A tutorial on using the paired t test for power calculations in repeated measures ANOVA with interactions

Area of Science:

• Behavioral and social sciences
• Psychology
• Statistics

Background:

• A priori statistical power calculations are crucial for determining sample sizes in research.
• Complex factorial repeated measures ANOVA designs can make power calculations cumbersome, particularly for higher-order interactions.

Purpose of the Study:

• To provide practical guidance on simplifying sample size calculations for repeated measures ANOVA.
• To demonstrate how to express main and interaction effects as single difference variables for power analysis.
• To facilitate the use of paired t-tests for power calculations in specific ANOVA designs.

Main Methods:

• Expressing ANOVA effects (main and interaction) as single difference variables.
• Calculating Cohen's d effect size for these difference variables using means, variances, and covariances.
• Transforming ANOVA F-statistics or partial eta-squared into Cohen's d.
• Utilizing the paired t-test framework for sample size determination with correctly specified effect sizes.

Main Results:

• Demonstrated a method to simplify complex repeated measures ANOVA power calculations.
• Provided formulas and practical steps for calculating Cohen's d from ANOVA outputs.
• Illustrated the application of the t-test for sample size considerations with an empirical example.

Conclusions:

• The proposed method simplifies sample size calculations for repeated measures ANOVA, especially for designs with two-level factors.
• Researchers can effectively use paired t-tests for power analysis by correctly specifying effect sizes derived from ANOVA.
• Accessible R code is provided to support the practical implementation of these methods.