Suppose I need an estimate of effect size for a power analysis. I read the relevant literature and calculated Cohen's $d$ from some number (3) of studies. If the Cohen's $d$s are, for example, $d_{1} = 0.2$, $d_{2} = 0.4$, and $d_{3} = 0.3$, is the best estimate of effect size now $\frac{0.2 + 0.4 + 0.3}{3} = 0.3$? How would I go about combining the data from several different studies?
1 Answer
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+1 to @Chris C's comment on reading up on meta analysis.
One thing to keep in mind for your particular question is each study's sample size. Suppose this is $n_1=20$, $n_2=50$ and $n_3=30$, then you should really calculate a weighted average:
$$\frac{n_1d_1+n_2d_2+n_3d_3}{n_1+n_2+n_3} = 0.33$$
This will have an impact if your studies are wildly different in sample size.
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2$\begingroup$ Just to expand a little, weighting by effect size is used because studies with a larger effect size (generally) have better power, and thus are more reliable. By giving them more "punch" in your model, you're getting more accurate and hopefully reproducible results. Not to suggest, @Stephan, that you are unaware; just wanted to put it here for OP. $\endgroup$– Chris CApr 10, 2015 at 13:13