View source for Neyman-Pearson lemma

A lemma asserting that in the problem of statistically testing a simple hypothesis <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066600/n0666001.png" /> against a simple alternative <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066600/n0666002.png" /> the [[Likelihood-ratio test|likelihood-ratio test]] is a [[Most-powerful test|most-powerful test]] among all statistical tests having one and the same given [[Significance level|significance level]]. It was proved by J. Neyman and E.S. Pearson [[#References|[1]]]. It is often called the fundamental lemma of mathematical statistics. See also [[Statistical hypotheses, verification of|Statistical hypotheses, verification of]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J. Neyman,   E.S. Pearson,   "On the problem of the most efficient tests of statistical hypotheses"  ''Philos. Trans. Roy. Soc. London Ser. A.'' , '''231'''  (1933)  pp. 289–337</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E.L. Lehmann,   "Statistical hypotheses testing" , Wiley  (1978)</TD></TR></table>