A Simple And Improved Score Confidence Interval For A Single Proportion

Wald interval for a single proportion is widely used for its simplicity.But in practice,the Wald interval generally has very poor properties.A wide variety of alternative confidence intervals(CI)have been proposed.Among them,the Wilson Score interval is the widely recommended one.Except for the exact methods which ensure the coverage probability be at least the nominal size,the performances of almost all the follow-up proposed methods are similar with the Wilson Score CI or a slight improvement at the cost of enlarging the interval length or increasing the computationally complex.While the widely used Wilson Score method suffers the problem of "downward spikes" when the proportion is close to 0 or 1.In this present study,we propose a simple and new way to construct the confidence interval which has very good performance in both the coverage probability,confidence width and the location.When the proportion is moderate(20%-80%)the Wilson Score method is the best and otherwise(<20%or>80%),the CI proposed in the present study is the best.In combination our new method with Newcombe hybrid way to construct CI for the difference of two independent proportions,we also get a better CI than the Newcombe hybrid Wilson Score CI when the proportions<20%or>80%.In considering that in practice proportions fallto<20%or>80%is very common,our new method is attractive.