Peter Reitmeir (National Research Center for Environment and Health, Germany)
On the use of Bootstrap Cut-Off Tests in a closed testing procedure
Tests for a global hypothesis can be derived by simultaneous consideration of p values based on tests for the corresponding single hypotheses. These so called cut-off tests, however, are highly conservative procedures, because the dependencies among the single tests are not incorporated in the test decision. In applying resampling methods Bootstrap cut-off tests lead to remarkable improvements. The construction of the tests are mainly based on a prespecified weight vector. This enables the selection of powerful tests for alternatives with any false single hypothesis or for alternatives, where at least a given number of false hypotheses contributes to the rejection of the global hypothesis. For the application of these tests in a closed testing procedure some modifications are necessary. Several strategies for the selection of Bootstrap cut-off tests are investigated. Especially for the common problem of all pairwise comparisons or for the case of ordered alternatives the proposed tests regard logical dependencies among false single hypotheses. By Monte Carlo simulations comparisons with Shaffer's step down procedure or with the free step down resampling procedure (Westfall, Young) are given and recommendations for practical use are discussed.