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371chapter9b

# 371chapter9b - Chapter 9 Comparing Two Populations Binomial...

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Chapter 9 Comparing Two Populations: Binomial and Poisson 9.1 Four Types of Studies We will focus on the binomial in this chapter. In the last section we extend these ideas to the Poisson distribution. When we have a dichotomous response we have focused on BT. The idea of finite population was introduced in Chapter 2 and presented as a special case of BT. In this section it is convenient to begin with finite populations. The four in the title of this section is obtained by multiplying 2 by 2. When we compare two populations both populations can be trials or both can be finite populations. In addition, as we shall discuss soon, a study can be observational or experimental . Combining these two dichotomies, we get four types of study, for example an observational study on finite populations. It turns out that the math results are (more or less) identical for the four types of studies, but the interpretation of the math results depends on the type of study. We begin with an observational study on two finite populations. This example is in Chapter 7 of my textbook; the interested reader can go there for more details. This was a real study performed over 20 years ago; it was published in 1988. The first finite population is undergraduate men at at the University of Wisconsin-Madison and the second popu- lation is undergraduate men at Texas A&M University. Each man’s response is his answer to the following question: If a woman is interested in dating you, do you generally prefer for her: to ask you out; to hint that she wants to go out with you; or to wait for you to act. The response ‘ask’ is labeled a success and either of the other responses is labeled a failure. The purpose of the study is to compare the proportion of successes at Wisconsin with the proportion of successes at Texas A&M. The two populations obviously fit our definition of finite populations. Why is it called ob- servational? The dichotomy of observational/experimental refers to the control available to the 83

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Table 9.1: Responses to the Dating Study. Observed Frequencies Row Proportions Prefer Women to: Prefer Women to: Population Ask Other Total Ask Other Total Wisconsin 60 47 107 0.56 0.44 1.00 Texas A&M 31 69 100 0.31 0.69 1.00 Total 91 116 207 researcher. Suppose that Matt is a member of one of these populations. As a researcher, I have control over whether I have Matt in my study, but I do not have control over the population to which he belongs. The variable that determines to which population a subject belongs, is often called a study factor . Thus, in the current study, the study factor is school attended and it has two levels : Wisconsin and Texas. This is an observational factor, sometimes called, for obvious reasons, a classification factor, b/c each subject is classified according to his school.
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371chapter9b - Chapter 9 Comparing Two Populations Binomial...

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