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Notes11 - 2 Chi-Square Introduction to Nonparametric Stats...

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1 Chi-Square: Introduction to Nonparametric Stats 2 χ Chi-square Parametric vs. nonparametric tests Hypotheses about Frequencies Two main uses: – Goodness of fit. 1 IV. – Test of independence. 2 or more IVs. Goodness-of-fit test Blind beer tasting study. Judges taste 4 beers and declare their favorite. 100 lucky judges. Results: 100 10 30 45 15 Frequency Total Sam Adams Miller Corona Coors If no difference in taste (or all the same beer) we expect about 25 people to choose each beer (null hypothesis). There are 100 people and 4 choices (100/4 = 25). We will test whether frequencies are equal across beers.

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2 Goodness-of-fit (2) = E E O 2 2 ) ( χ Where O is an observed frequency and E is an expected frequency under the null. 30 = test value 9 1 16 4 (O-E) 2 /E 225 25 400 100 (O-E) 2 -15 5 20 -10 O-E 25 25 25 25 Expected 100 10 30 45 15 Freq Total Sam Adams Miller Corona Coors Goodness-of-fit 3 Our test statistic was 30. The df for this test are k-1, where k is the number of cells. In our example k=4 and df = 3. Chi-square has a distribution found in tables.
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