Familywise Robustness Criteria Revisited for Newer Multiple Testing Procedures

Abstract

As the availability of large datasets becomes more prevalent, so does the need to discover significant findings among a large collection of hypotheses. Multiple testing procedures (MTP) are used to control the familywise error rate (FWER) or the chance to commit at least one type I error when performing multiple hypotheses testing. When controlling the FWER, the power of a MTP to detect significant differences decreases as the number of hypotheses increases. It would be ideal to discover the same false null hypotheses despite the family of hypotheses chosen to be tested. Holland and Cheung (2002) developed measures called familywise robustness criteria (FWR) to study the effect of family size on the acceptance and rejection of a hypothesis. Their analysis focused on procedures that controlled FWER and false discovery rate (FDR). Newer MTPs have since been developed which control the generalized FWER (gFWER (k) or k-FWER) and false discovery proportion (FDP) or tail probabilities for the proportion of false positives (TPPFP). This dissertation reviews these newer procedures and then discusses the effect of family size using the FWRs of Holland and Cheung. In the case where the test statistics are independent and the null hypotheses are all true, the Type R enlargement familywise robustness measure can be expressed as a ratio of the expected number of Type I errors. In simulations, positive dependence among the test statistics was introduced, the expected number of Type I errors and the Type R enlargement FWR increased for step-up procedures with higher levels of correlation, but not for step-down or single-step procedures.