what kinds of information, other than, the effect size are needed? Second, can correlational studies be mixed with experimental studies in doing a Meta-analysis?
In addition to an effect size for each study, you also need a variance for each study. Beware that this is not the same variance as calculated in traditional descriptive statistics (i.e., equal to SD2). The study variances are needed to calculate the weighting of the study effect sizes in the calculation of the overall effect size.
Yes, correlations can mathematically be combined with other types of effect sizes but the question become "Should you?". Correlations and other effect sizes answer different types of questions. It becomes the proverbial "apples and oranges" saying.
Dear Mohammad,
As Dr. Warren stated above, except for the effect size you have to extract its variance. If you deal with a large N of studies, in case of missing variance in single studies, it can be imputed using appropriate methods.
Regarding combing correlation coefficients with different effect sizes, first of all, it has to be reasonable from the theoretical point of view. You can run a sensitivity analysis to check to see whether the exclusion of studies providing correlation influences pooled estimates. For further details about converting and pooling different types of effect sizes please refer to Chapter 7 of "Introduction to Meta-analysis" by M. Borenstein: https://www.meta-analysis.com/downloads/Meta-analysis%20Converting%20among%20effect%20sizes.pdf
Best,
Jakub
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