Improved exact confidence intervals for a proportion using ranked-set sampling

We develop new exact confidence intervals for a proportion using ranked-set sampling (RSS). The existing intervals arise from applying the method of Clopper and Pearson (1934) to the total number of successes. We improve on the existing intervals by using the method of Blaker (2000) and by replacing the total number of successes with the maximum likelihood estimator of the proportion. The new intervals outperform the existing intervals in terms of average expected length, and they are also good in an absolute sense, as they come within a few percentage points of a new theoretical bound on the average expected length. Like the existing intervals, the new intervals use a perfect rankings assumption. They are no longer exact under imperfect rankings, but provide coverage close to nominal for mild departures from perfect rankings.