Play-the-winner sampling for selecting the better of two binomial populations

Abstract

The sequential allocation of treatments by an experimenter is considered for determining which of two binomial populations has the larger probability of success. Of particular interest in this study is a 'Play-the-Winner' (PW) sampling rule which prescribes that one continues with the same population after each success and one switches to the opposite population after each failure. The performance of the PW rule is examined for the selection problem, i.e. for selecting the better population with probability P* when the two singletrial probabilities of success, p and p', differ by at least A*, where P* and i\* are prescribed. A comparison is made between PW sampling and 'Vector-at-a-Time' (VT) sampling. In comparing results a criterion used is the expected number of failures that could have been avoided by using the better population throughout. It is shown for a particular common termination rule that with A* close to zero the PW sampling is superior to VT sampling if and only if I (p +p') > J. Other comparisons are also discussed.