[R-meta] Meta-analyzing studies that failed to account for their nested data

[James Pustejovsky]

Hi Tim,

One important issue here is that the sampling variance of the effect size
estimate calculated from such a study will be inaccurate---possibly even an
order of magnitude smaller than it should be. If you ignore this, the
consequence will be to make the effect size estimates appear far more
precise than they actually are.

To properly correct the sampling variance estimate, you would need to know
the intra-class correlation describing the proportion of the total
variation in the outcome that is at the cluster level (in this case, what
fraction of the total variance is between classes?). If this isn't
reported, then it may be possible to develop a reasonable estimate based on
external information. The Cochrane Handbook describes how to correct the
sampling variance based on an imputed intra-class correlation:
https://training.cochrane.org/handbook/current/chapter-23#section-23-1
Hedges (2007; https://doi.org/10.3102/1076998606298043) and (2011;
https://doi.org/10.3102/1076998610376617) provides slightly more elaborate
methods that can be used if you have more details about the study designs.
Hedges and Hedberg's Variance Almanac (http://stateva.ci.northwestern.edu/)
is a helpful source for developing estimates of ICCs for educational
outcomes.

James

On Thu, Sep 30, 2021 at 4:58 PM Timothy MacKenzie <fswfswt using gmail.com> wrote:

> Hello All,
>
> I've noticed almost all the studies I have selected for meta-analysis
> have ignored the nested structure of their data (subjects nested in
> classrooms) and have conducted only single-level analyses.
>
> I've extracted the condition-level summaries from those studies (i.e.,
> Means and SDs for C vs. T groups).
>
> But I'm wondering if I can/should make any adjustment to my
> meta-regression model to account for the nested structure of the data
> in those studies AND if not, whether such a situation poses a
> limitation to my meta-analysis?
>
> Thank you very much for your assistance,
> Tim M
>
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