Chapter 14 Multiple hypothesis testing

This chapter presents a survey of multiple hypothesis testing procedures with an emphasis on those procedures that can be applied in the context of the classical linear regression model. Multiple hypothesis testing is the testing of two or more separate hypotheses simultaneously. The t and F tests are the most frequently used tests in econometrics. In regression analysis, there are two different procedures that can be used to test the hypothesis that all the coefficients are zero. One procedure is to test each coefficient separately with a t test, and the other is to test all coefficients jointly using an F test. The investigator usually performs both procedures when analyzing the sample data. It has been proved that the F test is equivalent to carrying out a set of simultaneous t tests. The chapter also discusses an induced test, which is either finite or infinite depending on whether there are a finite or infinite number of separate hypotheses. In the case of finite induced tests, the exact sampling distributions of the test statistics can be complicated, so that, in practice, the critical regions of the tests are based on probability inequalities. On the other hand, infinite induced tests are commonly constructed such that the correct critical value can be readily calculated.