Abstract
The data are n independent random binomial events, each resulting in success or failure. The event outcomes are believed to be trials from a binomial distribution with success probability p, and tests of p=1/2 are desired. However, there is the possibility that some unidentified event has a success probability different from the common value p for the other n−1 events. Then, tests of whether this common p equals 1/2 are desired. Fortunately, two-sided tests can be obtained that simultaneously are applicable for both situations. That is, the significance level for a test is same when one event has a different probability as when all events have the same probability. These tests are the usual equal-tail tests for p=1/2 (based on n independent trials from a binomial distribution).
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Research partially supported by Mobil Research and Development Corporation and by Nasa Grant NGR 44-007-028. Also associated with ONR Contract NOOO14-68-A-0515.
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Walsh, J.E., Kelleher, G.J. Exact tests of binomial p=1/2 when one binomial event possibly has different probability. Statistische Hefte 12, 325–328 (1971). https://doi.org/10.1007/BF02923574
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DOI: https://doi.org/10.1007/BF02923574