1. HS 1679B: Comparing Proportions1 9B: Comparing two proportions

2. HS 1679B: Comparing Proportions2 Proportions from two groups The risk difference is the difference (subtraction) in proportions: A trial compares heart attack occurrences over 5-years in two groups of middle-aged men. Group 1 receives a placebo while group 2 receives the cholesterol-lowering drug Gemfibrozil. We want to determine whether the drug reduces heart attack risk. Heart attacks nini Incidence Proportions (“Risks”) Placebo (Group 1) 842030 Drug (Group 2) 562051

3. HS 1679B: Comparing Proportions3 CI for risk difference (+4 methods) 95% CI for p 1 – p 2 is given by: Goal: Estimate parameter p 1 – p 2 “Plus four” method adds one pretend success and failure to each group: Example: same data GroupX i + 1n i +2 Placebo (Group 1) 84 + 1 = 85 2030 + 2 = 2032 85 / 2032 = 0.0418 Drug (Group 2) 56 + 1 = 57 2051 + 2 = 2053 57 / 2053 = 0.0278 Interpretation references parameter: We are 95% confidence the risk difference in the population is between 0.3% and 2.5%.

4. HS 1679B: Comparing Proportions4 Significance test A. H 0 : p 1 = p 2 (no difference in population proportions) B. Test statistics C. P = 0.01351 D. The evidence against the null is significant. Example: same data GroupXiXi nini p-hats Placebo8420300.0414 Drug5620510.0273.