# How can I calculate an effect size (cohen's d) from a linear random effects model (beta)

I am trying to figure out how to calculate a Cohen's d statistic for a linear random effects model. I did not do the analysis myself, I have read it in a journal article so I'm left to figure it out with the information that the authors put in the article text. It concerns a linear random effects analysis of a certain treatment on IQ scores and the total sample size and sample sizes of the treatment and control groups are known.

• Total N=27
• Treatment 14
• Control 13.

Known variables for the linear random affects analysis are:

• $\beta$=0.82
• SE of $\beta$=0.6
• p-value = 0.19.

Since I am working a a meta-analysis with all effect sizes as Cohen's d statistics (standard mean difference) I need to convert this beta to a cohen's d.

• This paper referenced a way to calculated Cohen's d using t statistics in MLM models. Arnow, B. A., Steidtmann, D., Blasey, C., Manber, R., Constantino, M. J., Klein, D. N., … Kocsis, J. H. (2013). The relationship between the therapeutic alliance and treatment outcome in two distinct psychotherapies for chronic depression. Journal of Consulting and Clinical Psychology, 81(4), 627–638. doi:10.1037/a0031530 – unicorndl Jan 26 '16 at 18:41
• Talking about $d = \frac{\mu_1 - \mu_2}{\sigma}$ doesn't seem well-defined in a random effect model, given that the model is partitioning the variance into multiple compartments. – Andrew M Feb 25 '16 at 20:47
• You generally need the variance components SD and residual SD to compute cohen's d. You would divide the coefficient by the sum of the variance components and residuals. Also, I would not really call it cohens d, instead delta subscript t, where the stands for total of variation. – D_Williams Dec 9 '16 at 2:14