Variance Stabilizing the Difference of Two Binomial Proportions

Abstract

The article studies estimation of Δ = p₁ − p₂, the difference of two proportions p₁ and p₂, based on two independent Binomial experiments of size n₁ and n₂. The usual estimator, the difference between the two sample proportions, is variance stabilized conditionally on a weighted average of p₁ and p₂. When using this variance stabilized statistic as a test, a new family of confidence intervals for Δ is found. We show with a simulation study that these confidence intervals compare favorably in coverage accuracy and width to two other popular intervals proposed by Newcombe and Agresti and Caffo. Because no additional study weights need estimating, the variance stabilized statistic is also well-suited for combining results from independent studies. This meta analysis is also explained in the article.

Keywords:  :

• Effect size
• Meta analysis
• Wald confidence interval