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Unformatted text preview: Chapter 2 Hypothesis Testing 2.1 Study Suggestions The analysis of Chapter 1 is called descriptive . Chapter 2 introduces statistical inference , in partic- ular, hypothesis testing. Chapter 2 is perhaps the most challenging chap- ter in the text. Chapter 2 contains a great many im- portant ideas and a substantial amount of new ter- minology. I encourage my students by emphasizing that these important new ideas will appear repeatedly throughout the text. Thus, it is not essential that these ideas be mastered during this first exposure. In Chapter 1 you learned how to perform a CRD. The end result of the study is a 2 2 table of ob- served frequencies. For example, the Infidelity study described in the text in Chapter 1 yielded the table below. Version S F Total 1 7 3 10 2 4 6 10 Total 11 9 20 Of Thereses friends who were told the husband was cheating (version 1), 70 percent said they would tell the wife if asked. Of Thereses friends who were told the wife was cheating, however, only 40 percent said they would tell the husband if asked. Given the results of Thereses study, there are two natural ques- tions: 1. Is the difference between versions of 30 per- centage points real? 2. If the difference of 30 percentage points is real, is it important? I put the word real in quotation marks because it is not obvious what I mean by that word. Hypothesis testing can be viewed as a technical device for ob- taining a quantitative, objective answer to the first question for a particular definition of the term real. The second question above is subjective, and any serious attempt to answer it must necessarily depend on the respondents expertise in the subject area of the study. The space I can devote in a general text to other subject areas is severely limited, so I cannot give the second question a thorough answer for every study in the text. The second question is, however, discussed briefly throughout the text, beginning in Chapter 7, under the heading practical importance. The debate between the Skeptic and the Advocate, I believe, is a useful metaphor for what statisticians mean by saying a difference is real. More precisely, the Advocate says the difference is real and the Skep- tic says it is not. Hypothesis testing quantifies the debate between the Skeptic and Advocate, and this quantification is called objective because it depends on the data collected and not on the opinion of the researcher or others. (In The Mismeasure of Man by Stephen Jay Gould, (Norton, 1981) the author con- vincingly argues how difficult it is to be objective, and how hard we must strive even to approach objec- tivity in our thinking. In addition, I understand that, from the point of view of a student, quantifying a debate is not necessarily a natural or good thing to do. I am reminded of the poetry text referenced in the movie The Dead Poets Society that explained how to quantify the value of a poem! I happen to believe that there is great value to quantifying the debate between...
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- Fall '09