A multiple directional decision procedure for successive comparisons of treatment effects

Suppose that the k treatments under comparison are ordered in a certain way. For example, there 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 μ_i's, namely the set of differences μ₂−μ₁,μ₃−μ₂,…,μ_k−μ_k−1. In particular, directional inferences on whether μ_i<μ_i+1 or μ_i>μ_i+1 for i=1,…,k−1 are useful. Lee and Spurrier (J. Statist. Plann. Inference 43 (1995) 323) present a one- and a two-sided confidence interval procedures for making successive comparisons between treatments. In this paper, we develop a new procedure which is sharper than both the one- and two-sided procedures of Lee and Spurrier in terms of directional inferences. This new procedure is able to make more directional inferences than the two-sided procedure and maintains the inferential sensitivity of the one-sided procedure. Note however this new procedure controls only type III error, but not type I error. The critical point of the new procedure is the same as that of Lee and Spurrier's one-sided procedure. We also propose a power function for the new procedure and determine the sample size necessary for a guaranteed power level. The application of the procedure is illustrated with an example.