I'm aware that it isn't possible to calculate a correlation coefficient from the means of two data sets.
However, I'm wondering if there is a way to get a correlation coefficient (with confidence intervals) in the following scenario:
We are planning on running a meta-analysis with the main question of looking at the association between two variables (A and B). However, nearly all studies report the means and standard deviations (or 95% confidence intervals etc) of the two variables individually; they do not report correlation coefficients.
As such, is there a way of taking these means from each study (i.e. each study will have a paired mean data set), and then calculating the correlation coefficient for this meta-data set.
My thinking is this would require knowledge of the mean, spread of the data (i.e. SD) and sample size. Combined this would then give a "best guess" at the correlation coefficient and then a confidence boundary based on the individual data sets spread etc.
Thank you for any thoughts/guidance on this.