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On the Optimality of Some Multiple Comparison Procedures

# On the Optimality of Some Multiple Comparison Procedures,10.1214/aoms/1177692621,The Annals of Mathematical Statistics,Emil Spjotvoll

On the Optimality of Some Multiple Comparison Procedures
Optimality criteria formulated in terms of the power functions of the individual tests are given for problems where several hypotheses are tested simultaneously. Subject to the constraint that the expected number of false rejections is less than a given constant $\gamma$ when all null hypotheses are true, tests are found which maximize the minimum average power and the minimum power of the individual tests over certain alternatives. In the common situations in the analysis of variance this leads to application of multiple $t$-tests. In that case the resulting procedure is to use Fisher's "least significant difference," but without a preliminary $F$-test and with a smaller level of significance. Recommendations for choosing the value of $\gamma$ are given by relating $\gamma$ to the probability of no false rejections if all hypotheses are true. Based upon the optimality of the tests, a similar optimality property of joint confidence sets is also derived.
Journal: The Annals of Mathematical Statistics , vol. 43, no. 1972, pp. 398-411, 1972
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## Citation Context (1)

• ...Actually, viewing all but one faults as nuisance parameters and exploiting possible invariance properties is a relevant approach, for which some optimality property has been established [30, 2]. Roughly speaking, the set of all ‘individual’ tests maximizes both the minimum and the sum of the individual powers...

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