Power of a statistical test

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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).


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