# chap8 - Chapter 8 Two Dichotomous Responses 8.1 Study...

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Unformatted text preview: Chapter 8 Two Dichotomous Responses 8.1 Study Suggestions Chapter 8 contains many interesting and important ideas, yet I often fail to cover it in my class. Or if I do cover Chapter 8, I only cover its first two sections. There are two explanations for this apparent paradox. First, the notation of Chapter 8 is very difficult; so cumbersome, in fact, that I wonder whether the value of the material outweighs the discomfort of learning it. Second, Chapter 8 is very different from the rest of the text. Chapter 8 is not primarily concerned with designing experiments or analyzing data. Rather, it is mostly concerned with the structure of probability on two features. Chapter 8 does, however, contain a new confidence interval formula in Section 8.5 and some important comments on sampling in Section 8.3. In Section 8.2, I use the application of a screen- ing test for a medical condition to motivate the def- initions conditional probabilities and independence, and related formulas. Remember that these ideas are applicable to a wide range of applications beyond screening tests. I consider, however, screening tests to be the application with the greatest general inter- est. Regarding inference, the main topic of Chapter 8 is the importance of noting how the sample is se- lected. There are three methods of random sampling that could occur in the problems of Chapter 8. • Sampling Method P : A random sample is se- lected from the population box. ( P is for popu- lation.) • Sampling Method A : The population box is divided into two boxes. Box A consists of all subjects with characteristic A and box A c con- sists of all subjects without characteristic A . In- dependent random samples are selected from boxes A and A c . • Sampling Method B : The population box is divided into two boxes. Box B consists of all subjects with characteristic B and box B c con- sists of all subjects without characteristic B . In- dependent random samples are selected from boxes B and B c . With sampling method P : 1. Inference may be performed validly for any individual unconditional probability, such as P ( A ) , P ( AB ) , and P ( B c ) , using the methods of Chapter 6. 2. Inference may be performed validly for p B | A- p B | A c using the methods of Chapter 7. 3. Inference may be performed validly for p A | B- p A | B c using the methods of Chapter 7. With sampling method A , however, only the sec- ond item in the above list is true. Finally, with sam- pling method B only the third item in the above list is true. Thus, it is critical that one take care to ascertain how a sample has been selected. For sampling method P , Section 8.5 presents in- ference for p A- p B . Hypothesis testing for this dif- ference reduces to the familiar McNemar’s test. Con- fidence interval estimation of this difference, how- ever, involves the use of a new formula. Note that for many applications, the difference p A- p B is not of interest....
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## This note was uploaded on 10/23/2009 for the course STAT STATS 371 taught by Professor Professorwardrop during the Fall '09 term at University of Wisconsin.

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chap8 - Chapter 8 Two Dichotomous Responses 8.1 Study...

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