A simple and improved score confidence interval for a single proportion

Confidence interval (CI) for a proportion has been a topic discussed repeatedly in the literature because of its omnipresence in applications. A wide variety of CIs have been proposed since the Wald CI for a proportion performs quite poorly. Among them, the Wilson score interval is widely recommended. However, the Wilson score method suffers from the so-called “downward spikes” when the proportion is close to 0 or 1. Except for the exact methods which ensure the coverage probability be at least the nominal size, the performances of existing proposed methods are similar to the Wilson score CI or its slightly improved version at the cost of increased interval width or computational complexity. In this study, we propose a simple CI which has very good performance in the coverage probability, confidence width, and the location. Especially when the proportion is <20% or >80% the CI proposed has a shorter confidence width than the Wilson score method. In combination our new method with the Newcombe’s hybrid way to construct CI for the difference of two independent proportions, we also get a better CI.