# [R-meta] Question Re: CI in metafor

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Wed May 30 16:03:46 CEST 2018

```Dear Caitlin,

I do not have a copy of S&H (2013), only the 2004 (i.e., 2nd) edition. So I cannot look up what exactly you mean by "square root of the variance of the corrected Rs/square root of k". Note that the notation and terminology used by H&S differs quite a bit from how statisticians/methodologists outside of the 'psychometric meta-analysis world' talk about these models/methods. Hence, I am also not entirely sure what you mean by "square root of Ave(ve)/square root of k".

The methods as implemented in metafor are based on mixed-effects models and use standard estimation methods (weighted least squares, maximum likelihood estimation, etc.). Hence, the calculations are just how things are calculated under such models and estimation methods.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Caitlin Porter
Sent: Tuesday, 29 May, 2018 22:17
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Question Re: CI in metafor

Recently, I have been using the metafor program to run analyses for a
meta-analysis based on the Hunter-Schmidt approach. I have been
double-checking my own calculations with the program, and I found that my
calculations of confidence intervals do not align with the calculations
provided by metafor.

I am using the SD of the corrected Rs as a basis for my CIs (square root of
the variance of the corrected Rs/square root of k), as noted in Schmidt and
Hunter (2013, p. 154, pp. 420-421). However, the confidence intervals that
appear in the metafor output appear to be based upon the sampling error
variance (the square root of Ave(ve)/square root of k).

1) Is there was a reason that the CIs in metafor are based upon this value
as opposed to the one suggested by HS?
2) Is one approach preferred over the other?

Thank you in advance for your insights on this matter!

--
Caitlin M. Porter, Ph.D.

Assistant Professor
Industrial and Organizational Psychology
Department of Psychology
University of Houston
3625 Cullen Blvd.
Houston, TX 77204

```

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