A Summary Chi Square Test of the Non-Null Hypothesis

Objective: A summary chi square test of the non-null hypothesis is proposed including two statistics. Meth-ods: The two statistics and their power functions are respectively derived from the classical Cochran test and the Mantel-Haenszel test using the non-null hypothesis in place of the null hypothesis. Their performance is exhibited by Monte Carlo method. Results: The two statistics are matched with their power functions respec-tively. The observed power of the statistics coincides with the prescribed power. They reduce to their classical counterparts when the minimal clinically relevant difference equals zero, to the Dunnett-Gent test when there is only one stratum, and to the common test on two binomial proportions （rates） when both the minimal clinically relevant difference equals zero and there is only one stratum. Conclusion: The test can be applied to analyzing the data from the clinical trials for establishing the clinical significance of treatment-control difference or clinical equivalence. A worked example illustrates the methodology.