Two-sided Coverage Intervals for Small Proportions Based on Survey Data

The standard two-sided Wald coverage interval for a small proportion, P, may perversely include negative values. One way to correct this anomaly when analyzing data from a simple random sample is to compute an asymmetric Wilson (or score) coverage interval. This approach has proven not only theoretically satisfying but empirically effective. Some have suggested computing an ad hoc Wilson-like coverage interval for P when it is weighted or is estimated with complex sample data. We propose an alternative, theoretically motivated, approach to two-sided coverage-interval construction. In the case where the population P is unweighted and the data from a simple random sample, the coverage interval generated by the new pivotal is asymptotically identical to the Wilson coverage interval. A modest empirical evaluation shows that our coverage intervals are slightly better than those derived from the ad hoc Wilson approach and much better than standard Wald intervals. Better yet is a model-based Wilson approach, but in our study the model was correct.