Approximate and Fiducial Confidence Intervals for the Difference Between Two Binomial Proportions

The problem of estimating the difference between two binomial proportions is considered. Closed-form approximate confidence intervals (CIs) and a fiducial CI for the difference between proportions are proposed. The approximate CIs are simple to compute, and they perform better than the classical Wald CI in terms of coverage probabilities and precision. Numerical studies indicate that these approximate CIs can be used safely for practical applications under a simple condition. The fiducial CI is more accurate than the approximate CIs in terms of coverage probabilities. The fiducial CIs, the Newcombe CIs, and the Miettinen-Nurminen CIs are comparable in terms of coverage probabilities and precision. The interval estimation procedures are illustrated using two examples.