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

Iain Hamlin iain.hamlin at strath.ac.uk
Tue Feb 27 19:48:43 CET 2018

```Dear Wolfgang,

Many thanks for this very useful explanation/illustration! I will give it a short in r.

Kind regards,

Iain

________________________________________
From: Viechtbauer Wolfgang (SP) [wolfgang.viechtbauer at maastrichtuniversity.nl]
Sent: Tuesday, February 27, 2018 2:00 PM
To: Iain Hamlin; r-sig-meta-analysis at r-project.org
Subject: RE: [R-meta] Meta-analysis of ANOVA interaction effects

Just compute the 'interaction effects' and corresponding sampling variances and feed this to your meta-analysis package of choice. Let's say there are 2 studies:

dat <- data.frame(study=c(1,2), ti=c(3.41,2.68), n11i=c(32,12),
n12i=c(39,13), n21i=c(35,15), n22i=c(36,14))

ti is the t-statistic for the interaction and the n..i variables indicate the cell sizes of the 2x2 factorial design. Then you can compute the standardized effect with:

dat\$yi <- with(dat, ti * sqrt(1/n11i + 1/n12i + 1/n21i + 1/n22i))

The corresponding sampling variances can be obtained with:

dat\$vi <- with(dat, 1/n11i + 1/n12i + 1/n21i + 1/n22i + dat\$yi^2 / (2*(n11i + n12i + n21i + n22i)))

And finally, using for example the metafor package:

library(metafor)
rma(yi, vi, data=dat)

(leaving aside whether fitting a RE model with k=2 is a wise thing to do).

Best,
Wolfgang

>-----Original Message-----
>From: Iain Hamlin [mailto:iain.hamlin at strath.ac.uk]
>Sent: Tuesday, 27 February, 2018 14:35
>To: Viechtbauer Wolfgang (SP); 전경남; r-sig-meta-analysis at r-project.org
>Subject: RE: [R-meta] Meta-analysis of ANOVA interaction effects
>
>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,
>
>Iain
>
>-----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.
>
>Best,
>Wolfgang
>
>>-----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.
>>
>>http://www.metafor-
>>project.org/doku.php/tips:multiple_factors_interactions
>>
>>Kyungnam
>>
>>-----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-
>>project.org>;
>>Cc:
>>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,
>>
>>Iain
```