Adaptive confidence intervals of desired length and power for normal means

• Published in: Journal of statistical planning and inference Vol. 140; no. 11; pp. 3317 - 3325
• Main Authors: Hartung, Joachim, Knapp, Guido
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.11.2010; Elsevier
• Subjects: Adaptive sample size planning; Exact sciences and technology; General topics; Group sequential trial; Length of a confidence interval; Mathematics; Multi-stage confidence interval; Multivariate analysis; Nonparametric inference; Parametric inference; Power of a confidence interval; Probability and statistics; Sciences and techniques of general use; Statistics; Group sequential trial; 62L12; Power of a confidence interval; Multi-stage confidence interval; Length of a confidence interval; 62F25; Adaptive sample size planning; Adaptive design; Sample size; Probability; Non parametric estimation; Statistical estimation; Probability distribution; Statistical decision; Multivariate analysis; Mean estimation; Confidence interval; Statistical method; Hypothesis test; Statistical test; Sampling theory; Sequential method; Point estimation; Sample survey
• DOI: 10.1016/j.jspi.2010.04.054
• ISSN: 0378-3758

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.