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chap 10 notes

# chap 10 notes - Lecture 18 page 1 Statistics 371-001 Sp 09...

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Statistics 371-001, Sp 09 Lecture #182 31 Mar 09 Chapter 10. Analysis of Categorical Data 1. Chi-Square Goodness of Fit Test Hypothesis testing Categorical data Multinomial instead of binomial Parameters – mean & SD, most common ways to describe a population. Nonparametric test, Chi-square, χ 2 Other questions; estimate proportions or relative frequencies of subjects in response categories of a distribution vs probability of a success. Eg., Number of women dentist compared to number of men dentist. Which cola is most preferred by Americans, Coke or Pepsi? Proportion of college students majoring in business today vs 10 yrs ago. Use sample data to test hypotheses about the shape or proportions of a population distribution. Chi-square Goodness of Fit Test Observed frequencies – number of items from sample classified in a particular category. Each subject or observational unit is counted in one and only one category. Data; relatively simple. Expected frequencies - number of items in each category predicted from the null hypothesis and the sample size, n . How well do observed frequencies fit frequencies specified by H 0 ?? Expected frequencies can specify H 0 of No Preference. Eg., Among leading brands of soft drinks, are there preferences? Coke Pepsi Mt. Dew H 0 : Expected frequencies can specify H 0 of No Difference from a Known Population. Eg., Same distribution eye color exits in newborns in Wisconsin in 2009 as in 1959? Lecture 18 page 1

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QuickTime  and a TIFF (Uncompressed) decompressor are needed to see this picture. Brown Blue Green Other H 0 : 20 10 4 4 Hypothetical Problem: Volunteers at a teen hotline are assigned based on the assumption that the primary issue raised by 40% of calls is drugs, for 25% of calls the primary issue is related to sex, for 25% it’s stress, and for 10% it’s educational issues. Is the assumption regarding the distribution of primary topic issue appropriate? 120 calls were randomly selected and categorized according to the primary issue addressed in the call.
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