[R-meta] (partial) eta squared

[Antonia Sudkaemper]

Hello Wolfgang,

thank you very much for your advice and your reading suggestions (will take
me a while to catch up on those...) - based on your instructions I am using
this code now to run the (mini) meta-analysis.

slope = c(-0.0478, 0.1307, 0.0941)               #regression coefficient
error = c(0.0075, 0.0083, 0.0077)                  #standard error squared
study<-c("Study 1", "Study 2", "Study 3")

summary(meta <- rma(yi=slope, vi= error, method= "FE", slab=c("Study 1",
"Study 2", "Study 3")))
forest(meta, xlab = "regression coefficient")

All the best, Antonia


On 7 August 2018 at 10:31, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> I would then meta-analyze the non-standardized regression coefficients.
> The square of the SEs of the coefficients are the appropriate sampling
> variances. Computing the correct SEs (and hence sampling variances) for
> standardized regression coefficients is a bit more tricky. See, for example:
>
> Jones, J. A., & Waller, N. G. (2015). The normal-theory and asymptotic
> distribution-free (adf) covariance matrix of standardized regression
> coefficients: Theoretical extensions and finite sample behavior.
> Psychometrika, 80(2), 365-378.
>
> Jones, J. A., & Waller, N. G. (2013). Computing confidence intervals for
> standardized regression coefficients. Psychological Methods, 18(4), 435-453.
>
> Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
> regression coefficients. Psychometrika, 76(4), 670-690.
>
> Alternatively, you could meta-analyze the (semi)partial correlation
> coefficients. See:
>
> Aloe, A. M., & Becker, B. J. (2012). An effect size for regression
> predictors in meta-analysis. Journal of Educational and Behavioral
> Statistics, 37(2), 278-297.
>
> Aloe, A. M., & Thompson, C. G. (2013). The synthesis of partial effect
> sizes. Journal of the Society for Social Work and Research, 4(4), 390-405.
>
> Aloe, A. M. (2014). An empirical investigation of partial effect sizes in
> meta-analysis of correlational data. Journal of General Psychology, 141(1),
> 47-64.
>
> See also help(escalc) and then search for "Partial and Semi-Partial
> Correlations".
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Antonia Sudkaemper [mailto:a.sudkaemper using gmail.com]
> Sent: Monday, 06 August, 2018 16:53
> To: Viechtbauer, Wolfgang (SP)
> Cc: r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] (partial) eta squared
>
> Hello Wolfgang,
>
> yes, I noticed that this is a difficult one...
>
> Yes, the studies are (almost) equivalent, using the same DV's and IV's.
> Would you then recommend meta-analyzing the standardized or
> non-standardized regression coefficients?
>
> Thank you so much for your help!
>
> All the best, Antonia
>
> On 6 August 2018 at 14:47, Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> It's not so much an issue with metafor, but with lack of methodology for
> this in general.
>
> Did all three studies use the same DV and IVs? Then you could meta-analyze
> the regression coefficient for the interaction directly.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Antonia Sudkaemper [mailto:a.sudkaemper using gmail.com]
> Sent: Monday, 06 August, 2018 15:41
> To: Viechtbauer, Wolfgang (SP)
> Cc: r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] (partial) eta squared
>
> Hello Wolfgang,
>
> thank you very much for your reply. It seems like eta squared might not be
> the most straightforward option then when intending to work with metafor.
>
> Would you recommend another effect size for an interaction effect from a
> linear regression that is more compatible with the analyses metafor runs?
>
> All the best, Antonia
>
> On 3 August 2018 at 15:09, Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> Dear Antonia,
>
> in principle, you could meta-analyze eta^2 values, but there are several
> issues to consider:
>
> 1) The sampling distribution of eta^2 isn't normal. So, one would first
> have to explore what kind of transformation would be appropriate for eta^2
> values to normalize their sampling distribution.
>
> 2) I do not know off the top of my head an equation for the sampling
> variance of eta^2 values.
>
> 3) eta^2 isn't a directional effect size measure. Two eta^2 values of the
> same magnitude could imply entirely opposite findings. So, one could
> question the usefulness of aggregating eta^2 values in the first place.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
> bounces using r-project.org] On Behalf Of Antonia Sudkaemper
> Sent: Friday, 03 August, 2018 12:33
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] (partial) eta squared
>
> Hello fellow meta-analysis colleagues,
>
> I have recently started using metafor and am still exploring. Currently, I
> am
> working on a mini meta-analysis of three studies I ran myself. In recent
> psychology journal I have seen the use of (partial) eta squared as an
> indicator of effect size. I was wondering if I can use the rma.uni command
> to run a meta-analysis on (partial) eta squared? And if so, which error
> (vi/sei) indicator would I use with it?
>
> Hope someone can help!
>
> All the best, Antonia
>
> --
> Antonia Sudkämper
> PhD Candidate in Organizational Psychology/University of Exeter
> www.antoniasudkaemper.com
> a.sudkaemper using gmail.com
>



-- 
Antonia Sudkämper
PhD Candidate in Organizational Psychology/University of Exeter
www.antoniasudkaemper.com
a.sudkaemper using gmail.com

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