The Language of Statistical Decision Making Lecture 2 Section 1.3 Mon, Sep 4, 2006.

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The Language of Statistical Decision Making Lecture 2 Section 1.3 Mon, Sep 4, 2006

Errors Recall the game with Envelopes A and B. Recall the game with Envelopes A and B. Our contestant decided that the other envelope was Envelope A. Our contestant decided that the other envelope was Envelope A. Could he have been wrong? Could he have been wrong? What would be the cause of his error? What would be the cause of his error?

Errors Had our contestant concluded that the sampled envelope was Envelope A, could he have been wrong? Had our contestant concluded that the sampled envelope was Envelope A, could he have been wrong? What would be the cause of his error? What would be the cause of his error?

Possible Errors We might reject H 0 when it is true. We might reject H 0 when it is true. This is a Type I error. This is a Type I error. We might accept H 0 when it is false. We might accept H 0 when it is false. This is a Type II error. This is a Type II error. See Making Intelligent Errors, by Walter Williams. See Making Intelligent Errors, by Walter Williams.Making Intelligent ErrorsMaking Intelligent Errors

Decisions and Errors Correct Type I Error Correct Type II Error State of Nature H 0 trueH 0 false Accept H 0 Reject H 0 Decision

Example Consider a study to determine the effectiveness of a new drug. Consider a study to determine the effectiveness of a new drug. What are the two possible conclusions (hypotheses)? What are the two possible conclusions (hypotheses)? Which should get the benefit of the doubt? Which should get the benefit of the doubt? What are the two possible errors? What are the two possible errors? Which is more serious? Which is more serious?

Example Now consider a study to determine the safety of a new drug. Now consider a study to determine the safety of a new drug. What are the two possible conclusions (hypotheses)? What are the two possible conclusions (hypotheses)? Which should get the benefit of the doubt? Which should get the benefit of the doubt? What are the two possible errors? What are the two possible errors? Which is more serious? Which is more serious?

Significance Level Significance Level – The likelihood of rejecting H 0 when it is true, i.e., the likelihood of committing a Type I error. Significance Level – The likelihood of rejecting H 0 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 I error.  – The likelihood of a Type II error.  – The likelihood of a Type II error. That is,  is the significance level. That is,  is the significance level. The quantity 1 –  is called the power of the test. The quantity 1 –  is called the power of the test.

Significance Level In the Envelope game, what was our contestant’s criterion for deciding which envelope was Envelope A? In the Envelope game, what was our contestant’s criterion for deciding which envelope was Envelope A? Based on this criterion, how likely was he to make a Type I error (I.e., decide the other envelope was Envelope A when in fact he was holding Envelope A)? Based on this criterion, how likely was he to make a Type I error (I.e., decide the other envelope was Envelope A when in fact he was holding Envelope A)? How likely was he to make a Type II error? How likely was he to make a Type II error?

Significance Level The value of  is determined by our criteria for rejecting the null hypothesis. The value of  is determined by our criteria for rejecting the null hypothesis. If we demand overwhelming evidence against H 0 before rejecting it, then  will be small (and  will be large). If we demand overwhelming evidence against H 0 before rejecting it, then  will be small (and  will be large). If we demand little evidence against it, then  will be large (and  will be small). If we demand little evidence against it, then  will be large (and  will be small).

An Interesting Study Porn can make you blind. Porn can make you blind. Porn can make you blind. Porn can make you blind. What were the hypotheses? What were the hypotheses? Describe a Type I error. Describe a Type I error. Describe a Type II error. Describe a Type II error.