11_ChiSquare

# 11_ChiSquare - Chi-Square 2 Introduction to Nonparametric...

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Chi-Square: Introduction to Nonparametric Stats 2 χ

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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: Coors Corona Miller Sam Adams Total Frequency 15 45 30 10 100 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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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. Coors Corona Miller Sam Adams Total Freq 15 45 30 10 100 Expected 25 25 25 25 O-E -10 20 5 -15 (O-E) 2 100 400 25 225 (O-E) 2 /E 4 16 1 9 30 = test value
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

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11_ChiSquare - Chi-Square 2 Introduction to Nonparametric...

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