Variance Stabilizing the Difference of Two Binomial Proportions
The article studies estimation of Delta = p(1) - p(2), the difference of two proportions p(1) and p(2), based on two independent Binomial experiments of size n(1) and n(2). The usual estimator, the difference between the two sample proportions, is variance stabilized conditionally on a weighted average of p(1) and p(2). When using this variance stabilized statistic as a test, a new family of confidence intervals for Delta 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.