[R-meta] (partial) eta squared

[Viechtbauer, Wolfgang (SP)]

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