This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ....
View
Full
Document
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).
 Fall '09
 SAMORODNITSKY

Click to edit the document details