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Biometrika 1972 59(2):317-322; doi:10.1093/biomet/59.2.317
© 1972 by Biometrika Trust
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A two-stage procedure for choosing the better of two binomial populations

DAVID G. HOEL, MILTON SOBEL and GEORGE H. WEISS

National Institute of Environmental Health Sciences, Research Triangle Park North Carolina
University of Minnesota
National Institutes of Health Bethesda

In an earlier paper Sobel & Weiss (1970) examined two sampling schemes for choosing the binomial population with the larger probability of success. The two sequential allocation procedures were discussed in the light of their ability to reach a decision while using as small a number as possible of tests with the poorer population. It was shown that neither sampling scheme was uniformly better than the other with respect to that criterion. However, one sampling procedure, the Play-the-Winner rule (Robbins, 1956; Zelen, 1969), was superior, provided that the probability of success of the better population was greater than a number roughly equal to 3/4. Here we investigate a two-stage procedure in which the first stage is used to estimate the probability of success of the better population. It is shown that a fairly small estimation stage, approximately five tests with each population, allows one to benefit considerably from the choice between the two sampling methods available in the second stage.

Key Words: Selection procedures • Binomial populations • Clinical trials • Two-stage design


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