Confidence Interval Construction by Stein's Method: A Practical and Economical Approach to Sample Size Determination

Abstract

A two-stage method of confidence interval construction developed by Stein is a practical and straightforward approach to sample size determination when one wants to estimate the mean of a normal distribution of unknown mean and variance. The technique has several advantages over the modified version of current informal practice proposed by Shiffler and Adams in a recent JMR article: (1) the need for correction factors is eliminated, (2) the precision of the confidence interval is fixed rather than uncertain and the desired level of confidence is guaranteed, irrespective of the unknown population variance, and (3) a sound theoretical basis is provided for making an economical choice of sample size.