I want to test the strength of a simple correlation in two groups and see whether there is a difference between these groups. Fisher's z-test is generally recommended, but I wonder whether there are other approaches towards this problem. Moderated regression might be an option by as far I understand the logic behind regression, it assumes that one is dependent and the other is independent; which I would not like to assume. Thank you!
Before addressing the issue of hypothesis testing, it is good to verify the correlation between the variables (if any).
It would also help to know the data matrix at your disposal, for a more accurate answer.
In any case, it is advisable to verify the possible correlation between the variables, using the most common indices (Spearman or Pearson, depending on the case).
Keep in mind that these are linear indices, not suitable for non-linear correlation.
In this case the variables must first be linearized, by "mathematical transformation".
This for starters.
To compare among correlations, see:
https://www.researchgate.net/post/How-can-I-compare-four-independent-correlation-coefficients-in-one-statistical-test
https://core.ecu.edu/wuenschk/W&W/Weaver&Wuensch_2013.pdf
To test if a correlation is moderated by another variable, one common approach is to conduct a moderation analysis, also known as an interaction effect analysis. This can be done in several steps:
It is important to keep in mind that the assumptions of linear regression must be met before conducting this analysis, including linearity, independence of errors, homoscedasticity, and normality. It is also important to check for confounding variables that may influence the results of the analysis.
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