J. Japan Statist. Soc., Vol. 31 (No. 2), pp. 153-174, 2001

Efficient Directional Inference Methodologies for the Comparisons of Three Ordered Treatment Effects

Anthony Hayter, Tetsuhisa Miwa and Wei Liu

Abstract. We consider the unbalanced one-way layout for comparing 3 treatment effects which can be assumed to satisfy the simple ordering m1 m2 m3. This problem arises often in the comparison of three dose levels in medical trials, for example. The one-sided studentised range test provides a set of simultaneous confidence intervals for the ordered pairwise differences mj - mi, i < j which are one-sided and have infinite upper bounds. The new confidence interval procedure proposed in this article maintains the sensitivity of the one-sided studentised range test in detecting each of the ordered differences mj - mi > 0 while at the same time providing two-sided finite confidence intervals. Consequently, this new procedure has the advantage of allowing the same directional inferences as the one-sided studentised range test while additionally providing upper bounds on the differences among the treatment effects.

Key words and phrases: Analysis of variance, bioassay, directional errors, medical trials, multiple comparisons, simultaneous inference, order restricted inference, experimentwise error rate.

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