An Economical Approach to Design with Precision Criteria

Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precisely estimating effect sizes are more valuable than binary decisions about statistical significance. Study design for estimation-based investigations often uses precision criteria to select sample sizes that control the length of interval estimates with respect to a sampling distribution. In this paper, we formally define a distribution that characterizes the probability of obtaining a sufficiently narrow interval estimate as a function of the sample size. This distribution can be used to determine the smallest sample size needed to ensure an interval estimate is sufficiently narrow. We prove that this distribution is approximately normal in large-sample settings for many data generation processes. However, this approximate normality may not hold for studies with moderate sample sizes, particularly when incorporating prior information or obtaining asymmetric interval estimates. Thus, we also propose an efficient simulation-based approach to approximate the distribution for the sample size by estimating the sampling distribution of interval estimate lengths at only two sample sizes. Our methodology provides a unified framework for design with precision criteria in Bayesian and frequentist settings. We illustrate the broad applicability of this framework with several examples.