Duke University : Estimating the difference between two proportions

Estimating the Difference Between Two Proportions

• Parameter of Interest: pA - pB
• Point Estimate: p̂A - p̂B
• Difference between the proportions of sampled A and sampled B

Conditions for Inference for Comparing Two Independent Proportions

1. Independence:

• Within groups: sampled observations must be independent within each group
  o Random sample / assignment
  o If sampling without replacement, n < 10% of population
• Between groups: the two groups must be independent of each other (non-paired)

2. Sample size / skew: Each sample should meet the success-failure condition

• n1p1 ≥ 10 and n1(1-p1) ≥ 10
• n2p2 ≥ 10 and n2(1-p2) ≥ 10

INSTRUCTIONS

1. Check the conditions
   • if we are not 100% sure about random sampling condition for one group, we need to be careful at making conclusions.
2. Construct a confidence interval by Estimating the Difference Between Two Proportions
   • The order (subtracting one from another) does not matter. Both will give the same conclusion regarding the hypothesis.

(See example)