[R-meta] effect size estimates regardless of direction

[Viechtbauer, Wolfgang (SP)]

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