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Biometrika 1973 60(3):517-523; doi:10.1093/biomet/60.3.517
© 1973 by Biometrika Trust
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An improved version of a Sobel-Weiss Play-the-Winner procedure for selecting the better of two binomial populations

MASANORI FUSHIMI {dagger}

Cornell University

A sequential decision procedure is considered for the problem of selecting the better of two Bernoulli populations. This procedure is a truncation of a Sobel-Weiss Play-the-Winner sampling procedure with a termination rule based on the difference in the number of successes. Exact expressions for the probability of correct selection and for the expected sample sizes are obtained. It is shown that this procedure is both asymptotically and also in many non-asymptotic cases uniformly better than the Sobel-Weiss procedure. It is also shown that this procedure compares favourably with some other procedures.

Key Words: Multiple comparisons • Sequential decision rules • Bernoulli populations • Play-the-Winner sampling • Selection


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