1. 12.2 Tests for Homogeneity and Independence in a two-way table Wednesday, June 22, 2016

2. Comparing 2 or more populations using chi-squared (Homogeneity) 1.Hypotheses H 0 : the true category proportions are the same for all the populations. H a : The true category proportions are not all the same for all of the populations. 2. Conditions -independently chosen random samples -Sample size large: all counts at least 5. If some are less rows or columns may be combined to achieve satisfactory counts

3. 3. Test statistic

4. Expected Cell counts

5. 4. p-value df = (# of rows – 1)(# of columns – 1) 5. Conclusion – Reject or fail to reject – in context of the problem.

6. Calculator commands 2 nd matrix→edit 1: A put in number of columns and rows enter Put the data in for the observed counts 2 nd matrix→edit 2: B put in number of columns and rows enter Put the data in for the expected counts STAT→TESTS C: Observed [A] Expected [B] Calculate

7. Example #1 We have reports from 4 colleges on the post-graduation activities of their 2006 graduating classes. Are the students’ choices of post-grad activities the same across all colleges?

8. Two-way table Agriculture Arts & science Engineering Social science Total Employed 3793052431251052 Grad school 18623820296722 Other1041233758322 total6696664822792096

9. Test for Independence 1.H 0 : the variables are independent H a : The variables are not independent 2. Conditions – same as homogeneity 3. Test statistic 4. p-value df = (# rows – 1)(# of columns – 1) 5. Conclusion in context of the problem.

10. Example #2 A study from the University of Texas Southwestern Medical Center examined whether the risk of hepatitis C was related to whether people had tattoos and to where they got their tattoos. Hepatitis C causes about 10,000 deaths each year in the US, but often lies undetected for years after infection. We have counts of 626 individuals categorized according to their “tattoo status” and their “hepatitis status.” Are tattoo status and hepatitis status independent?

11. Two-Way Table Hep CNo Hep CTotal Tattoo, parlor 173552 Tattoo, elsewhere 85361 None22491513 total47579626