Coverage Properties of Confidence Intervals for Proportions in Complex Sample Surveys ∗

Abstract The challenges of constructing confidence intervals for a binomial proportion and the deficiencies of the popular Wald interval in achieving its nominal coverage — particularly when the true proportion is close to 0 or 1 or when the sample size is moderate — have been well documented (Brown et al. 2001, 2002). The problem is further compounded when inference is based on complex survey data. Yet intervals resembling the Wald interval are often applied to complex surveys, an example being the confidence intervals used in the American Community Survey (ACS). In the literature, confidence intervals designed for binomial proportions with modifications based on the design effect are often used for complex surveys. Here, we adopt this approach and study the coverage and expected length properties of 7 different intervals. We focus on how phenomena such as clustering, stratification, misspecification of variances, and patterns of variation of stratum expected sampling fractions and stratum survey attribute-proportions, affect coverage. A simulation study examines the effect of such factors.