371chapter9f2011 - Chapter 9 Comparing Two Populations...

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Chapter 9 Comparing Two Populations: Binomial and Poisson 9.1 Four Types of Studies We will focus on the binomial distribution in this chapter. Inthelast(optional)sectionweextend these ideas to the Poisson distribution. When we have a dichotomous response we have focused on BT. The idea of Fnite populations was introduced in Chapter 2 and presented as a special case of BT. In this section it is convenient to begin with Fnite 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 Fnite populations. In addition, as we shall discuss soon, a study can be observational or experimental .Comb in ingthe setwod icho tom ie s , we get four types of study, for example an observational studyonFnitepopulations. It turns out that the math results are (more or less) identicalforthefourtypesofs tud ies ,bu t the interpretation of the math results depends on the type of study. We begin with an observational study on two Fnite populations. This was a real study per- formed over 20 years ago; it was published in 1988. The Frst Fnite population is undergraduate men at at the University of Wisconsin-Madison and the second population 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 preferforher:toaskyouout; 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 otherresponsesislabe ledafa ilure .The purpose of the study is to compare the proportion of successesatW isconsinwiththeproportionof successes at Texas A&M. The two populations obviously Ft our deFnition of Fnite populations. Why is it called ob- servational? The dichotomy of observational/experimenta lreferstothe control available to the 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 91
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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 he belongs. The variable that determines to which populationasubjectbelongs,isoftencalledthe study factor .Thus ,inthecu r ren ts tudy ,thes tudyfac to risschoo la t tended and it has two levels : Wisconsin and Texas A&M. This is an observational factor, sometimes called, for obvious reasons, aclassi±cationfactor ,becauseeachsubjectisclassi±edaccording to his school. Table 9.1 presents the data for this Dating Study . Next, we have an example of comparing ±nite populations in an experimental study. Medical researchers were searching for an improved treatment for persons with Crohn’s Disease .T h e y wanted to compare a new drug therapy, cyclosporine ,toaninertdrug,calleda placebo .
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371chapter9f2011 - Chapter 9 Comparing Two Populations...

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