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

Fabian Schellhaas f@bi@n@@chellh@@@ @ending from y@le@edu
Sat Nov 3 21:22:22 CET 2018

```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

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Fabian M. H. Schellhaas | Ph.D. Candidate | Department of Psychology | Yale
University

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