Pre/post effect sizes for meta-analysis: baseline SD or change-score SD?
Quick summary
- In a controlled pre/post study, the effect numerator can be the between-group difference in mean change.
- For a standardized effect, the pooled baseline SD provides a between-participant scale for the effect.
- The SD of change answers a different question: how variable were participants’ changes? It is therefore important for the SE and sampling variance.
- If SD of change is missing, it can be reconstructed from baseline SD, post SD and the within-person pre/post correlation.
- The Blazon Study Effect Size Calculator keeps these roles separate rather than using the change-score SD automatically as the standardizer.
Why pre/post effect sizes need special treatment
Suppose an intervention group and a control group are both measured before and after treatment. A natural unstandardized treatment effect is the difference between their mean changes:
(Post₁ − Pre₁) − (Post₂ − Pre₂)
The numerator is straightforward. The more difficult question is which SD should be used if the effect needs to be standardized.
The SD used for standardization and the SD used for precision are not necessarily the same
A standardized mean effect needs a denominator that provides a meaningful scale for between-participant differences. Hopkins and Rowlands argue that change-score SDs are generally not an appropriate default standardizer for controlled pre/post effects because the variability of change can contain measurement error, ordinary within-person variation and potentially individual-response variability.
For a conventional two-group pre/post study, a practical default is therefore the pooled baseline SD:
SDpre,pooled = √{[(n₁−1)SDpre₁² + (n₂−1)SDpre₂²] / (n₁+n₂−2)}
The standardized difference in change is then the between-group difference in mean changes divided by this pooled baseline SD, followed by an appropriate small-sample correction where required.
So why do we still need the SD of change?
The change-score SD quantifies how much individual participants varied in their pre-to-post changes. That variability determines how precisely the group mean change has been estimated.
For two independent groups, the sampling variance of the raw between-group difference in change contains:
SDchange₁²/n₁ + SDchange₂²/n₂
In other words, the baseline SD sets the scale of the standardized effect, while change-score variability contributes to the uncertainty around that effect.
Where does the pre/post correlation enter?
If a study does not report SD of change, it can be reconstructed from the baseline SD, post SD and the within-person correlation:
SDchange = √(SDpre² + SDpost² − 2r·SDpre·SDpost)
Repeated measurements on the same person are normally correlated. Ignoring this relationship can substantially misrepresent the variability of change.
See the dedicated pre/post correlation resource and SD-of-change guide for more detail.
What if the correlation was not reported?
Do not silently pretend that the correlation is known. An assumed correlation makes the precision calculation assumption-dependent. A reasonable workflow is to state the assumed value and conduct a sensitivity analysis across plausible correlations.
When the numerator and pooled baseline standardizer are unchanged, changing the assumed correlation changes the reconstructed SD of change and therefore the SE, variance and CI — but not the standardized point estimate itself.
How the Study Effect Size Calculator handles controlled pre/post data
The Study Effect Size Calculator:
- calculates each group’s mean change;
- calculates the between-group difference in change;
- uses reported SDs of change or reconstructs them from pre/post correlations;
- uses the pooled baseline SD as the default standardizing denominator;
- applies an exact Hedges small-sample correction;
- uses the Hopkins–Rowlands framework for sampling variance and confidence-interval degrees of freedom;
- labels calculations based on assumed correlations as assumption-dependent.
What about ANCOVA?
A randomized trial may estimate treatment effects using post-intervention values adjusted for baseline rather than raw change scores. This can be statistically preferable to analysing change scores in many settings. Do not replace a reported model-based adjusted SE with an SE reconstructed from arm-level change-score data.
For further context, see Change scores vs ANCOVA and Standardized effects in pre/post studies.
References
- Hopkins WG, Rowlands DS. Standardization and other approaches to meta-analyze differences in means. Statistics in Medicine. 2024;43:3092–3108.
- Morris SB. Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods. 2008;11:364–386.
- Cochrane Handbook, Chapter 6.
Calculate a controlled pre/post effect: Open the Study Effect Size Calculator →