Abstract
Somerville (1964) proposed a one-stage and a two-stage procedure for the selection of the popopulation with the largest mean from a set of normal populations with unknown means and a common, known variance. The two-stage procedure eliminates one population after the first stage. For these procedures he assumed that a certain loss was incurred when an incorrect selection was made and also that a cost was due to sampling. The sample sizes which would minimize the maximum expected loss, the maximum being taken over all possible configurations of the true population means, were derived. For the special case of three populations he showed that the two-stage procedure, using appropriate allocations of observations between stages, has a smaller maximum expected loss than does the onestage procedure. This paper generalize Somerville's formulation of the two-stage procedure to an arbitrary finite number of populations and presents results for the special case of four populations, where two two-stage procedures are considered.
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