On a Lower Confidence Bound for the Probability of a Correct Selection: Analytical and Simulation Studies.

For the problem of selecting the best of several populations using the indifference preference zone formulation, a natural rule is to select the population yielding the largest sample value of an appropriate statistic. For this approach, it is required that the experimenter specify a number delta, say, which is a lower bound on the difference separation between the largest and the second largest parameter. However, in many real situations, it is hard to assign the value of delta and, therefore, in case that the assumption of indifference zone is violate, the probability of a correct selection cannot be guaranteed to be at least P, a prespecified value. This paper concerns the derivation of a lower confidence bound for the probability of a correct selection for the general location model Fx-Theta, i l,...,k. First, derive simultaneous lower confidence bounds on the differences between the largest best and each of the other non-best population parameters. Based on these, a lower confidence bound is obtained for the probability of a correct selection. The general result is then applied to the selection of the best mean of k normal populations with both the known and unknoWn common variances. In the first case one needs a single stage procedure while in the second case a two stage procedure is required. Some simulation investigations are described and their results are provided.