How Many Participants Do We Have to Include in Properly Powered Experiments? A Tutorial of Power Analysis with Reference Tables

TLDR

Psychological studies targeting a small effect size (d = .4) require over 50 participants for 80 % power, yet many use fewer; adding between‑group factors or interactions pushes needed samples to 100, 200, or more, and without this awareness studies remain underpowered and inconclusive. The paper seeks to shift evaluation practices and supply reference sample sizes for common psychological designs, guiding researchers toward adequately powered studies. It provides reference sample sizes for frequentist (p < .05) and Bayesian (BF > 10) analyses across single‑variable between‑groups, repeated‑measures, and two‑factor split‑plot designs, and shows how adding multiple observations per condition per participant boosts power. These numbers give researchers a standard to determine and justify the sample size of an upcoming study.

Abstract

Given that an effect size of d = .4 is a good first estimate of the smallest effect size of interest in psychological research, we already need over 50 participants for a simple comparison of two within-participants conditions if we want to run a study with 80% power. This is more than current practice. In addition, as soon as a between-groups variable or an interaction is involved, numbers of 100, 200, and even more participants are needed. As long as we do not accept these facts, we will keep on running underpowered studies with unclear results. Addressing the issue requires a change in the way research is evaluated by supervisors, examiners, reviewers, and editors. The present paper describes reference numbers needed for the designs most often used by psychologists, including single-variable between-groups and repeated-measures designs with two and three levels, two-factor designs involving two repeated-measures variables or one between-groups variable and one repeated-measures variable (split-plot design). The numbers are given for the traditional, frequentist analysis with p < .05 and Bayesian analysis with BF > 10. These numbers provide researchers with a standard to determine (and justify) the sample size of an upcoming study. The article also describes how researchers can improve the power of their study by including multiple observations per condition per participant.