How to compute the total standard deviation of the (true) effect sizes, σ, in random/mixed-effects meta-analytic models? I have the following meta-analytic model (effect sizes nested within samples):
rma.mv(yi, vi, random = ~ 1 | SampleID/ESID, data=noOverlap, method = "REML", tdist=TRUE)

Which results in the following output:
Multivariate Meta-Analysis Model (k = 566; method: REML)

Variance Components:

            estim    sqrt  nlvls  fixed         factor
sigma^2.1  0.0045. 0.0669    264     no       SampleID
sigma^2.2  0.0120  0.1095    566     no  SampleID/ESID

Test for Heterogeneity:
Q(df = 565) = 4362.7212, p-val < .0001

Model Results:

estimate      se     tval   df    pval   ci.lb   ci.ub
  0.1328  0.0074  17.8823  565  <.0001  0.1182  0.1473  ***

I would like to calculate the standard deviation of true effect sizes, sigma, so as to have an interpretable index of the total substantive heterogeneity in the model (i.e., within-samples and across-samples).
Can this be computed by taking the square root of the sum of the two sigma^2s? I suspect not; does anyone have a better approach?
Thanks so much.

Yes, you can indeed add up the two variance components to obtain an estimate of the total amount of heterogeneity. If you take the square root thereof, the total amount of heterogeneity is given as a standard deviation. In fact, if you fit the model like this:
rma.mv(yi, vi, random = ~ ESID | SampleID, data=noOverlap, method="REML", tdist=TRUE)

you will find that the estimate of tau^2 given in that model is identical to the sum of the two variance components you obtained above.
For further details, see: https://www.metafor-project.org/doku.php/analyses:konstantopoulos2011
