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3. Test of Homogeneity Summary page 214 From Utts, Jessica M. and Robert F. Heckard. Mind on Statistics, Fourth Edition. 2012. Used with permission.

4. Try it! What is your Decision? Chi-square test of homogeneity: 3 populations and 4 possible values of discrete characteristic. If H 0 is true, that is, the distribution for the response is the same for all 3 populations, what is the expected value of the test statistic?

5. Try it! Treatment for Shingles pg 215 Headline “For adults, chicken pox vaccine may stop shingles”. Clinical trial conducted: 420 subjects were randomly assigned to receive chicken pox vaccine or a placebo vaccine. Side effects: swelling and rash around injection site.

6. Treatment for Shingles a.Name of test for assessing if the distribution of swelling status is the same for the two treatment populations.

7. Treatment for Shingles b.Based on data, among those chicken pox vaccinated subjects, what percent had major swelling around the injection site?

8. Treatment for Shingles c.Based on data, among those placebo vaccinated subjects, what percent had major swelling around the injection site?

9. Treatment for Shingles d.Assuming distribution of swelling status is same for two trt populations, how many chicken pox vaccinated subjects would you expect to have major swelling around site?

10. Treatment for Shingles e.Use a level of 0.05 to assess if the distribution of swelling status is the same for the two treatment populations. Test Statistic Value: _________ p-value: __________ Think about this p-value, your decision and get ready to click in for the conclusion…

11. Thus, the distribution of swelling status __________ appears to be the same for the two treatment populations. A) does B) does not

12. Test of Independence page 216 to assess if 2 discrete (categorical) variables are independent for a population.  1 population  1 random sample  2 variables measured, both categorical or discrete

13. Smoking and Hypertension Scenario:One population of interest – factory workers. Question: Is there a relationship between smoking habits and whether or not a factory worker experiences hypertension. Data: 1 random sample of 180 factory workers, measured: X = hypertension status (yes or no) Y = smoking habit (non, moderate, heavy) Find row and column totals … Note: neither row nor column totals known before measuring variables. Y=SmokingHabit X=NonModHeavy Hyper Yes213630 Status No482619

14. Smoking & Hypertension Null Hypothesis Scenario:1 population of factory workers Question: Is there an association between smoking habit and hypertension status? H 0 :There is no association between smoking habit and hypertension status for population of factory workers. We say it in words (following math way from page 216)… P( heavy smoker and have hypertension) = P( heavy smoker) P( have hypertension)

15. Observed and Expected Counts Cross-Product Rule Expected Counts Y=SmokingHabit X=NonModHeavy Hyper Yes21 ( )36 ( )30 ( )87 Status No48 ( )26 ( )19 ( )93 696249180

16. Smoking & Hypertension Test Statistic Y=SmokingHabit X=NonModHeavy Hyper Yes21 ( 33.35 )36 ( 29.97 )30 ( 23.68 )87 Status No48 ( 35.65 )26 ( 32.03 )19 ( 25.32 )93 696249180

17. Smoking & Hypertension Example Do you think the value of ____________ is large enough to reject H 0 ? If H 0 is true, then X 2 has the  2 distribution with df = _________________ Use our frame of reference first … then find the p-value

18. Using our Frame of Reference So, if H 0 true, we would expect our X 2 test statistic to be about ______ give or take about ___________. About how many standard deviations is the observed X 2 value of 14.5 from the expected value under H 0 ?

19. p-value for Smoking & Hypertension Example Observed value = __________ df = ___________ Find the p-value using your Table A.5 Keep the p-value in mind and be ready to click in answers to whether statistically significant and the conclusion.

20. A = Yes or B = No Are the results statistically significant at the 1% level?

21. Which is the appropriate conclusion? A) There is an association between smoking and hypertension for this population of workers represented by this sample. B) There is no association between smoking and hypertension for this population of workers represented by this sample.

22. Relationship between Age Group and Appearance Satisfaction Are you satisfied with your overall appearance? Random sample of 150 women were surveyed.  Answer (Yes or No) recorded and  Age category (1 = under 30, 2 = 30 to 50, and 3 = over 50). Solutions will be posted on Ctools …

23. Yellow Card