Cochran-Mantel-Haenszel (CMH) test:
The Cochran-Mantel-Haenszel (CMH) test compares two groups on a binary response, adjusting for control variables. The initial data are represented as a series of K 2x2 contingency table s, where K is the number of strata. Traditionally, in each table the rows correspond to the "Treatment group" values (e.g "Placebo", "Drug A") and the columns to the "Response" values (e.g "No change," "Improvement").
The null hypothesis is that the response is conditionally independent of the treatment in any given strata.
The stratification of the subjects into K groups (according to the values of controlled variables - e.g. "Age group") increases the power of the test to detect association. This increase in power comes from comparing like subjects to like subjects.
The CMH statistic is described by this formula: