[R-meta] Correcting Hedges' g vs. Log response ratio in nested studies

[James Pustejovsky]


Wolfgang is correct. The WWC correction factor arises because the sample variance is not quite unbiased as an estimator for the total population variance in a design with clusters of dependent observations, which leads to a small bias in the SMD. 

The thing is, though, this correction factor is usually negligible. Say you’ve got a clustered design with n = 21 kids per cluster and 20 clusters, and an ICC of 0.2. Then the correction factor is going to be about 0.99 and so will make very little difference for the effect size estimate. It only starts to matter if you’re looking at studies with very few clusters and non-trivial ICCs.

James

> On Nov 2, 2023, at 3:04 AM, Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org> wrote:
> Dear Yuhang,
> 
> I haven't looked deeply into this, but an immediate thought I have is that for SMDs, you divide by some measure of variability within the groups. If that measure of variability is affected by your study design, then this will also affect the SMD value. On the other hand, this doesn't have any impact on LRRs since they are only the (log-transformed) ratio of the means.
> 
> Best,
> Wolfgang
> 
>> -----Original Message-----
>> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
>> Of Yuhang Hu via R-sig-meta-analysis
>> Sent: Thursday, November 2, 2023 05:42
>> To: R meta <r-sig-meta-analysis using r-project.org>
>> Cc: Yuhang Hu <yh342 using nau.edu>
>> Subject: [R-meta] Correcting Hedges' g vs. Log response ratio in nested studies
>> 
>> Hello All,
>> 
>> I know that when correcting Hedges' g (i.e., bias-corrected SMD, aka "g")
>> in nested studies, we have to **BOTH** adjust our initial "g" and its
>> sampling variance "vi_g"
>> (https://ies.ed.gov/ncee/wwc/Docs/referenceresources/WWC-41-Supplement-
>> 508_09212020.pdf).
>> 
>> But when correcting Log Response Ratios (LRR) in nested studies, we have to
>> **ONLY** adjust its initial sampling variance "vi_LRR" but not "LRR" itself
>> (https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-October/003486.html).
>> 
>> I wonder why the two methods of correction differ for Hedge's g and LRR?
>> 
>> Thanks,
>> Yuhang
> 
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