[R-meta] effect size estimates regardless of direction

Daniel Noble d@niel@w@@noble @ending from gm@il@com
Mon May 21 23:39:12 CEST 2018

Hi Dave and Wolfgang,

If you don't mind going Bayesian, you can try the "analyse and transform"
option. This is done by estimating the overall mean estimate and applying
that to the folded normal. Check out Mike's two papers.

Morrisey,M.B.(2016). Meta-analysis of magnitudes, differences and variation
in evolutionary parameters. Journal of Evolutionary Biology 29, 1882–1904.

Morrisey,M.B.(2016). Rejoinder: further considerations for meta-analysis of
transformed quantities such as absolute values. Journal of Evolutionary
Biology 29, 1922–1931.

The second one has some R code that can help.


Dr. Daniel Noble | ARC DECRA Fellow
Level 5 West, Biological Sciences Building (E26)
Ecology & Evolution Research Centre (E&ERC)
School of Biological, Earth and Environmental Sciences (BEES)
*The University of New South Wales*
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On Tue, May 22, 2018 at 7:03 AM, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

> Hi Dave,
> You cannot just take absolute values and proceed with standard methods. As
> you noted, by taking absolute values, you end up with folded normal
> distributions. My approach would be to use ML estimation where the absolute
> values have folded normal distributions and then compute a profile
> likelihood confidence interval for the mean parameter, since I suspect a
> Wald-type CI would perform poorly.
> Best,
> Wolfgang
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
> bounces at r-project.org] On Behalf Of Dave Daversa
> Sent: Monday, 21 May, 2018 13:47
> To: r-sig-meta-analysis at r-project.org
> Subject: [R-meta] effect size estimates regardless of direction
> ATTACHMENT(S) REMOVED: forest.plot.example.pdf | dummy.forest.plot.code.R
> Hi all,
> My question regards how to estimate overall magnitudes of effect sizes
> from compiled studies regardless of the direction.  I have attached a
> figure to illustrate, which I developed using made-up data and the attached
> code.
> In the figure five studies have significantly positive effect sizes, while
> 5 have significantly negative effect sizes.  Each have equal variances.
> So, the overall estimated mean effect size from a random effects model is
> 0.   However, what if we simply want to estimate the mean effect size
> regardless of direction (i.e. the average magnitude of effects)?  In this
> example, that value would be 9.58 (CI: 6.48, 12.67), correct?
> I have heard that taking absolute values of effect sizes generates an
> upward bias in estimates of the standardized mean difference.  Also, this
> would create a folded normal distribution, which would violate assumptions
> of the model and would require an alternative method of estimating
> confidence intervals.  What would be your approach to setting up a model
> for answering the question of how much the overall magnitude of responses
> is?
> I suspect this question has come up in this email group in the past.  If
> so, my apologies for the redundancy, and please send me any reference that
> may be helpful.
> Dave Daversa
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