# *Geek Box: Standardised Mean Difference

#### *Geek Box: Standardised Mean Difference

In a meta-analysis, it is common to see “SMD” as the outcome measure. And it is actually important to distinguish between “mean difference” [MD] and “standardised mean difference” [SMD]. For MD, the outcomes are expressed in the unit of measurement, e.g., bodyweight. This assumes all studies have used the same outcome measure.

For example, suppose we are looking at a meta-analysis of 10 studies on the effects of meal timing on blood glucose levels, and all studies have measured plasma glucose response in mg/dL or mmol/L. Because one can easily be converted into the other, the researchers could decide to use MD expressed as mmol/L. Thus, if the outcome was a difference of 0.6 [95% CI 0.2 – 0.9], you would interpret this as 0.6mmol/L with a confidence interval range of 0.2mmol/L to 0.9mmol/L.

Now, suppose the analysis wanted to look at insulin sensitivity, and of our 10 studies, 4 had used HOMA-IR, 4 had used hyperinsulinemic/euglycemic clamp, and 2 had used the Matsuda Index. These are all different outcome measures for the same conceptual outcome, i.e., insulin sensitivity. This is when SMD is used, where the included studies have measured the exposure and outcome using different methods.

SMD is calculated by taking the mean difference from each study and dividing it by the standard deviation in that study. By doing this for each study, the SMD for each study may be combined in a meta-analysis. However, it is crucial to correctly interpreting an outcome expressed as SMD that, unlike MD, SMD is not expressed in the unit of measurement.

Rather, SMD is a measure of effect size, which is also referred to as Cohen’s d after the statistician who proposed these measures. As a general rule, effect sizes of 0.2, 0.6, and 0.8, are considered small, medium, and large effect sizes, respectively. So, if the outcome now was an SMD of 0.6 [95% CI 0.2 – 0.9], you would interpret this as a medium effect size with a confidence interval range of small to large.