[R-meta] correlational meta-analyses and Egger's regression test

James Pustejovsky jepu@to @end|ng |rom gm@||@com
Sat Jan 22 20:54:26 CET 2022

Hi Catia,

I don't know of any studies on this. But the statistical theory here is
pretty straight-forward, so perhaps it's not necessary to do simulations to

For the sample Pearson correlation coefficient r, the (estimated) standard
error is (1 - r^2) / sqrt(N - 1), which is strongly correlated with the
point estimator. This implies that there will tend to be an asymmetric
funnel plot and non-zero slope to Egger's regression (or the
multi-level/multi-variate extensions thereof) even in the absence of
selective reporting. To avoid this artifact, Wolfgang suggests using
1 / sqrt(N - 1) as the predictor in Egger's regression because then it will
be independent of the effect size estimator. Alternately, you could do the
analysis using Fisher's z transformation. The z transformed correlation has
standard error 1 / sqrt(N - 3), which will be independent of the effect
size estimator.


On Sat, Jan 22, 2022 at 11:53 AM Cátia Margarida Oliveira <
catiamargarid using gmail.com> wrote:

> Hello,
> I am running a correlational meta-analysis and I was wondering if there are
> guidelines for which measure to use as a predictor in Egger's test with
> multilevel models. I have encountered a few sources (e.g. the paper by
> James - Testing for funnel plot asymmetry of standardized mean differences)
> on how using measures of variance may be problematic with logs odds ratios
> and standardised mean difference effect size estimates, but does anyone
> know if there's such research for meta-analyses examining correlations?
> The only reference I found was here:
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2020-May/002086.html
> Thank you,
> Catia
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