EXTENSIONS OF MULTIPLE TESTING PROCEDURES BASED ON SIMES TEST

Shaffer (J. Amer. Statist. Assoc. 81 (1986) 826-831) gave simple and more powerful modifications of Helm's (Scand. J. Statist. 6 (1979) 65-70) procedure to families of Logically Related Hypotheses (LRH). Since then, several procedures more powerful than Helm's (based on Simes (Biometrika 73 (1986) 751-754)) have been introduced, with partial or no discussion of their improvements in cases of LRH. In this article, simple and more powerful modifications of these procedures (analogous to Shaffer's modifications) for general problems of LRH are given. These modified procedures are more powerful than the modified Holm's procedure in general problems of LRH. The various modifications are demonstrated and their superiority over existing procedures is indicated for some LRH. Another extension concerns one-sided tests with normal correlated test statistics. Some analysis of the type-I error-rate associated with Simes' type procedures in this case indicates satisfactory control. A class of problems suitable for applications of a Simes' type procedure in view of the given results, is indicated.