b.lect26 - Outline Specification of a Test Procedure...

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Unformatted text preview: Outline Specification of a Test Procedure Nonparametric Tests Lecture 26 Chapter 9: Testing of Hypotheses Michael Akritas Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Specification of a Test Procedure Type I and Type II Errors The Philosophy for Choosing a Rejection Rule Nonparametric Tests Nonparametric tests for a population mean Nonparametric tests for a population proportion The Sign Test for the Median and Percentiles Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Type I and Type II Errors The Philosophy for Choosing a Rejection Rule Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Type I and Type II Errors The Philosophy for Choosing a Rejection Rule I It is possible for the TS to take value in the RR even when H is true. Rejecting H when it is true is called a type I error . Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Type I and Type II Errors The Philosophy for Choosing a Rejection Rule I It is possible for the TS to take value in the RR even when H is true. Rejecting H when it is true is called a type I error . I The probability of committing type I error is denoted by and is called the level of significance of the test . Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Type I and Type II Errors The Philosophy for Choosing a Rejection Rule I It is possible for the TS to take value in the RR even when H is true. Rejecting H when it is true is called a type I error . I The probability of committing type I error is denoted by and is called the level of significance of the test . I It is also possible for the value of the TS not to be in the RR even when H a is true. Not rejecting H when it is false is called a type II error . Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Type I and Type II Errors The Philosophy for Choosing a Rejection Rule I It is possible for the TS to take value in the RR even when H is true. Rejecting H when it is true is called a type I error . I The probability of committing type I error is denoted by and is called the level of significance of the test . I It is also possible for the value of the TS not to be in the RR even when H a is true. Not rejecting H when it is false is called a type II error . I For example, consider testing H : = 28 , 000 vs H a : < 28 , 000 using the RR X < 27 , 000. Then, Michael Akritas Lecture 26 Chapter 9: Testing of Hypotheses Outline Specification of a Test Procedure Nonparametric Tests Type I and Type II Errors The Philosophy for Choosing a Rejection Rule I It is possible for the TS to take value in the RR even when H is true. Rejectingis true....
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This note was uploaded on 03/19/2009 for the course STAT 401 taught by Professor Akritas during the Spring '00 term at Pennsylvania State University, University Park.

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b.lect26 - Outline Specification of a Test Procedure...

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