Lecture 13

# Lecture 13 - Probability and Statistics in the Life Sciences(Spring 2010 AMS 110.02 Lecture 13(chap7 Donghyung Lee Chapter 7(supplements P-Values

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Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 13 (chap7) Donghyung Lee

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Chapter 7 (supplements) P-Values P-Value (1) . . ( ), ( L U The P value is observed significance level It measures how extreme data is The lower one sided p value P P Test Statistic Observed Value of the Test Statistic the upper one sided p value P P Test Statistic Observed Value of t - - - = - - = ), 2min( , ). L U he Test Statistic and the two sided p value is defined as P P - -
Chapter 7 (supplements) P-Values P-Value (2) 0 0 0 0 0 0 0 0 0 0 0 0 , ( ) ( ) 2 ( ) , ( ) ( ) 2 ( ) For z tests P Z z for an upper tailed test P value P Z z for an lower tailed test P Z z for a two tailed test For t tests P T t for an upper tailed test P value P T t for an lower tailed test P T t for a t - - - = - - - - - = - wo tailed test e e e e -

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Chapter 7 (supplements) P-Values Example 7-5 Let μ denote the mean reaction time to a certain stimulus. For a large-sample z test of H 0 :μ=5 versus H a :μ>5, find the P-value associated with each of the given values of the z test statistic. (a) 1.42 (b) -.11 Example 7-6 Let μ denote the mean reaction time to a certain stimulus. For a large-sample z test of H 0 :μ=5 versus H a :μ<5, find the P-value associated with each of the given values of the z test statistic. (a) .90 (b) -1.20
Chapter 7 (supplements) P-Values Example 7-7 Let μ denote the mean reaction time to a certain stimulus. For a large-sample z test of H 0 :μ=5 versus H a 5, find the P-value associated with each of the given values of the z test statistic. (a) .42 (b) -1.56 Example 7-8 Give as much information as you can about the P-value of a t test in each of the following situations: (a) Upper-tailed test, n=9, t 0 =2.0 (b) Lower-tailed test, n=12, t 0 =-2.4 (c) Two-tailed test, n=16, t 0 =-1.6

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Chapter 7 (supplements) P-Values P-Value (3) 0 ( ) . , The P value or observed significance level is the smallest level of signficance at which H would be rejected when a specified test procedure is used on a given data set Once the P value has been determined the conclusion at any particu - - 0 0 : 1. . 2. . lar level results from comparing the P value to P value reject H at level P value do not reject H at level α - - = - =
Chapter 7 (supplements) P-Values P-Value (4) 0 0 0 , , . , . The P value is the probability calculated assuming H is true of obtaining a test statistic value at least as contradictory to H as the value that actually resulted The smaller the P value the more contradictory is the data to H - -

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Chapter 7 (supplements) P-Values Example 7-3 (Again)
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## This note was uploaded on 03/28/2011 for the course AMS 110 taught by Professor N/a during the Spring '08 term at SUNY Stony Brook.

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Lecture 13 - Probability and Statistics in the Life Sciences(Spring 2010 AMS 110.02 Lecture 13(chap7 Donghyung Lee Chapter 7(supplements P-Values

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