Robust confidence intervals for a proportion using ranked-set sampling

We develop two new approximate confidence interval methods for estimating a population proportion using balanced ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper-Pearson-type interval. Both methods rely on a new maximum-likelihood-based method for estimating the proportions in the judgment strata when the overall proportion is given, and both can be computed even for large sample sizes.