparametric Analysis of Variance: Competing Methodologies," Stats, MDPI, vol. 5(4), pages 1-7, October.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:56-976:d:944608
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