9B: Comparing two proportions

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9B Comparing two proportions
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Proportions from two groups
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 ni Incidence Proportions (Risks)
Placebo (Group 1) 84 2030
Drug (Group 2) 56 2051
The risk difference is the difference
(subtraction) in proportions
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CI for risk difference (4 methods)
Goal Estimate parameter p1 p2 Plus four
method adds one pretend success and failure to
each group
Example same data
Group Xi 1 ni 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
95 CI for p1 p2 is given by
Interpretation references parameter We are 95
confidence the risk difference in the population
is between 0.3 and 2.5.
4
Significance test
Example same data
Group Xi ni p-hats
Placebo 84 2030 0.0414
Drug 56 2051 0.0273

• A. H0 p1 p2 (no difference in population
  proportions)
• B. Test statistics
• C. P 0.01351
• D. The evidence against the null is significant.

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