Garnica V, Shah D, Esker P, Ojiambo PS. MSE FINDR: A Shiny R Application to Estimate Mean Square Error Using Treatment Means and Post-hoc Test Results.
Plant Dis 2024. [PMID:
38319624 DOI:
10.1094/pdis-11-23-2519-sr]
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Abstract
Research synthesis methods such as meta-analysis rely primarily on appropriate summary statistics (i.e., means and variance) of a response of interest for implementation to draw general conclusions from a body of research. A commonly encountered problem arises when a measure of variability of a response across a study is not explicitly provided in the summary statistics of primary studies. Typically, these otherwise credible studies, are omitted in research synthesis leading to potential small-study effects and loss of statistical power. We present MSE FINDR, a user-friendly Shiny R application for estimating the mean square error (i.e., within-study residual variance, σ2) for continuous outcomes from ANOVA-type studies, with specific experimental designs and treatment structures (Latin square, completely randomized, randomized complete block, two-way factorial, and split-plot designs). MSE FINDR accomplishes this by using commonly reported information on treatment means, significance level (α), number of replicates and post-hoc mean separation tests (Fisher's LSD, Tukey's HSD, Bonferroni, Šidák and Scheffé). Users upload a CSV file containing the relevant information reported in the study, then specify the experimental design and post-hoc test that was applied in the analysis of the underlying data. MSE FINDR then proceeds to recover σ2, based on user-provided study information. The recovered within-study variance can be downloaded and exported as a CSV file. Simulations of trials with variable number of treatments and treatment effects showed that the MSE FINDR-recovered σ2 was an accurate predictor of the actual ANOVA σ2 for one-way experimental designs when summary statistics (i.e., means, variance and post-hoc results) were available for the single factor. Similarly, σ2 recovered by application accurately predicted the actual σ2 for two-way experimental designs when summary statistics were available for both factors and the sub-plot factor in split-plot designs, irrespective of the post-hoc mean separation test. The MSE FINDR Shiny application, documentation and an accompanying tutorial are hosted at https://garnica.shinyapps.io/MSE_FindR/ and https://github.com/vcgarnica/MSE_FindR/. With this tool, researchers can now easily estimate the within-study variance absent in published reports that nonetheless provide appropriate summary statistics, thus enabling the inclusion of such studies that would have otherwise been excluded in meta-analyses involving estimates of effect sizes based on a continuous response.
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