Dear R-Community, I'm currently trying to find a way to conduct a meta-analysis in R. I would like to analyze data from mostly-cross-sectional survey-studies. The effect sizes would be correlations. The R packages "meta" and "rmeta" are, as far as I can see, set up for analysis with effect sizes for differences (i.e. comparison of the means/odds-ratios of experimental and control group). Only the function "metagen" from the "meta"-package looks like it would work with correlations. The problem here: One would need to know the standard error of the correlation. The SE is not usually reported in the studies I have (only means, SDs and Alphas for the single variables). So the SE would have to be calculated somehow... But maybe "metagen" is the wrong function to start with in the first place? I'm wondering whether there might be anyone knowing how to conduct a meta-analysis based on correlations in R? Thanks in advance Sebastian P.S.: Of course, I'm dreaming of such a step-by-step-script like the absolutely marvellous ones provided by Bliese for multilevel-analysis in R :-) --------- Dipl.-Psych. Sebastian Stegmann Managing Editor, British Journal of Management Goethe University Institute of Psychology Department of Social Psychology Kettenhofweg 128 60054 Frankfurt am Main Germany http://www.sozialpsychologie.uni-Frankfurt.de/ Phone: +49 (0) 69 / 798-23078 Fax: +49 (0) 69 / 798-22384
Sebastian Stegmann schrieb: [...]> The R packages "meta" and "rmeta" are, as far as I can see, set up for > analysis with effect sizes for differences (i.e. comparison of the > means/odds-ratios of experimental and control group). > > Only the function "metagen" from the "meta"-package looks like it would work > with correlations. The problem here: One would need to know the standard > error of the correlation. The SE is not usually reported in the studies I > have (only means, SDs and Alphas for the single variables). So the SE would > have to be calculated somehow... But maybe "metagen" is the wrong function > to start with in the first place?Dear Sebastian, Have a look at the psychometric package which is capable of doing meta-analysis of correlations. In most cases you use Fisher-z transformed correlation coefficients. For that purpose, the psychometric package offers the function r2z(). Given that you know the number of cases N, the standard error can be easily computed as se_z = sqrt(1/(N-3)) (see also <http://rss.acs.unt.edu/Rdoc/library/psychometric/html/SEz.html>). Once you have computed Fisher's-z transformed r's and appropriate standard errors, it shouldn't be a problem to use the metagen-function. However be aware that the psychometric package does not use Fisher's-z transformed effect sizes when computing an overall effect size (as far as I have understood checking the source of rbar() ... which is somewhat strange... Mmmh). A quick replication of Hedges/Olkin's (1985) analysis (p. 231f; z_total = 0.469) revealed that metagen's computations are correct: library(meta) library(psychometric) ## table 2, p. 232 n <- c(20,30,27,42,49,12,17,35,38,40) r <- c(0.41,0.53,0.51,0.43,0.37,0.39,0.45,0.40,0.36,0.52) z <- r2z(r) se.z <- 1/sqrt((n-3)) metagen(TE = z, seTE = se.z) [... some output omitted ...] 95%-CI z p.value Fixed effect model 0.4686 [0.3515; 0.5857] 7.8415 < 0.0001 Random effects model 0.4686 [0.3515; 0.5857] 7.8415 < 0.0001> I'm wondering whether there might be anyone knowing how to conduct a > meta-analysis based on correlations in R?Feel free to ask if you have any further questions. Bernd Hedges, Larry V., und Ingram Olkin, 1985: Statistical Methods for Meta-Analysis. Orlando: Academic Press.
Dear Sebastian,
Many researchers may transform the Pearson coefficients into Fisher's
z scores first by using
z <- 0.5*log((1+r)/(1-r)).
The standard errors of the Fisher's z scores are z.SE <- 1/sqrt(n-3)
where n are the sample sizes (see
http://en.wikipedia.org/wiki/Fisher_transformation).
Either metagen {meta} or meta.summaries {rmeta} can be used to conduct
a fixed- or a random-effects meta-analysis.
--
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Mike W.L. Cheung Phone: (65) 6516-3702
Department of Psychology Fax: (65) 6773-1843
National University of Singapore
http://courses.nus.edu.sg/course/psycwlm/internet/
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On Fri, Feb 13, 2009 at 7:11 PM, Sebastian Stegmann <
stegmann@psych.uni-frankfurt.de> wrote:
> Dear R-Community,
>
> I'm currently trying to find a way to conduct a meta-analysis in R.
> I would like to analyze data from mostly-cross-sectional survey-studies.
> The
> effect sizes would be correlations.
>
> The R packages "meta" and "rmeta" are, as far as I can
see, set up for
> analysis with effect sizes for differences (i.e. comparison of the
> means/odds-ratios of experimental and control group).
>
> Only the function "metagen" from the "meta"-package
looks like it would
> work
> with correlations. The problem here: One would need to know the standard
> error of the correlation. The SE is not usually reported in the studies I
> have (only means, SDs and Alphas for the single variables). So the SE would
> have to be calculated somehow... But maybe "metagen" is the wrong
function
> to start with in the first place?
>
> I'm wondering whether there might be anyone knowing how to conduct a
> meta-analysis based on correlations in R?
>
> Thanks in advance
> Sebastian
>
> P.S.: Of course, I'm dreaming of such a step-by-step-script like the
> absolutely marvellous ones provided by Bliese for multilevel-analysis in R
> :-)
>
> ---------
> Dipl.-Psych. Sebastian Stegmann
> Managing Editor, British Journal of Management
> Goethe University
> Institute of Psychology
> Department of Social Psychology
> Kettenhofweg 128
> 60054 Frankfurt am Main
> Germany
> http://www.sozialpsychologie.uni-Frankfurt.de/
> Phone: +49 (0) 69 / 798-23078
> Fax: +49 (0) 69 / 798-22384
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
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