A Sequential Multiple-Decision Procedure for Selecting the Best One of Several Normal Populations with a Common Unknown Variance, and Its Use with Various Experimental Designs

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Abstract
The procedure described is a generalization of one which was previously proposed to handle the same problem when the common variance is known. Both procedures terminate with probability unity and guarantee that the probability of a correct selection is at least equal to some specified probability whenever the largest population mean is greater than the 2d-largest by some specified amount. For any given configuration of the population means, the average sample size required for termination of experimentation decreases as the population variance underlying the experiment decreases. Hence, the use of an experimental design which is effective in cutting down on this underlying variance will result in a decrease in the average sample size required for termination. The average sample size also decreases as the configuration of the population means becomes more favorable. The method of applying the procedure with various experimental designs is described. Approximate methods involving substantially less computation than the exact method are also given. A worked-out numerical example is provided.

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