Converting Medians and Ranges to Means and Standard Deviations: A Practical Guide for Evidence Synthesis

Quantitative pooling in meta-analysis requires standardized effect measures, typically expressed as mean differences or standardized mean differences. However, many primary studies report continuous outcomes as medians with ranges or interquartile ranges (IQR), particularly when data are skewed. This reporting practice complicates evidence synthesis because means and standard deviations (SD) are required for conventional meta-analytic models. Over the past two decades, multiple statistical methods have been developed to convert medians and dispersion measures into approximate means and SDs, each with specific assumptions and limitations. This tutorial provides a structured overview of the main approaches, illustrates their application through simulated examples, and discusses their strengths and weaknesses in different scenarios. Practical guidance is offered on software implementation, interpretation of skewed data, and best practices to ensure transparency. These methods enable the inclusion of studies that would otherwise be excluded, but their use requires caution, explicit reporting, and acknowledgment of inferential limitations.