# Neyman-Pearson lemma

From Encyclopedia of Mathematics

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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.

#### References

[1] | 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 |

[2] | E.L. Lehmann, "Statistical hypotheses testing" , Wiley (1978) |

**How to Cite This Entry:**

Neyman–Pearson lemma.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Neyman%E2%80%93Pearson_lemma&oldid=22846