We have conducted a meta-analysis and meta-analysed the effect sizes. This is a meta-analysis of 2x2 experimental designs, so we meta-analysed two main effect effect sizes and one interaction. Now we would like to illustrate the findings by creating a visualisation where the four meta-analysed means are plotted (allowing us to show the effect sizes as well), in a plot similar to this:
ggplot(data.frame(x=factor(c(0, 0, 1, 1)), y=c(0.9, 1.1, 1.8, 0.3), z=factor(c(0,1,0,1))), aes(x=x,y=y, group=z, color=z)) + geom_point(size=2) + geom_line(size=1) + theme_minimal();
We have standard deviations and means for each of the four cells, so we can standardize those (e.g. using the grand mean and the standard deviation of the total sample) to get four means that each represent the deviation from the grand mean in standard deviations.
For example, for one study, we have:
means <- c(0.32, 0.28, 0.36, 0.54); sds <- c(0.41, 0.41, 0.41, 0.58); ns <- c(36, 36, 36, 36); grandMean <- sum((means*ns)/sum(ns)); grandSD <- sqrt(sum(sds^2 * (ns-1)) / (sum(ns) - 4)); zMeans <- (means - grandMean) / grandSD;
And here we go:
print(zMeans);  -0.11996986 -0.20722067 -0.03271905 0.35990959
But, how can a series of such means be meta-analysed?
Is it so simple so as to simply consider them means from the same study? So could we just compute new means, weighing each mean using the sample size of that cell in that study?
On the one hand, this seems to be what we're doing. We have means from the same conditions but from different samples - not too different from when you aggregate means of different conditions but from the same sample like you do when you compute the grand mean.
I've found this post, but that package doesn't seem to provide an answer either.
metafor to do meta-analyses of proportions (i.e. prevalences) before, and there were dedicated methods for that. But I can't seem to find anything for this situation, perhaps because it is as simple as it seems? Or because I'm missing something.
I'd be grateful for any pointers! Or simply the confirmation that yes, it's this simple :-)