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I am using the package Metafor in R to do a meta-analysis, my models are derived from lmer (lme4). I am using the package -> EMAtools -> lme.dscore to retrieve the Cohen's d values which will be used in the meta-analysis.

What I am really stuck on is the variance for Cohen's d.

Last time we did this, we did the standard error to the power to 2 (SE^2) and that was sufficient to be considered the variance, however I am finding it difficult to find a citation as to how this would be considered correct.

Lowpar
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The standard approach to meta-analysis is called the inverse-variance weighted method. The practical effect is that you are giving greater weight to the more precise effect sizes. The standard error is a direct measure of a statistics precision and the standard error is a type of standard deviation. Hence, if you square a standard error it becomes a variance. The metafor package is asking as inputs the vector of effect sizes and associated variances. For Cohen's $d$, the variance is: $$ v_d = \frac{n_1 + n_2}{n_1 n_2} + \frac{d^2}{2(n_1+n_2)} $$ where $n_1$ and $n_2$ are the sample sizes for the two groups and $d$ is the calculated Cohen's $d$. The standard error for Cohen's $d$ is simply the square-root of the above. Any text on how to do meta-analysis will have this information.

dbwilson
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