# Computing Paired Samples (pre/post) Effect Size with Limited Information

I'm conducting a meta-analysis using the Hedge's g effect size statistic. Many of the studies are only reporting:

1. pre-treatment mean score
2. pre-treatment standard deviation
3. post-treatment mean score
4. post-treatment standard deviation
5. sample size

With this information, is it possible to derive either:

1. standard deviation of the difference (gain scores), or
2. the paired group t-value

If not, is there any other way to compute the paired samples effect size/standard error with the aforementioned limited information?

• Jake is right. The standard deviation of the gain scores is $s_d = \sqrt{s_1^2 + s_2^2 - 2 r s_1 s_2}$. You have $s_1$ and $s_2$, but based on that alone (or any other information you have listed), there is no way to figure out $s_d$ unless you know the correlation between pre- and post-test scores. You can of course calculate the range of $s_d$ by plugging in $r = {-1, +1}$, but that's about it. And that range will be next to useless. So, unless you want to start making assumptions about $r$, you are, so to speak, facing an impossibility. – Wolfgang Mar 27 '15 at 18:46

Unfortunately, if that really is all the information you have, then there is no way to get either #1 or #2 -- one way or another you need to know (or be able to deduce) the correlation between pre-test and post-test scores.

Yes, as others have mentioned, you will need to know the correlation between pre- and post-test scores to calculate an effect size.

However, this correlation value can be imputed to obtain reasonable results, especially if you can draw upon previous research and/or have a strong theoretical rationale for the particular value. After an initial effect size estimate is calculated from the imputed correlation, sensitivity analyses (within a reasonable range of imputed values) should be conducted . If they result in similar final aggregate/omnibus estimates you can (usually) have greater confidence in those initial estimates.

I am also working with a similar meta-analysis.

SDd can be imputed by several methods. 1. Taking it from other studies. Use maximum of observed from other studies. 2. If any of other studies have reported r, use it. Base it on maximum of observed r values. 3. If any of other studies in your meta-analysis is has mentioned, SE or 95% CI or P-value all these could be used to derive your SD for mean change.

Here is a good paper that addresses all these with formulas.

Fu R, Vandermeer BW, Shamliyan TA, O’Neil ME, Yazdi F, Fox SH, Morton SC. Handling Continuous Outcomes in Quantitative Synthesis. Methods Guide for Comparative Effectiveness Reviews.