A Framework for Planning Sample Sizes Regarding Prediction Intervals of the Normal Mean Using R Shiny Apps

Replication is a core principle for research, and the recent recognition of the importance of constructing prediction intervals for precise replications highlights the need for robust sample-size planning methodologies. However, methodological and technical complexities often hinder researchers from efficiently achieving this task. This study addresses this challenge by developing five R Shiny apps specifically tailored to determine sample sizes concerning prediction intervals for the mean of the normal distribution. Two measures of precision, absolute and relative widths, are considered. Additionally, the apps consider unequal sampling unit costs and sample size allocations to achieve optimal results by exhaustive search. Simulation results validate the proposed methodology, demonstrating favorable coverage rates. Two illustrative examples of one-sample and two-sample problems showcase these apps’ versatility and user-friendly nature, providing researchers with a valid and straightforward approach for systematically planning sample sizes.