Summary-statistics-based power analysis: A new and practical method to determine sample size for mixed-effects modelling

This article proposes a summary-statistics-based power analysis --- a practical method for conducting power analysis for mixed-effects modelling with two-level nested data (for both binary and continuous predictors), complementing the existing formula-based and simulation-based methods. The proposed method bases its logic on conditional equivalence of the summary-statistics approach and mixed-effects modelling, paring back the power analysis for mixed-effects modelling to that for a simpler statistical analysis (e.g., one-sample t test). Accordingly, the proposed method allows us to conduct power analysis for mixed-effects modelling using popular software such as G*Power or the pwr package in R and, with minimum input from relevant prior work (e.g., t value). We provide analytic proof and a series of statistical simulations to show the validity and robustness of the summary-statistics-based power analysis and show illustrative examples with real published work. We also developed a web app (https://koumurayama.shinyapps.io/summary_statistics_based_power/) to facilitate the utility of the proposed method. While the proposed method has limited flexibilities compared to the existing methods in terms of the models and designs that can be appropriately handled, it provides a convenient alternative for applied researchers when there is limited information to conduct power analysis.