MSE FINDR: A Shiny R application to estimate mean square error using treatment means and post hoc test results

Abstract

Research synthesis methods such as meta-analysis rely primarily on appropriate summary statistics (i.e., means and variance) to draw general conclusions from a body of research. However, many studies report only treatment means and post hoc test results without providing a measure of variability, leading to exclusion of otherwise credible studies and loss of statistical power. We present MSE FINDR, a user-friendly Shiny R application for estimating mean square error (within-study residual variance, ̂σ²) for continuous outcomes from ANOVA-type studies with common experimental designs (Latin square, completely randomized, randomized complete block, two-way factorial, and split-plot designs). MSE FINDR uses reported treatment means, number of replicates, significance level (α), and post hoc tests (Fisher’s LSD, Tukey’s HSD, Bonferroni, Šidák, and Scheffé) to recover ̂σ². Users upload a CSV file with the relevant study information, specify the experimental design and post hoc test, and MSE FINDR outputs the recovered variance as a CSV file. Simulations showed that the recovered ̂σ² accurately predicts the actual within-study variance for both one-way and two-way designs, including split-plot experiments. The Shiny application, documentation, and tutorial are available at https://garnica.shinyapps.io/MSE_FindR/ and https://github.com/vcgarnica/MSE_FindR/. This tool enables inclusion of studies in meta-analyses that would otherwise be excluded due to missing variance data, facilitating more complete and reproducible quantitative synthesis.