A non-iterative accurate asymptotic confidence interval for the difference between two proportions.

I propose a new confidence interval for the difference between two binomial probabilities that requires only the solution of a quadratic equation. The procedure is based one estimating the variance of the observed difference at the boundaries of the confidence interval, and uses least squares estimation rather than maximum likelihood as previously suggested. The proposed procedure is non-iterative, agrees with the conventional test of equality of two binomial probabilities, and, even for fairly small sample sizes, appears to yields actual 95 per cent confidence intervals with mean or median probabilities of coverage very close to 0.95. The Yates continuity correction appears to generate confidence intervals with the conditional probability of coverage at least equal to nominal levels.