[R-meta] Effect Sizes and Beta Coefficients

[Viechtbauer, Wolfgang (NP)]

Dear Rebecca,

This is my personal opinion: I would consider this approach outdated.

Typically, in a situation like this, one also knows the t-statistic for the coefficient of interest (or its p-value from which one can back-calculate the t-statistic). In that case, one can compute the (semi)partial correlation coefficient for the coefficient.

However, whether one should combine such 'partial' effect sizes with bivariate correlations is debatable in the first place. A relevant article that essentially argues against this is:

Aloe, A. M. (2015). Inaccuracy of regression results in replacing bivariate correlations. Research Synthesis Methods, 6(1), 21-27. https://doi.org/10.1002/jrsm.1126

At least, one could try to capture some of the heterogeneity introduced by this by including a moderator in the model that indicates the type of correlation coefficient. With enough studies, one could even go a step further and include moderators that indicate which covariates were included in the original regression models from which the (semi)partial correlations were obtained (as a bunch of dummy variables).

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Hall, Rebecca via R-sig-meta-analysis
> Sent: Tuesday, June 11, 2024 17:57
> To: r-sig-meta-analysis using r-project.org
> Cc: Hall, Rebecca <r.hall5 using lancaster.ac.uk>
> Subject: [R-meta] Effect Sizes and Beta Coefficients
>
> Dear all,
>
> I have a question regarding the use of a beta coefficient as a substitute for
> effect size where a paper lacks statistical data for Pearson's r to otherwise be
> calculated.
>
> Peterson & Brown (2005) support the use of standardised beta coefficients and
> relative SE in the place of correlations, but Roth et al. (2018) criticise this.
> I'm therefore wondering whether there is a general consensus regarding the use
> of beta coefficients, and should Peterson & Brown's approach no longer be
> appropriate then I would be gladly advised on the alternative method that should
> be utilised.
>
> Many thanks,
> Rebecca
>
> Dr Rebecca Hall | Research Associate
> Department of Psychology | Lancaster University