I am currently preparing to conduct a meta-analysis that aims to incorporate correlations from various studies. I have observed that different studies employ different types of correlations, such as Pearson's correlation coefficient, Spearman's correlation coefficient, Heterotrait-Monotrait ratio of correlations, correlations of latent variables, and so on so forth. I am seeking guidance on whether it is appropriate to include all of these correlation types in my meta-analysis or if I should focus on a specific type. Any insights would be greatly appreciated.
Meta-analytic data analysis requires that effect sizes are comparable. Different correlations are usually not equivalent. Thus, it is necessary to define a target effect size (e.g., Pearson correlation) and ensure that all effect sizes are available as this type of effect size in the meta-analytic data set.
Theoretically, it is possible to transform effect sizes into other effect sizes (e.g., Spearman correlation into Pearson correlation), but it can bias the results: https://onlinelibrary.wiley.com/doi/full/10.1002/jrsm.1560
Therefore, some researchers only include one type of effect size (e.g., Pearson correlation). If other effect sizes are reported in the primary studies, then one could ask the authors to provide the desired effect size (e.g., Pearson correlation) or data set so that one can estimate the relevant effect size.
I think it is very difficult to answer to this question because it depends on what is your question of interest and whether a specific correlation indicator is more suitable than the other.
The different correlation parameters you present have different meaning and calculation.
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