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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Page1 / 8

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online