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 [mu]i's, namely the set of differences [mu]2-[mu]1,[mu]3-[mu]2,...,[mu]k-[mu]k-1. In particular, directional inferences on whether [mu]i<[mu]i+1 or [mu]i>[mu]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.
Critical points; Directional decision; Multivariate-t distribution; Pairwise comparisons; Simultaneous confidence intervals
Journal of Statistical Planning and Inference
Liu, Wei and KWONG, Koon Shing.
A Multiple Directional Decision Procedure for Successive Comparisons of Treatment Effects. (2003). Journal of Statistical Planning and Inference. 116, (1), 49-59. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/315
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