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In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data.It allows an investigator to test the association between a binary predictor or treatment and a binary outcome such as case or control status while taking into account the stratification. [1]
Cochran-Mantel-Haenszel test allows to test the association between a binary outcome and a binary predictor while taking into account stratification with arbitrary strata size. When its conditions of application are verified, it is identical to the conditional logistic regression score test .
Bowker's test of symmetry; Categorical distribution, general model; Chi-squared test; Cochran–Armitage test for trend; Cochran–Mantel–Haenszel statistics; Correspondence analysis
The first independent variable, M, is the matching variable used to link individuals on ability, in this case a total test score, similar to that employed by the Mantel-Haenszel procedure. The group membership variable is denoted G and in the case of regression is represented through dummy coded variables.
The test is sometimes called the Mantel–Cox test. The logrank test can also be viewed as a time-stratified Cochran–Mantel–Haenszel test . The test was first proposed by Nathan Mantel and was named the logrank test by Richard and Julian Peto .
The McNemar's test is a special case of the Cochran–Mantel–Haenszel test; it is equivalent to a CMH test with one stratum for each of the N pairs and, in each stratum, a 2x2 table showing the paired binary responses. [18] Multinomial confidence intervals are used for matched pairs binary data.
The test is commonly used in ecology, where the data are usually estimates of the "distance" between objects such as species of organisms. For example, one matrix might contain estimates of the genetic distances (i.e., the amount of difference between two different genomes) between all possible pairs of species in the study, obtained by the methods of molecular systematics; while the other ...
Nathan Mantel (February 16, 1919 – May 25, 2002) [1] was an American biostatistician best known for his work with William Haenszel that led to the Mantel–Haenszel test and its associated estimate, the Mantel–Haenszel odds ratio. The Mantel–Haenszel procedure and its extensions allow data from several sources or groups to be combined ...