NotesDec3 - Terminology : the significance level of the...

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Unformatted text preview: Terminology : the significance level of the test : an upper bound on the probability of type 1 error. It is also often denoted by . typical values of the significance level: 0 . 1 , . 05 , . 01 , . 005. The significance level of the test is also called the size of the test. For a simple null hypothesis H we choose the critical region so that = probability of type 1 error = significance level = . For a composite null hypothesis H we choose the critical region so that ( ) = P (reject H | the true parameter is ) significance level = . The critical region of a test with signifi- cance level is called a size critical re- gion. The power function of a test : ( ) = 1- ( ) = P (reject H | the true parameter is 1 ) . Among alternative tests with a given signifi- cance level , the one with a higher power is better. Constructing powerful tests using likelihood ratios Testing simple hypothesis We need to test a simple hypothesis against a simple alternative H : = vs. H 1 : = 1 at a significance level ....
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This note was uploaded on 12/03/2010 for the course OR 3500 taught by Professor Samorodnitsky during the Fall '09 term at Cornell University (Engineering School).

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NotesDec3 - Terminology : the significance level of the...

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