[R-meta] SMD from three-level nested design (raw data available)

James Pustejovsky jepu@to @ending from gm@il@com
Mon Nov 5 04:48:48 CET 2018

```Fabian,

Your calculations make sense to me for a two-level model (participants
nested within groups), but you've described a three-level model. What
happened to the other level (repeated measures, nested within
participants)? If you have a positive variance component estimate for it,
then I think it would make sense to include it in the denominator of the
effect size. If X is the estimated variance of the repeated measures nested
within participant, then take

d = 6.95 / sqrt(X + 143.64 + 217.17)

James

On Sat, Nov 3, 2018 at 3:22 PM Fabian Schellhaas <fabian.schellhaas using yale.edu>
wrote:

> Hi all,
>
> I have a question about computing a standardized mean difference (SMD) from
> a primary study with a three-level nested design. The study in question
> randomly assigned groups of participants to a treatment or control
> condition, and then measured individual participants' resource allocations.
> While some respondents made only one such decision, others made two. As
> such, the data in this study has three levels: resource allocation
> decisions, which are nested in participants, which in turn are nested in
> groups.
>
> I would like to compute an effect size that reflects the
> between-participant effect of treatment vs. control. I have the raw data,
> which the authors luckily made available. As such, I can easily fit a
> linear mixed model with a fixed effect for treatment vs. control, and a
> nested random effect to account for the three-level design. However, how do
> I extract a SMD from the fitted model that is comparable to SMDs from
> single-level designs?
>
> The estimate for the fixed effect is 6.95, with a SE of 6.27. The variance
> components of the random effects are 143.64 for participant nested in
> group, and 217.17 for group. Based on formula 18.17 in Hedges (2009), I
> believe I would compute *d* = 6.95/sqrt(143.64 + 217.17) = 0.366. However,
> I would like to confirm that this is indeed the correct approach before I
> proceed.
>
> Many thanks!
> Fabian
>
> ---
> Fabian M. H. Schellhaas | Ph.D. Candidate | Department of Psychology | Yale
> University
>
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>
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