Meta-analysis in R: how to calculate standard error for study with multiple outcomes? for my PhD, I am working on a meta-analysis. The studies we have identified have means/SDs and % to compare conditions. Several of these studies also have multiple outcomes that we want to pool.
For that, we use the Borenstein 2009 book to calculate Cohen’s D for each outcome, and then calculate a combined effect size D per study, as well as a new variance from this combined D (page 229, formula 24.3).
However, if we want to run the meta in metafor in R, we need to have standard error, instead of variance.
metagen(TE, seTE, studlab, data = NULL, subset = NULL)
Can we just square root that new variance? It seems too easy, particularly given all the other more elaborate formulas...
 A: In this context, the standard error is just the square root of the variance.
Lest somebody gets confused about this: When we are dealing with raw data, then we can compute their variance, the square root thereof is the standard deviation, and if we divide the standard deviation by the square root of the sample size, we have the standard error of the mean. The latter can also be called a standard deviation, but it is not the standard deviation of the raw data, but of a statistic (in this case, the mean). The term "standard error" simply helps to differentiate the standard deviation of the raw data from the standard deviation of the mean. Also, if we square the standard error, we can call this a variance, but again, not of the raw data but of the statistic. To differentiate the variance of the raw data from the latter, we can use the term "sampling variance" to emphasize that we are not talking about the variance of the raw data, but how much variance there is in the statistic (if one were to repeatedly sample the same number of individuals from the same population and compute the statistic in each sample).
PS: The metagen() function is not part of the metafor package, but of the meta package.
