Extending MinP tests for global and multiple testing

Empirical economic studies often involve multiple propositions or hypotheses, with researchers aiming to assess both the collective and individual evidence against these propositions or hypotheses. To rigorously assess this evidence, practitioners frequently employ tests with quadratic test statistics, such as F-tests and Wald tests, or tests based on minimum/maximum type test statistics. This paper introduces a combination test that merges these two classes of tests using the minimum p-value principle. We illustrate our proposed tests to reevaluate two empirical applications reported in the literature. One concerns the evaluation of the effectiveness of a matching grant on charitable giving. The other examines the effectiveness of exercise.