A Guide to Transformations for Standardized Mean Difference Effect Sizes: Presenting Meta-Analytic Findings With...

Evidence synthesis research has great potential for informing decision-making, as it provides a holistic understanding of an entire body of literature. Meta-analyses are particularly important because they estimate intervention effects that can be used to inform both policy and practice. However, outside the field of healthcare, there has been little evidence that policymakers and practitioners use findings from meta-analyses in their work. A key barrier to the use of meta-analyses is that researchers often report advanced statistical estimates that non-research audiences struggle to comprehend. A critical first step to closing this gap is for researchers to translate meta-analytic average effect sizes in ways that may be more accessible to non-research audiences. This guide provides evidence synthesis researchers with easily accessible effect size transformations that can be performed on meta-analytic estimates of average standardized mean difference (SMD) effect sizes from random-effects models. The guide includes calculations, R code, statistical interpretations, and interpretations for non-research audiences for the average SMD (and its corresponding confidence interval and prediction interval), along with four transformations: Cohen's U₃, overlapping coefficient, common language effect size, and probability of study effect superiority. Importantly, we summarize literature exploring how well non-research audiences comprehend these transformations so that researchers can be informed when choosing which transformation(s) to report (if any). We also note where more research is needed to better understand how non-researchers interpret these different transformations. Overall, this guide provides practical tools for researchers to present effect sizes in ways that may enhance the accessibility of evidence synthesis findings.