chap10 - Chapter 10 One Multicategory Response 10.1 Study...

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Chapter 10 One Multicategory Response 10.1 Study Suggestions In retrospect, I do not like the advice I give in the text for the visual presentation of an unordered categori- cal response. Insisting, as I do, that the categories be ordered by frequency of responses can lead to confu- sion when, for example, the most common response is “None of the above,” or “About the same.” If no confusion will result, as, for example, in the winning lottery numbers example, I advocate following my advice. For situations in which my advice leads to confusion, the categories may be presented in a nat- ural sequence, but you should remember not to place any significance on the shape of the bar chart. The chi-squared goodness of fit test is very fa- mous. It was developed by Karl Pearson to provide a mathematical evaluation of the important work by Gregor Johann Mendel. Despite its fame, modern statisticians are largely indifferent to the test. The test’s main problems are twofold. First, one popula- tion inference is inherently less interesting than com- paring two populations. Second, the applicability of the test is severely restricted by the requirement of having k special values of interest. The goodness of fit test does, however, provide a good motivation and framework for the more useful test of Chapter 11. I use the example of the Wisconsin lottery daily game on pages 345 and 346 to illustrate one of my main concerns with the teaching of introductory statistics: If the only tool students have for analyz- ing one multicategory response is the chi-squared test, then should we be surprised if they apply this test indiscriminately? This example in the text il- lustrates the power and flexibility of computer sim- ulation to answer questions that the standard theory cannot handle. (Note: I wrote letters to the heads of the lottery commissions in every state that has a lotto-type game, asking if they perform any statis- tical analyses of the winning numbers to check for fairness. Approximately 25 heads wrote back and said that they did, and all but one of these 25 states uses the chi-squared goodness of fit test, without any adjustments.) The computer simulation experiment for the Wis- consin lottery daily game also provides you with the first example of how to study robustness. This topic is discussed further in Chapter 15. 10.2
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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 Wisconsin.

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chap10 - Chapter 10 One Multicategory Response 10.1 Study...

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