[R-meta] Collapsing a between subject factor

[Oliver Clark]

Hi all,

I am currently coding studies for a meta-analysis and have come across a case in which I have a set of studies in which all but one do not include sex as a between subject factor.  The reason given was unequal cell sizes, differences in visual stimuli (it is not clear what these differences are so they are unlikely to be systematic, rather an artefact)  and strength differences between men and women.

With my limited experience, I don’t see the benefit in treating these both as separate cases and was wondering whether it would make sense to merge the means and SDs for both groups and use that with the total N to calculate an effect size?

Combining the means seems relatively straightforward but I am not sure how to do the standard deviations.  I have tried averaging the variance in the following simulation to get there but must admit that I am stabbing in the dark!:

> M <- rnorm(10,5,2)
> F <- rnorm(10,5,2)
> 
> comb <- c(M,F)
> 
> (mean(M) + mean(F)) / 2 == mean(comb)
[1] TRUE
> 
> sqrt((sd(M)^2 + sd(F)^2)/2) == sd(comb)
[1] FALSE

Can anyone offer any advice on the best path for this? Should I treat them as different studies, attempt to merge the means and SDs, use a different aggregation method or omit this study?

Many thanks,

Oliver Clark

PhD Student
Manchester Metropolitan University