[R-meta] [External] RE: Effect Sizes and Beta Coefficients

Thu, Jun 13, 2024 5:43 AM

Dear Rebecca,

Please see below for my answer.

Best,
Wolfgang

I assume you are asking about a p-value from a regression model. First of all, this is typically a two-sided p-value, so the given p-value must first be divided by 2. Also, the degrees of freedom are n-p-1 for a regression model with p regression coefficients. So it would be:

qt(1-pval/2, df=n-p-1)

Note that the (two-sided) p-value does not tell you anything about the sign of the regression coefficient (which in turn corresponds to the sign of the test statistic and hence the sign of the (semi)partial correlation), so additional information reported needs to be used to determine the correct sign.

You can't. A one-sample t-test is used to test if the mean of a single variable differs significantly from some value. It is not possible to compute the partial correlation for a single variable.

________________________________________
From: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Sent: 11 June 2024 17:21
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-
project.org>
Cc: Hall, Rebecca <r.hall5 at lancaster.ac.uk>
Subject: [External] RE: [R-meta] Effect Sizes and Beta Coefficients

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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This is my personal opinion: I would consider this approach outdated.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 at 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 at r-project.org
Cc: Hall, Rebecca <r.hall5 at 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

[R-meta] [External] RE: Effect Sizes and Beta Coefficients

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