The Language of Statistical Decision MakingErrorsSlide 3Possible ErrorsDecisions and ErrorsSlide 6Slide 7Slide 8Case Study 2ExampleSlide 11Type I Error vs. Type II ErrorSignificance LevelTwo Unusual DiceWhich Die Did We Pick?The DecisionThe Significance LevelAre Two Rolls Better Than One?Slide 19The Language of Statistical Decision MakingLecture 3Section 1.3Mon, Jan 21, 2008The Language of Statistical Decision Making - Part 22Mon, Jan 21, 2008ErrorsRecall our conclusion that the distribution of M&M colors agreed with what the company said.Could our conclusion have been wrong?What would be the cause of our error?The Language of Statistical Decision Making - Part 23Mon, Jan 21, 2008ErrorsHad we concluded that the distribution was not what the company said it was, could we have been wrong? What would be the cause of our error?The Language of Statistical Decision Making - Part 24Mon, Jan 21, 2008Possible 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.The Language of Statistical Decision Making - Part 25Mon, Jan 21, 2008Decisions and ErrorsCorrectType IErrorCorrectType IIErrorState of NatureH0 true H0 falseAccept H0Reject H0DecisionThe Language of Statistical Decision Making - Part 26Mon, Jan 21, 2008Decisions and ErrorsCorrectType IErrorCorrectType IIErrorTrue distributionIt is what company saysIt is not what company saysIt is what company saysIt is not what company saysDecisionThe Language of Statistical Decision Making - Part 27Mon, Jan 21, 2008Decisions and ErrorsCorrectType IErrorCorrectType IIErrorState of NatureH0 true H0 falseAccept H0Reject H0DecisionThe Language of Statistical Decision Making - Part 28Mon, Jan 21, 2008Decisions and ErrorsCorrectType IErrorCorrectType IIErrorState of NatureH0 true H0 falseAccept H0Reject H0DecisionThe Language of Statistical Decision Making - Part 29Mon, Jan 21, 2008Case Study 2Hair May Help Reveal Eating DisordersThe Language of Statistical Decision Making - Part 210Mon, Jan 21, 2008ExampleConsider 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?The Language of Statistical Decision Making - Part 211Mon, Jan 21, 2008ExampleNow 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?The Language of Statistical Decision Making - Part 212Mon, Jan 21, 2008Type I Error vs. Type II ErrorSee Making Intelligent Errors, by Walter Williams.The Language of Statistical Decision Making - Part 213Mon, Jan 21, 2008Significance 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.The Language of Statistical Decision Making - Part 214Mon, Jan 21, 2008Two Unusual DiceSuppose that we have two 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.The Language of Statistical Decision Making - Part 215Mon, Jan 21, 2008Which Die Did We Pick?We pick up one of the dice.Suppose the null hypothesis is that we picked up die A and the alternative hypothesis is that we picked up die B.We will roll the die one time and, based on the outcome, decide which die we think it is.The Language of Statistical Decision Making - Part 216Mon, Jan 21, 2008The DecisionWhat should be our criterion (decision rule) for choosing between the two hypotheses?That is, if the die turns up 1, which hypothesis do we choose? What if it turns up 6?Describe a Type I error.Describe a Type II error.The Language of Statistical Decision Making - Part 217Mon, Jan 21, 2008The Significance LevelWhat is the value of ?What is the value of ?The Language of Statistical Decision Making - Part 218Mon, Jan 21, 2008Are Two Rolls Better Than One?Suppose now that we roll the chosen 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.The Language of Statistical Decision Making - Part 219Mon, Jan 21, 2008Are Two Rolls Better Than One?What would be a good criterion for deciding which die it is?Based on this criterion,What is ?What is
View Full Document
Unlocking...