Mean Difference, Standardized Mean Difference (SMD), and Their Use in Meta-Analysis: As Simple as It Gets

Abstract

In randomized controlled trials (RCTs), endpoint scores, or change scores representing the difference between endpoint and baseline, are values of interest. These values are compared between experimental and control groups, yielding a mean difference between the experimental and control groups for each outcome that is compared. When the mean difference values for a specified outcome, obtained from different RCTs, are all in the same unit (such as when they were all obtained using the same rating instrument), they can be pooled in meta-analysis to yield a summary estimate that is also known as a mean difference (MD). Because pooling of the mean difference from individual RCTs is done after weighting the values for precision, this pooled MD is also known as the weighted mean difference (WMD). Sometimes, different studies use different rating instruments to measure the same outcome; that is, the units of measurement for the outcome of interest are different across studies. In such cases, the mean differences from the different RCTs cannot be pooled. However, these mean differences can be divided by their respective standard deviations (SDs) to yield a statistic known as the standardized mean difference (SMD). The SD that is used as the divisor is usually either the pooled SD or the SD of the control group; in the former instance, the SMD is known as Cohen's d, and in the latter instance, as Glass' delta. SMDs of 0.2, 0.5, and 0.8 are considered small, medium, and large, respectively. SMDs can be pooled in meta-analysis because the unit is uniform across studies. This article presents and explains the different terms and concepts with the help of simple examples.