A comparison of approximate confidence interval methods for the difference between two independent binomial proportions : theory and methods

Conventional methods to determine confidence intervals for the difference between two independent binomial proportions P1 and P2 are prone to violations of the definition interval [-1; 1] for P1 - P2 and may have very poor coverage properties. In this paper several less known methods are described. A simulation study was done to compare the different confidence interval methods with respect to length, coverage, zero width interval and violation of the definition interval. The best methods were found to be Mee's and Miettinen and Numinen's method. These methods, however, are computer intensive. The Jeffreys-Perks and Score interval methods seem to be the best of the more easily calculable methods to use in most practical situations.