[R-meta] Meta-analysis of ANOVA interaction effects

Iain Hamlin iain.hamlin at strath.ac.uk
Tue Feb 27 14:35:28 CET 2018

Dear Kyungnam and Wolfgang,

Kyungnam, thanks for the link, and, Wolfgang, thanks for clarifying that the link actually relates to the interaction of moderators in meta-regression, rather than ANOVA interaction effects.

It had similarly been suggested to me by someone else that I treat the interaction effect as the difference between the two mean difference scores. However, I was – and still am – unsure as to how I can use r to perform the meta-analysis. Does one simply meta-analyse the pairs of mean difference scores in a similar way to the most basic meta-analyses which meta-analyse the differences between pairs of means?

Kind regards,


-----Original Message-----
From: Viechtbauer Wolfgang (SP) [mailto:wolfgang.viechtbauer at maastrichtuniversity.nl] 
Sent: 27 February 2018 12:02
To: 전경남 <fstyle71 at naver.com>; Iain Hamlin <iain.hamlin at strath.ac.uk>; r-sig-meta-analysis at r-project.org
Subject: RE: [R-meta] Meta-analysis of ANOVA interaction effects

The URL links to a discussion of how to examine the interaction between two moderators in a meta-regression model. Iain is asking about how to meta-analyze interaction effects directly. That's not the same issue.

Iain - the interaction in a 2x2 ANOVA is the difference between two simple effects. So, for factors A and B, each with two levels, this is:

(mean_A1 - mean_A2) - (mean_B1 - mean_B2)

or equivalently

(mean_A1 - mean_B1) - (mean_A2 - mean_B2)

If needed (because studies use different scales), one can standardize this based on sqrt(MSE) of the model (MSE = mean squared error).

In fact, it isn't difficult to show that the t-test for the interaction is directly related to this standardized interaction effect:

((mean_A1 - mean_A2) - (mean_B1 - mean_B2)) / sqrt(MSE) = t * sqrt(1/n_A1 + 1/n_A2 + 1/n_B1 + 1/n_B2)

If all studies use the same scale, then I would recommend to meta-analyze the unstandardized interaction effects; otherwise go with the standardized ones.


>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-
>project.org] On Behalf Of ???
>Sent: Tuesday, 27 February, 2018 2:22
>To: Iain Hamlin; r-sig-meta-analysis at r-project.org
>Subject: Re: [R-meta] Meta-analysis of ANOVA interaction effects
>Dear Lian,
>Wolfgang's web site for the metafor package has an example with 
>detailed explanations for interaction effects.
>You can find the information in the following URL.
>-----Original Message-----
>From: "Iain Hamlin"<iain.hamlin at strath.ac.uk>
>To: "r-sig-meta-analysis at r-project.org"<r-sig-meta-analysis at r-
>Sent: 2018-02-27 (화) 03:38:48
>Subject: [R-meta] Meta-analysis of ANOVA interaction effects
>Dear all,
>Using r to do a meta-analysis of differences between means looks 
>simple, even for an r novice like me. However, I can find worryingly 
>little information - in books or on the internet - about how to use r 
>to meta- analyse the interaction effects stemming from 2X2 ANOVAs.
>I would be very grateful if someone could provide me with, or point me 
>in the direction of, information on how to do this in r.
>Many thanks,

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