The Language of Statistical Decision Making Lecture 3 Section 1 3 Mon Jan 21 2008 Errors Recall 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 2 Errors Had 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 3 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 4 Decisions and Errors State of Nature H0 true H0 false Accept H0 Correct Type II Error Reject H0 Type I Error Correct Decision Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 5 Decisions and Errors True distribution It is what It is not what company sayscompany says It is what compan Decision y says It is not what compan y says Mon Jan 21 2008 Correct Type II Error Type I Error Correct The Language of Statistical Decision Mak ing Part 2 6 Decisions and Errors State of Nature H0 true H0 false Accept H0 Correct Type II Error Reject H0 Type I Error Correct Decision Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 7 Decisions and Errors State of Nature H0 true H0 false Accept H0 Correct Type II Error Reject H0 Type I Error Correct Decision Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 8 Case Study 2 Hair May Help Reveal Eating Disorders Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 9 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 10 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 11 Type I Error vs Type II Error See Making Intelligent Errors by Walter Williams Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 12 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 13 Two Unusual Dice Suppose 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 14 Which 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 15 The Decision What 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 16 The Significance Level What is the value of What is the value of Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 17 Are Two Rolls Better Than One Suppose now that we roll the chosen 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 Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 18 Are Two Rolls Better Than One What would be a good criterion for deciding which die it is Based on this criterion is What is What Mon Jan 21 2008 The Language of Statistical Decision Mak ing Part 2 19
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