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Robert E. Bechhofer, Saul Blumenthal, A Sequential Multiple-Decision Procedure for Selecting the Best One of Several Normal Populations with a Common Unknown Variance, II: Monte Carlo Sampling Results and New Computing Formulae, Biometrics, Vol. 18, No. 1 (Mar., 1962), pp. 52-67
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Bechhofer et al. (1962) studied this question.
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