Standardized mean difference
A standardized mean difference (SMD) is the difference between two group averages divided by a standard deviation, so results measured on different scales can be pooled in one meta-analysis.
What it means in practice
When every trial in a review measures an outcome with the same test, reviewers can pool the raw differences between groups into a mean difference, kept in that test's units [1]. When trials assess the same outcome in different ways, though, the raw differences cannot be pooled because their units differ [1][2].
The SMD handles this by dividing each trial's difference by a standard deviation, a measure of how spread out participants' scores were [1]. The result expresses the size of the effect relative to the variation between participants in that study [2]. If the divisor is the pooled standard deviation of both groups, the SMD is called Cohen's d; if it is the control group's standard deviation, it is called Glass' delta [1]. Because every trial is then on the same scale, SMDs can be pooled in a meta-analysis [1].
By a common convention, SMDs of 0.2, 0.5 and 0.8 are called small, medium and large [1]. The term "effect size" usually, though not always, refers to a version of the SMD [2].
Why it matters when reading nootropics research
An SMD is reported in standard deviation units, not in the units of any test, which makes it hard to interpret as points on a memory score or milliseconds of reaction time [2]. A meta-analysis might report a small SMD for a memory outcome; that describes the difference relative to the spread of scores, not how many extra words a participant recalled.
The method also rests on assumptions. It assumes that differences in standard deviations between trials reflect differences in measurement scales, not real differences between the people studied [2]. If two trials have the same raw effect but different standard deviations, their SMDs differ, and trials that enroll a wider range of participants may have larger standard deviations [2]. The SMD does not correct for scales that run in opposite directions, so reviewers have to make all the scales point the same way before standardizing [2].
NootropicsWork reports SMDs exactly as the paper gives them, with the population and the comparison, and does not convert them into test scores.
References
- Andrade C. Mean Difference, Standardized Mean Difference (SMD), and Their Use in Meta-Analysis: As Simple as It Gets. J Clin Psychiatry. 2020.
- Cochrane. Cochrane Handbook for Systematic Reviews of Interventions, Chapter 6: Choosing effect measures and computing estimates of effect (version 6.5). Chapter last updated August 2023; Handbook version 6.5, 2024.