Interpreting the three tests reported by the CMH option in PROC FREQ


The CMH option in the TABLES statement of PROC FREQ produces three different versions of the Cochran-Mantel-Haenszel statistic. All three test the null hypothesis of no association, but the tests have different assumptions regarding the scale of the row and column variables, and they test for different alternative hypotheses. The table below lists the assumptions underlying each test and the corresponding alternative hypothesis.

TestAssumptionAlternative Hypothesis
General AssociationDoes not require an ordinal scale for either the row or column variableFor at least one stratum, there is some kind of association between X and Y
Row Mean Scores DifferThe column variable lies on an ordinal (or interval) scaleFor at least one stratum, the mean scores of the R rows are unequal
Correlation StatisticBoth variables lie on an ordinal scaleThere is a linear association between rows and columns in at least one stratum.