[R-meta] The effect size of a moderator in a meta-regression

Michael Dewey li@t@ @ending from dewey@myzen@co@uk
Tue Jul 31 17:10:31 CEST 2018

Dear Angeline

Comments inline below

On 30/07/2018 18:08, Angeline Tsui wrote:
> Hello all,
> I have a question about the effect size of a moderator in a meta-regression.
> In my meta-analysis, I used Cohen's d as the effect size, I ran a
> meta-regression with a number of moderators (i.e., like a multiple
> regression). I recently have received a feedback of a reviewer asking me
> specifically how to interpret the magnitude of the effect size of a
> significant moderator. In this case, the beta coefficient of this is about
> 0.19 and the weighted mean effect size of this meta-analysis is fairly low
> (around 0.3 but it is significant).
> So my question is how to interpret the magnitude of the beta coefficient
> here? In the context of a small weighted effect size, it is fairly large,
> for example, a unit change of x1 will lead to 0.19 increase in the Cohen's
> d (holding all other moderators constant). In terms of percentage, it is a
> large increase, approximately 63% increase (i.e., 0.19/0.3). However, in
> terms of the "rule of thumb" of Cohen's d size, it is small, as 0.2 is
> small Cohen's d.

I would prefer the first of these as it puts it in the context of the 
overall picture. You would be less impressed by a coefficient of 0.19 if 
the summary were 1.3 rather than 0.3.

Disclaimer: I find Cohen's rule of thumb very unhelpful even though I am 
sure he meant well.

> What do you think? Do you think that I should interpret the size of beta
> coefficient in the context of the weighted mean effect size or stick to the
> Cohen's d rule of thumb?
> Thanks very much and I look forward to receiving your reply.
> Best,
> Angeline


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