Question E.

The expected frequencies in the table below show a hypothetical relationship among these variables: Y = response, X = drug treatment, and Z = clinic. Show that X and Y are conditionally independent, given Z, but marginally associated. Explain how the marginal XY association can be so different from its conditional association. using the values of the conditional X2 and YZ odds ratios. Explain why it would be misleading to study only the marginal table and conclude that successes are more likely with treatment A than with treatment B. Response Clinic Drug Treatment Success Failure 1 A 18 12 B 12 8 2 A 2 8 B 3 32 True of false? 1. Suppose that income (high,low) and gender are conditionally independent, given type of job (secretarial. construction, service. professional, . . .). Then, income and gender are also independent in the 2 X 2 marginal table. According to the Pew Research Center. when adults in the US were asked in 2010 whether there is solid evidence that the average temperature on Earth has been getting warmer over the past Few decades, the estimated odds of a yes response for a Democrat was 2.96 times higher than for an Independent, and it was 2.08 times higher for an Independent than for a Republican. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican equals 2.96 X 2.08 = 6.2. True of false? 1. A95% confidence interval for the odds ratio between Ml (yes, no) and treatment (placebo, aspirin) is (1.44, 2.33). lfwe form the table with aspirin in the first row (instead of placebo). the 95% confidence interval is (1/233, 1/144) : (0.43, 0.69). A survey of college students analyzes the association between opinion about whether it should be legal to (1) use marijuana, (2) drink alcohol if you are 18 years old. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable. lnterchanging two rows or interchanging two columns in a contingency table has no effect on the value of the X2 or G2 chisquared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test ignores that information