Reducing the width of confidence intervals for the difference between two population means by inverting adaptive tests

In the last decade, it has been shown that an adaptive testing method could be used, along with the Robbins–Monro search procedure, to obtain confidence intervals that are often narrower than traditional confidence intervals. However, these confidence interval limits require a great deal of computation and some familiarity with stochastic search methods. We propose a method for estimating the limits of confidence intervals that uses only a few tests of significance. We compare these limits to those obtained by a lengthy Robbins–Monro stochastic search and find that the proposed method is nearly as accurate as the Robbins–Monro search. Adaptive confidence intervals that are produced by the proposed method are often narrower than traditional confidence intervals when the distributions are long-tailed, skewed, or bimodal. Moreover, the proposed method of estimating confidence interval limits is easy to understand, because it is based solely on the p-values from a few tests of significance.