Research statistics guide
How to Calculate SD of Change From Pre/Post Data
When a study reports baseline and follow-up means and standard deviations but not the standard deviation of the change score, you can often reconstruct it — provided you know or can reasonably estimate the correlation between the two measurements.
SD of change formula
For paired baseline and follow-up measurements:
where SDpre is the baseline SD, SDpost is the follow-up SD, and r is the correlation between baseline and follow-up measurements.
Worked example
Suppose a study reports:
- baseline SD = 15;
- follow-up SD = 14;
- pre/post correlation = 0.50.
= √211
= 14.526
The estimated SD of the individual change scores is therefore approximately 14.53.
Why does the pre/post correlation matter?
The baseline and follow-up values belong to the same participants. If people who have relatively high values at baseline also tend to have relatively high values at follow-up, the measurements are positively correlated. That covariance changes the variability of the difference between the two measurements.
Holding the baseline and follow-up SDs constant, a higher positive correlation generally produces a smaller SD of change. A smaller SD of change then produces a smaller standard error of the mean change and a narrower confidence interval.
How to calculate the SE and confidence interval of change
Once the SD of change is known, the standard error of the mean change is:
where n is the number of participants who contributed both baseline and follow-up measurements.
A confidence interval for mean change can then be calculated using the appropriate Student’s t critical value:
What if the pre/post correlation is not reported?
Do not assume that there is one universally correct value. Better options are to use a study-specific correlation if available, reconstruct it when the SD of change is reported, use an external estimate from a sufficiently comparable dataset, or perform a sensitivity analysis across plausible correlations.
For a detailed guide, see What pre/post correlation should I use?
How to reconstruct the pre/post correlation
If a paper reports the baseline SD, follow-up SD, and SD of change, the correlation can be rearranged from the variance-of-change equation:
A reconstructed value must lie between −1 and +1. If it does not, the reported summary statistics are incompatible with the formula, perhaps because of rounding, different analysis populations, adjusted values, or transcription errors.
Common mistakes
| Mistake | Why it matters |
|---|---|
| Treating baseline and follow-up as independent | This ignores within-participant covariance and generally gives the wrong SD of change. |
| Using the enrolled sample size | Use the number of participants with both measurements for a paired change calculation. |
| Assuming r = 0.50 is universally correct | 0.50 can be a sensitivity value, but it is not a universal empirical constant. |
| Using SD of change as the default standardizer for an effect size | Change-score variability and the SD used to standardize an effect are different statistical roles. |
Calculate it automatically
The Blazon Scientific Pre/Post Change Calculator calculates SD of change, standard errors, confidence intervals, Hedges’ g, and correlation sensitivity from summary data. Calculations run locally in your browser.
Open the Pre/Post Change CalculatorReferences and further reading
- Clifton L, Clifton DA. The correlation between baseline score and post-intervention score, and its implications for statistical analysis. Trials. 2019. PubMed
- Cochrane Handbook. Analysing data and undertaking meta-analyses: change scores. Cochrane
Frequently asked questions
Can I calculate SD of change from the two SDs alone?
Not uniquely. You also need the correlation between baseline and follow-up measurements, or equivalent information from which that correlation can be reconstructed.
What sample size should I use?
Use the number of participants who contributed both baseline and follow-up measurements to the paired analysis.
Does the correlation affect mean change?
No. Mean change is follow-up mean minus baseline mean. The correlation affects the variance and precision of that change.
Can I derive the correlation if SD of change is reported?
Yes. Rearranging the variance-of-change formula allows the pre/post correlation to be reconstructed from the baseline SD, follow-up SD, and SD of change.
What should I do if the correlation is unknown?
Use a defensible external estimate where possible and examine a sensitivity analysis across plausible values rather than treating one arbitrary correlation as certainly correct.