A PAIRWISE COMPARISON PROCEDURE FOR COMPARING UMBRELLA PATTERN TREATMENT EFFECTS WITH A CONTROL

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  • Hoshino Naoto
    Department of Systems and Information Engineering, Ashikaga Institute of Technology

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  • アンブレラ処理群と対照群の対比較法
  • アンブレラ ショリグン ト タイショウグン ノ ツイヒカクホウ

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Dunnett's procedure is a pairwise comparison procedure for comparing several treatment effects with a control in a one-way layout, under the normality assumption about the data. In such a Dunnett type multiple comparison problem, this paper supposes that we can utilize the prior information of an umbrella ordering in the treatment effects. This ordering represents a pattern of treatment effects that increase up to a certain group, which is called the peak of the umbrella, and conversely decrease beyond the group. We propose a pairwise comparison procedure using test statistics based on the difference between the maximum likelihood estimators of the treatment means under the umbrella restriction and the sample mean of the control. Critical values for the proposed procedure are determined to guarantee the type I FEW (familywise error rates) requirement. Furthermore, all-pairs powers are compared between the proposed procedure and Dunnett's procedure by means of a Monte Carlo simulation.

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