Calculating weighted average of effect sizes per outcome

Hello everyone,

I’m a graduate student conducting meta-analysis of correlation studies for my dissertation. I’m interested to use Comprehensive Meta-Analysis software. In my research, I have two outcome variables : reading - accuracy, fluency and comprehension; math - accuracy, fluency and problem-solving). I would like to know how to calculate the weighted average of the correlations for each outcome per study. It would be a great help if someone could assist me.
Thanks in advance for consideration

You can find that in many texts on meta-analysis. There is still some question on how to derive the optimal set of weights.

For simplicity and consistency with the NHST (Null Hypothesis Significance Testing) seen in many areas of research, I recommend the following text:

Meta-Analysis: Calibrating and Combining Statistical Evidence (link)

They recommend using \sqrt{n}_i for each effect size, and \sqrt{ \Sigma{n}_1 ... n_i } for the denominator.

Alternatives include the inverse variance approach.

The authors of the text I referred to have many papers available on the current statistical challenges in meta-analysis that are available online.