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A locally most powerful test for the symmetric folded binomial distribution.

This paper derives a locally most powerful test of the hypothesis of the folded binomial with p = against the alternative of a folded binomial with p 0 1. The resulting 'variance test' is also shown to be a locally most powerful test against the folded symmetric compound binomial alternative. Some approximations to the distribution of the test statistic are discussed and their accuracy is calculated exactly for a small sample example. For the same example, the test's power is compared with the power of the goodness-of-fit chisquare test which was suggested by Urbakh [1967] for this problem. These exact calculations confirm the superiority of the 'variance test.' The tests are applied to some data of Jordansky et al. [1966] on the radio-autographical analyses of DNA-reproduction in sister-chromatids.