Adaptive confidence intervals of desired length and power for normal means

Abstract

In all empirical or experimental sciences, it is a standard approach to present results, additionally to point estimates, in form of confidence intervals on the parameters of interest. The length of a confidence interval characterizes the accuracy of the whole findings. Consequently, confidence intervals should be constructed to hold a desired length. Basic ideas go back to Stein (1945) and Seelbinder (1953) who proposed a two-stage procedure for hypothesis testing about a normal mean. Tukey (1953) additionally considered the probability or power a confidence interval should possess to hold its length within a desired boundary. In this paper, an adaptive multi-stage approach is presented that can be considered as an extension of Stein's concept. Concrete rules for sample size updating are provided. Following an adaptive two-stage design of O'Brien and Fleming (1979) type, a real data example is worked out in detail.