A Multiple-Step Selection Procedure with Sequential Protection of Preferred Treatments

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Abstract
Dunnett (1955, Journal of the American Statistical Association 50, 1096-1121) proposed a one-step many-one test to compare several experimental treatment means with a control. However, after the control treatment is rejected, one would want to make comparisons among the experimental treatments. We assume that there is an order of decreasing preference among the experimental treatments based on other considerations. We propose in this paper a multiple-step selection procedure, an extension of Dunnett's one-step many-one test that will give protection to the preferred treatments and guarantee a high selection probability of the correct treatment when that selection is appropriate. We also provide methods to calculate the sample size required to carry out this test for normal, binomial, and exponential data with random censoring.

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