How to create common effect size estimate for meta-analysis based on a mix of mean changes and raw group means and standard deviations?

Question

I am trying to do a meta analysis, involving continuous data. I am trying to do this meta analysis in Stata using the metan command.

However, this data is organized in different fashions, where I have some studies with data listed as change in means with their standard errors and other data which is listed as the raw means and standard deviations.

Is there a way to combine this data and proceed with the analyses?

Answer 1

I'm assuming that you want to compute standardised group mean differences for all studies (i.e., Cohen's $d$).

• raw group means and standard deviations
  • There are various ways of calculating $d$. In general they are of the form of (mean1 - mean2) / sd. See here for some calculators and formulas for various formulas. In particular there are various ways of calculating the standard deviation.
• change in means with standard errors:
  • I am assuming that you are referring to standard errors in the difference between means and that you are interested in a between subjects effect. Obviously the change in means corresponds to the numerator for the formula for Cohen's D. The challenge is to calculate the group standard deviations from the standard error of the difference between group means. If you know group sample sizes and are happy to assume that group standard deviations are equal then I think you can use the denominator of the formula for independent groups t-test to calculate the group standard deviation through a bit of algebra.