title: Reducing the width of confidence intervals for the difference between two population means by inverting adaptive tests.
abstract: 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.
authors: Division of Statistics, Northern Illinois University, Dekalb, IL, USA.
authors: Thomas W
authors: TW
authors: O'Gorman
mesh_terms: D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D013223:Statistics as Topic
keywords: Permutation tests; Robbins–Monro process; adaptive confidence intervals; randomization tests; test inversion