Standardised mean difference (SMD) estimation.

The standardised mean difference (SMD) summarises the statistical analysis in a meta-analysis when all the studies evaluate the same result but measure it in diverse methods. When the meta-analysis outcome is a continuous variable, SMD or means difference (M.D.) is employed. 1,2The difference in the means of the treatment group and the control group gives the M.D., whilst SMD is derived by dividing M.D. by the standard deviation (S.D.), drawn from either group.

Based on the choice of S.D., the SMD has types like Cohen’s d, Glass’s Δ, and Hedges’ g. In Cohen’s d, the difference between sample means of a continuous response is divided by the pooled standard deviation. The Hedges’ (adjusted) g employs pooled S.D., where S.D. is based on result data from both the intervention groups, deducing that two groups had similar S.D.s. Glass’ delta (Δ) utilises S.D. only from the comparator set.Cohen proposed the following criteria to infer the degree of the SMD in the social sciences: small SMD = 0.2; medium SMD = 0.5; and large SMD = 0.8.2,3,

References

  1. Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.2 (updated February 2021). Cochrane, 2021.
  2. Takeshima N, Sozu T, Tajika A, Ogawa Y, Hayasaka Y, Furukawa TA. Which is more generalisable, powerful and interpretable in meta-analyses, mean difference or standardised mean difference? BMC Med Res Methodol. 2014 Feb 21;14:30.
  3. Lin L, Aloe AM. Evaluation of various estimators for the standardised mean difference in meta-analysis. Stat Med. 2021 Jan 30;40(2):403-426. doi: 10.1002/sim.8781. Epub 2020 Nov 12.