Sequential tests controlling generalized familywise error rates

Abstract Sequential methods are developed for conducting a large number of simultaneous tests while controlling the Type I and Type II generalized familywise error rates. Namely, for the chosen values of α , β , k , and m , we derive simultaneous tests of d individual hypotheses, based on sequentially collected data, that keep the probability of at least k Type I errors not exceeding level α and the probability of at least m Type II errors not greater than β . This generalization of the classical notions of familywise error rates allows substantial reduction of the expected sample size of the multiple testing procedure.

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