A single—stage selection procedure for multi-factor multinomial experiments with multiplicativity

. A single—stage procedure is proposed for selecting the event which has the largest probability in multi—factor multinomial experiments with multiplicativity, i.e., experiments in which the factor—level responses of any one factor are independent of those of all other factors. The procedure is a generalization of one proposed for single—factor multinomial experiments by Bechhofer, Elmaghraby and Morse (B— E—M) (1959). Tables necessary to implement the procedure are provided, and properties of the procedure are obtained. It is shown that if independence holds it is much more efficient in terms of minimizing total sample size to conduct the experiment as a factorial experiment rather than as independent single—factor experiments. Specifically, if an f—factor (f > 2) experiment is conducted, and certain symmetry conditions hold, the factorial experiment requires 1/f as many observations to guarantee the same indifference—zone probability requirement, as do f independent single-factor experiments. If multiplicability does not hold the experimenter can use the original B-E-M single-stage, single-factor procedure but for a different goal and probability requirement than the one employed for the 2-factor problem.