A comparison of sequential sampling procedures for selecting the better of two binomial populations

A comparison is made between play-the-winner sampling and vector-at-a-time sampling for selecting the better of two binomial populations when the selection requirement is defined in terms of the ratio of the single trial probabilities of success rather than the difference. Thus the probability of correct selection is to be at least P* when the true ratio of probabilities of success θ is at least θ*, where P* and θ* are prescribed. Termination rules based on the difference in the number of successes and inverse sampling are considered. It is shown that play-the-winner sampling is uniformly preferable to vector-at-a-time sampling for both termination rules, and that for θ* close to one the success lead termination rule leads to a smaller expected number of trials on the poorer treatment unless θ is even closer to one.