Stepwise multiple tests for successive comparisons of treatment effects

Suppose that the k treatments under comparison are ordered in a certain way. For example, they may be a sequence of increasing dose levels of a drug. It is interesting to look directly at the successive differences between the treatment effects mu(i)'s, namely the set of differences mu(2) - mu(1), mu(3) - mu(2)...,mu(k) - mu(k-1). Lee and Spurrier (J, Statist. Plann. Inference 43 (1995) 323) propose a one-sided and a two-sided simultaneous confidence interval procedures for making successive comparisons between treatments. In this paper we develop step-down and step-up tests for testing the families of hypotheses H-i0: mu(i+1) - mu(i) = 0 vs H-ia: mu(i+1) > 0, i = 1,...,k - I (one-sided alternatives) H-i0: mu(i+1) - mu(i) = 0 vs H-ia: mu(i+1) - mu(i) not equal 0, i = 1,...,k - 1 (two-sided alternatives) These stepwise tests are uniformly more powerful than the simultaneous confidence interval procedures in terms of rejection of the null hypotheses, though the simultaneous confidence interval procedures provide information on the magnitudes of the mu(i+1) - mu(i)'s. The critical constants required for applying these multiple tests are provided, and the tests are illustrated with a numerical example. (C) 2003 Published by Elsevier B.V.