The Cochran-Mantel-Haenszel(CMH)test, developed in the 1950s, is a classic in health
research, especially in epidemiology and other fields in which dichotomous and
polytomous variables are frequent. This nonparametric test makes it possible to
measure and check the effect of an antecedent variable X on a health outcome Y,
statistically controlling the effect of a third variable Z that acts as a
confounding variable in the relationship between X and Y. Both X and Y are
measured on a dichotomous qualitative scale and Z on a polytomous-qualitative
or ordinal scale. It is assumed that the effect of X on Y is homogeneous
between the k strata of Z, which is usually tested by the Breslow-Day test with the Tarone’s correction or the Woolf’s test. The main
statistical programs have the CMH test together with a test to verify the
assumption of a homogeneous effect across the strata, so that it is easy to
apply. However, its fundamentals and details of calculations are a mystery to
most researchers, and even difficult to find or understand. The aim of this
article is to present these details in a clear and concise way, including the
assumptions and alternatives to non-compliance. This technical knowledge is
applied to a simulated realistic example of the area of epidemiology in health
and, finally, an interpretive synthesis of the analyses is given.In addition, some suggestions for the test report
are made.
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