The Language of Statistical Decision Making Lecture 3 Section 1 3 Mon Jan 22 2007 Errors Recall our conclusion about the die being fair Could our conclusion have been wrong What would be the cause of our error Errors Had we concluded that the die was not fair could he have been wrong What would be the cause of our error Possible Errors We might reject H0 when it is true This We might accept H0 when it is false This is a Type I error is a Type II error See Making Intelligent Errors by Walter Williams Decisions and Errors State of Nature H0 true H0 false Accept H0 Correct Type II Error Reject H0 Type I Error Correct Decision Decisions and Errors State of Nature H0 true H0 false Accept H0 Correct Type II Error Reject H0 Type I Error Correct Decision Decisions and Errors State of Nature H0 true H0 false Accept H0 Correct Type II Error Reject H0 Type I Error Correct Decision Example Consider a study to determine the effectiveness of a new drug What are the two possible conclusions hypotheses Which should get the benefit of the doubt What are the two possible errors Which is more serious Example Now consider a study to determine the safety of a new drug What are the two possible conclusions hypotheses Which should get the benefit of the doubt What are the two possible errors Which is more serious Safe and Effective Criteria Safe and effective Significance Level Significance Level The likelihood of rejecting H0 when it is true i e the likelihood of committing a Type I error The likelihood of a Type I error The likelihood of a Type II error That is is the significance level Significance Level Suppose that we have two very unusual dice Die A rolls a 1 80 of the time and a 6 only 20 of the time It never lands 2 3 4 or 5 Die B rolls a 1 only 10 of the time and a 6 90 of the time It never lands 2 3 4 or 5 Visually the two dice are indistinguishable Significance Level We are given one of the dice and we roll it one time We get a 1 Suppose the null hypothesis is that we rolled die A and the alternative hypothesis is that we rolled die B Which hypothesis do we choose Significance Level What is our criterion for choosing between the two hypotheses Describe a Type I error Describe a Type II error What is the value of What is the value of Two Rolls Suppose now that we roll the selected die twice and average the two rolls We must get either A pair of 1s with an average of 1 A 1 and a 6 with an average of 3 5 A pair of 6s with an average of 6 Two Rolls What would be a good criterion for decided which die it is Based on this criterion is What is What An Interesting Study Hair May Help Reveal Eating Disorders What were the hypotheses Describe a Type I error Describe a Type II error
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