Power of a statistical test
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).
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|||B.L. van der Waerden, "Mathematische Statistik" , Springer (1957)|
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Power of a statistical test. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Power_of_a_statistical_test&oldid=18477