A Step-Up Multiple Test Procedure

Abstract We consider the problem of simultaneously testing k ≥ 2 hypotheses on parameters θ1, …, θk . In a typical application the θ's may be a set of contrasts, for instance, a set of orthogonal contrasts among population means or a set of differences between k treatment means and a standard treatment mean. It is assumed that least squares estimators 1, …, k are available that are jointly normally distributed with a common variance (known up to a scalar, namely the error variance σ 2) and a common known correlation. An independent χ 2-distributed unbiased estimator of σ 2 is also assumed to be available. We propose a step-up multiple test procedure for this problem which tests the t statistics for the k hypotheses in order starting with the least significant one and continues as long as an acceptance occurs. (By contrast, the step-down approach, which is usually used, starts with the most significant and continues as long as a rejection occurs.) Critical constants required by this step-up procedure to co...

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