A Single-Sample Multiple-Decision Procedure for Selecting the Multinomial Event Which Has the Highest Probability

The problem of selecting the multinomial event which has the highest probability is formulated as a multiple-decision selection problem. Before experimentation starts the experimenter must specify two constants (θ^, P^) which are incorporated into the requirement: "The probability of a correct selection is to be equal to or greater than P^ whenever the true (but unknown) ratio of the largest to the second largest of the population probabilities is equal to or greater than θ^." A single-sample procedure which meets the requirement is proposed. The heart of the procedure is the proper choice of N, the number of trials. Two methods of determining N are described: the first is exact and is to be used when N is small; the second is approximate and is to be used when N is large. Tables and sample calculations are provided.