Improved multiple test procedures for discrete distributions: New ideas and analytical review

We review and compare most of the existing non-randomized multiple hypotheses testing procedures for discrete distributions. Three new procedures are proposed: TWWkTWWk, stepwise TWWkTWWk and an expansion of Paroush integer programming (IP) procedure for multiple tests. All procedures are compared to each other using mathematical and/or simulation analysis. Simulation analysis included several test cases where procedures for multiple hypotheses for discrete distributions are applicable. This work clarifies that discrete analysis procedures should be used with multiple hypotheses testing in order to gain power. Additionally, it more precisely couples the most appropriate discrete procedures with the specific test case.