# Independent measures for pre-post data

In conducting a meta-analysis, I have pre-post data from single case designs. Unfortunately, I do not have access to the correlations between the pre and post scores. Is it correct that if I calculate the effect sizes using the independent measures, then the effect sizes will remain the same, but the standard error will increase and the confidence intervals will widen?

The formula for the standard error of the difference between two correlated means $m1$ and $m2$ is $$s_{md} = \sqrt{s^2_{m1} + s^2_{m2} - 2 r_{12} s_{m1} s_{m2}}$$
So if $r_{12}$ is positive the third term under the radical $2 r_{12} s_{m1} s_{m2}$ is also positive and so the standard error is reduced. By all means try a grid of values for the correlation but assuming it to be zero is conservative.
• Effect size here is being used in the sense it has in meta-analysis not in the sense of Cohen's $d$. So it could be anything: log odds ratio, log relative risk, log hazard ratio, proportion (possibly transformed), mean difference, standardised mean difference, correlation (presumably transformed), or anything else you can extract from the primary studies with a standard error. – mdewey Jun 13 '16 at 17:54