Extensions to the Cochran–Mantel–Haenszel Mean Scores and Correlation Tests

ABSTRACT

The Cochran–Mantel–Haenszel (CMH) methodology is a suite of tests applicable to tables of count data. The traditional CMH tests assess association, mean, and correlation effects. Here, testing for mean effects is extended to testing for higher order moment effects. Of especial interest are dispersion effects, reflecting, for example, market segmentation in certain scenarios. Correlation testing is extended to testing for generalized correlations. Of especial interest are correlations of order (1, 2) and (2, 1), which may reveal umbrella effects.

KEYWORDS:

• Generalized correlations
• orthonormal polynomials
• randomized block designs
• umbrella effects

AMS SUBJECT CLASSIFICATION:

• 62G10
• 62F03