```
= filtered_data;
Proc freq data * X * Y / cmh;
tables K * the order of K, X, and Y appearing on the line is important!;
run;
```

# CMH Test

# Cochran-Mantel-Haenszel Test

The CMH procedure tests for conditional independence in partial contingency tables for a 2 x 2 x K design. However, it can be generalized to tables of X x Y x K dimensions.

## CMH in SAS

The cmh test is calculated in SAS using the PROC FREQ procedure. By default, it outputs the chi square statistic, degrees of freedom and p-value for each of the three alternative hypothesis: `general association`

, `row means differ`

, and `nonzero correlation`

. It is up to the statistical analyst or statistician to know which result is appropriate for their analysis.

When the design of the contingency table is 2 x 2 x K (i.e, X == 2 levels, Y == 2 levels, K >= 2 levels), the Mantel-Haenszel Common Odds Ratio (odds ratio estimate, 95% CI, P-value) and the Breslow-Day Test for Homogeneity of the Odds Ratios (chi-square statistic, degrees of freedom, P-value) are also output.

Below is the syntax to conduct a CMH analysis in SAS:

# References

SAS documentation (Specification): https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.3/statug/statug_freq_examples07.htm

SAS documentation (Theoretical Basis + Formulas): https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/procstat/procstat_freq_details92.htm