1. Chi Square Fr Chris - St Francis High School March 2006

2. Two Applications Goodness of Fit (one way) Two-Way (Contingency) Table

3. 1-Way (Univariate) Data Observed frequencies are from a RANDOM SAMPLE Large Sample size (expect at least 5 in each category)

4. Stolen Cars by Color Null Hypothesis: Color makes no difference San Luis Obispo Telegram-Tribune 9/2/96 Alternative Hypothesis: Color makes a difference 15% white, 15% blue, 35% red, 30% black, 5% other whiteblueredblackother Observed 14010027023090 Expected 124.5 290.5249.541.5

5. whiteblueredblackother Observed 14010027023090 Expected 124.5 290.5249.541.5 SRS, and All EXPECTED cells >5 so large enough sample Since P(Chi-sq, df=4 > 18.46) <.001 so we reject the null hypothesis, and conclude certain colors are more likely to be stolen

6. Now you try: According to SLO Trib, 12/15/99, SRS of 200 purchases of California Lotto tix: Age18-3435-6465+ played3613034 California in 1999 had 35% 18-34, 51% 35-64, 14% over 65 Try a Chi-Sq Goodness of Fit Test

7. 2 way Chi-Square is even more Fun! According to Research Quarterly for Exercise and Sport, (1990) p 315-320, SRS of 1200 looked at hours of TV and a cardiovascular test Hrs of TVFitUnfit 035147 1-2101629 3-428222 5+434

8. But we compute df=(r-1)(c-1) and the expected frequencies are computed with by the marginal totals Hrs of TV FitUnfitTotals 035147182 1-2101629730 3-428222250 5+43438 16810321200

9. Hrs of TV FitUnfitTotals 025.5156.5182 1-2102.2627.8730 3-435.0215.0250 5+5.332.738 16810321200 Expected Frequency = (Row)(Col)/total df=(4-1)(2-1)=3, So we reject the Null Hypothesis at the.05 level for any Chi Square over 12.83

10. less than 12.83, so there is not enough evidence to reject the null hypothesis at the.05 level, so there is little evidence here that would suggest that the hours watching TV is associated with one’s cardiovascular fittness.

11. sexdiedlived men630168 women136323 classdiedlived high117187 middle163112 low536192 Would you rather be rich or a woman if you were on the Titanic? Actually the Chi-Square statistic tests against the null hypothesis (no difference according to category)... you need to look at the numbers to see what’s going on...