The Language of Statistical Decision MakingErrorsSlide 3Possible ErrorsDecisions and ErrorsSlide 6Slide 7ExampleSlide 9Safe and Effective CriteriaSignificance LevelSlide 12Slide 13Slide 14Two RollsSlide 16An Interesting StudyThe Language of Statistical Decision MakingLecture 3Section 1.3Mon, Jan 22, 2007ErrorsRecall our conclusion about the die being fair.Could our conclusion have been wrong?What would be the cause of our error?ErrorsHad we concluded that the die was not fair, could he have been wrong? What would be the cause of our error?Possible ErrorsWe might reject H0 when it is true.This is a Type I error.We might accept H0 when it is false.This is a Type II error.See Making Intelligent Errors, by Walter Williams.Decisions and ErrorsCorrectType IErrorCorrectType IIErrorState of NatureH0 true H0 falseAccept H0Reject H0DecisionDecisions and ErrorsCorrectType IErrorCorrectType IIErrorState of NatureH0 true H0 falseAccept H0Reject H0DecisionDecisions and ErrorsCorrectType IErrorCorrectType IIErrorState of NatureH0 true H0 falseAccept H0Reject H0DecisionExampleConsider 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?ExampleNow 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 CriteriaSafe and effectiveSignificance LevelSignificance 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 LevelSuppose 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 LevelWe 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 LevelWhat 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 RollsSuppose now that we roll the selected die twice and average the two rolls.We must get eitherA 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 RollsWhat would be a good criterion for decided which die it is?Based on this criterion,What is ?What is ?An Interesting StudyHair May Help Reveal Eating Disorders What were the hypotheses?Describe a Type I error.Describe a Type II
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