# Power of a statistical test

From Encyclopedia of Mathematics

The probability with which a statistical test for testing a simple hypothesis against a simple hypothesis rejects when in fact is true. In the case when the hypothesis , competing with in the test, is compound ( itself may be either simple or compound, which is written symbolically: : , : ), the power of the statistical test for against is defined as the restriction of the power function , , of this test to .

In addition, this definition has been broadly generalized to the following: The power of a statistical test for testing : against a compound alternative : is , where is the power function of the test (see Power function of a test).

#### References

[1] | E.L. Lehmann, "Testing statistical hypotheses" , Wiley (1959) |

[2] | J. Hájek, Z. Sidák, "Theory of rank tests" , Acad. Press (1967) |

[3] | B.L. van der Waerden, "Mathematische Statistik" , Springer (1957) |

[4] | H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946) |

**How to Cite This Entry:**

Power of a statistical test.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Power_of_a_statistical_test&oldid=18477

This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article