Multiple Comparison Procedures for Location Parameters: Logistic Populations Case

Abstract

SYNOPTIC ABSTRACTConsider k (≥2) independent populations π1, …, πk such that population πi, is characterized by the logistic distribution with unknown location parameter μi and common known scale parameter σ2, i = 1, …, k. In this article, we propose a multiple comparison procedure for all pairwise comparisons, μi – μj, 1 ≤ i ≠ j ≤ k. In addition, we also address comparisons of adjacent pairs of means in the case when it is known that the k populations are ordered in a certain way. This situation may arise in a dose response study where the k populations represent the responses of a sequence of increasing dose levels of a drug. Specifically, we propose procedures for testing the family of hypothesesthat control the family wise type-I error rate at a level α. We further propose a procedure for testing the null hypothesis H0 : μ1 = … = μk against the umbrella alternative HA : μ1 ≤ … ≤ μh ≥ … ≥ μk, with at least one strict inequality. The associated (l – α)% simultaneous confidence intervals are also provided. The critical constants, required for each procedure, are computed numerically and tabulated for different significance levels and testing scenarios.