For a meta-analysis, we are interested in the comparison of two groups. From the articles, we can extract four means: two baseline measures on one of our dependent variables, and two measures collected after some manipulation took place. We also have the standard deviations for these means. The sample sizes are generally very small (which is one of the reasons why we usually have both pre- and post-measures; the researchers were probably aware of their low sample sizes and wanted to increase their power).
Although these means and SD's (variances) are often reported, the only statistics we have are usually from multivariate analyses, rendering them, at best, tricky to use (because the models (included covariates) differ substantially between studies). So we'd prefer to stick to the means and variances.
So, we want to compute the effect size. The go-to measure would be Cohen's d, to see how strongly these groups differ. We could ignore the baseline measure and compute d for post-test only, but this would of course yield a much lower power; ideally we'd look at change from baseline.
However, we don't have individual scores - we can't compute change over time per participant. We only have 'within-group variance' (to use oneway anova vocabulary).
I'd say this means that we might as well not have the baseline means: there is not way to use them to compute an effect size measure. But I want to make sure this is true - I'm not sure there's not something I miss. It feels like I do, but I'm not sure.
To provide an example, we have from one of the studies the following means (SD's):
control 33.2 (12.4) 33.1 (11.2)
experimental 29.5 (13) 30.9 (14.1)
Our goal is to express this association (columns 'within', rows 'between' subjects) in an effect size measure.
Is my intuition/fear, that we're forced to discard the first column because we can't remove or model the dependency between the two columns, correct? Or am I missing something and is there a way to use all available data after all?