[R-meta] (partial) eta squared

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 at 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 at gmail.com]
Sent: Monday, 06 August, 2018 16:53
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis at 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 at 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 at gmail.com]
Sent: Monday, 06 August, 2018 15:41
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis at 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 at 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 at r-project.org] On Behalf Of Antonia Sudkaemper
Sent: Friday, 03 August, 2018 12:33
To: r-sig-meta-analysis at 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 Sudk?mper
PhD Candidate in Organizational Psychology/University of Exeter
www.antoniasudkaemper.com
a.sudkaemper at gmail.com