Quantum mechanics

Statistical power

Analysis of variance

Algorithm

Philosophy

Factorial experiment

Statistics

Fractional factorial design

Accounting

Design of experiments

Power (physics)

Computer science

A priori and a posteriori

Business

Physics

Power analysis

Variance (accounting)

Mathematics

Epistemology

Mixed-design analysis of variance

Mathematical analysis

Sample size determination

Cryptography

Homogeneity (statistics)

Factorial

Advances in Methods and Practices in Psychological Science

Researchers often rely on analysis of variance (ANOVA) when they report results of experiments. To ensure that a study is adequately powered to yield informative results with an ANOVA, researchers can perform an a priori power analysis. However, power analysis for factorial ANOVA designs is often a challenge. Current software solutions do not allow power analyses for complex designs with several within-participants factors. Moreover, power analyses often need [Formula: see text] or Cohen’s f as input, but these effect sizes are not intuitive and do not generalize to different experimental designs. We have created the R package Superpower and online Shiny apps to enable researchers without extensive programming experience to perform simulation-based power analysis for ANOVA designs of up to three within- or between-participants factors. Predicted effects are entered by specifying means, standard deviations, and, for within-participants factors, the correlations. The simulation provides the statistical power for all ANOVA main effects, interactions, and individual comparisons. The software can plot power across a range of sample sizes, can control for multiple comparisons, and can compute power when the homogeneity or sphericity assumption is violated. This Tutorial demonstrates how to perform a priori power analysis to design informative studies for main effects, interactions, and individual comparisons and highlights important factors that determine the statistical power for factorial ANOVA designs.

Simulation-Based Power Analysis for Factorial Analysis of Variance Designs