Another Statistical Paradox
نویسندگان
چکیده
We show that a single binomial observation carries absolutely no evidential value for discriminating the null hypothesis θ = 1/2 from a broad class of alternative hypotheses that allow θ to be between 0 and 1. In contrast, interval estimation methods suggest that a single binomial observation does provide some evidence against the null hypothesis. The resolution of this paradox requires the insight that interval estimation methods may not be used for model comparison; interval estimates are postdictive rather than predictive, and therefore fail to take model complexity properly into account.
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