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.