Confidence Interval on the Difference Between Proportions (4 of 4)


  1. lower limit = p1 - p2 - (z) (estimated)

  2. upper limit = p1 - p2 + (z) (estimated)

  3. Confidence interval: lower limit ≤ π1 - π2 ≤ upper limit.

  1. The two proportions are independent.

  2. The adequacy of the normal approximation depends on the sample size (N) and π. Although there are no hard and fast rules, the following is a guide to needed sample size:

    If π is between 0.4 and 0.6 then an N of 10 is adequate. If π is as low as 0.2 or as high as 0.8 then N should be at least 25. For π as low as 0.1 or as high as 0.9, N should be at least 30.

    A more conservative rule of thumb that is often recommended is that Nπ and N(1 - π) should both be at least 10.

Click here for an interactive demonstration of the normal approximation to the binomial to explore the validity of these rules of thumb.