Exact Tests of Binomial P=1/2 When One Binomial Event Possibly Has Different Probability

摘要

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). (Author)