Sample size planning for studies with multiple measurement trials.

When planning a study that uses multiple measurement trials, both the number of participants and the number of measurement trials are fundamental design elements. In multiple measurement trial studies, each participant is repeatedly exposed to a particular treatment condition, and the dependent variable is the average of multiple measurement trials. Increasing the number of measurement trials will increase the reliability of the dependent variable, which will reduce the sample size needed to obtain a confidence interval with desired precision or a hypothesis test with desired power. In studies where the dependent variable is an average of multiple measurement trials, the investigator may want to compare the required sample size for different numbers of measurement trials. Closed-form sample size formulas are derived to determine the sample size needed for desired confidence interval precision or statistical power, given a specified number of measurement trials. Sample size formulas are derived for the two-group design and the paired-samples design and then extended to the case of general linear contrasts in between-subjects and within-subjects designs. R functions for each sample size formula are given in the online supplemental materials. (PsycInfo Database Record (c) 2026 APA, all rights reserved).