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12.6.4  Re-expressing SMDs using a familiar instrument

The final possibility for interpreting the SMD is to express it in the units of one or more of the specific measurement instruments. Multiplying a SMD by a typical among-person standard deviation for a particular scale yields an estimate of the difference in mean outcome scores (experimental versus control) on that scale. The standard deviation could be obtained as the pooled standard deviation of baseline scores in one of the studies. To better reflect among-person variation in practice, it may be preferable to use a standard deviation from a representative observational study. The pooled effect is thus re-expressed in the original units of that particular instrument and the clinical relevance and impact of the intervention effect can be interpreted. However, authors should be aware that such back-transformation of effect sizes can be misleading if it is applied to individual studies rather than for a summary measure of effect (Scholten 1999). Consider two studies that did use the same instrument and observed the same effect, but observed different among-participant variability (perhaps due to different inclusion criteria). Then back-transformations using the different standard deviations from these studies would yield different sizes of effect for the same scale and the same effect.