Figure 1. How SMDs enable us to combine different scale-specific units into one pooled effect. The illustration shows how data standardisation process allows us to mix ‘apples’ and ‘oranges’ making them ‘juice’. MD: Mean Difference.
HOW TO COMPUTE STANDARDISED MEAN DIFFERENCES
When we standardise data, we divide the mean difference (MD) between the treatment and control groups (i.e., the effect size of the treatment) by the pooled sample standard deviation (SD) in each study (i.e., the between-participant variability in outcome measurements observed in each study) at one specific follow-up time point [3].
\begin{equation} SMD=\ \frac{\text{MD\ between\ groups}}{SD\ of\ outcome\ among\ participants\ at\ follow-up\ time\ point}\nonumber \\ \end{equation}
Equation 1. SMD calculation using pooled sample SD at a specific follow-up time point.
For a better understanding of this terminology, we are going to apply different standardisation methods on data extracted from a published meta-analysis [4]. Therefore, we select the Ortiz-Alonso et al. (2020) study [5] included in this meta-analysis, which reported results using the overall score of the Short Physical Performance Battery (an instrument to assess the physical function; SPPB), and extract the ‘raw’ data (i.e., data directly extracted from the study without any transformation) (Table 1).
Table 1. ‘Raw’ data extracted from Ortiz-Alonso et al. (2020) study.