# Neyman-Pearson lemma

(Redirected from Neyman–Pearson lemma)
A lemma asserting that in the problem of statistically testing a simple hypothesis $H_0$ against a simple alternative $H_1$ the likelihood-ratio test is a most-powerful test among all statistical tests having one and the same given significance level. It was proved by J. Neyman and E.S. Pearson [1]. It is often called the fundamental lemma of mathematical statistics. See also Statistical hypotheses, verification of.