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Statistica Sinica 18(2008), 1593-1602





MULTIPLE TESTING OF TWO-SIDED ALTERNATIVES

WITH DEPENDENT DATA


Arthur Cohen and Harold B. Sackrowitz


Rutgers University
Abstract: Multiple testing procedures have become an integral element of analysis in many practical problems. The development of sound procedures has become an important statistical issue. Many procedures have been suggested and many criteria of goodness have been used. Most recent procedures are stepwise in nature. Perhaps the most fundamental (and typically overlooked) issue is the behavior of the multiple testing procedure as it relates to each individual testing problem.

In this paper we study two of the most popular stepwise procedures. We demonstrate that the individual tests they induce are inadmissible in some important two-sided testing models when correlation is present. That is, for each individual hypothesis testing problem, a test exists whose size is less than or equal that of the stepwise procedure test and whose power is greater than or equal that of the stepwise procedure test with some strict inequality. This means that the overall multiple testing procedure is inadmissible whenever a loss based on the number of Type I and Type II errors is used.



Key words and phrases: Closure principle, general linear model, inadmissibility, stepwise procedures, treatments vs control, vector risk.

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