I have two questions with respect to comparing two correlation coefficients.
Cohen (1977) suggested to use Cohen's q to compare two Pearson's correlation coefficients by first transforming r with Fisher's zr transformation into z values.
Cohen's q = z1 – z2.
The estimated variance for Cohen's q is calculated as follows (see here): 1/(N1-3)+1/(N2-3)
Question 1:
I would like to calculate the 95% CI for Cohen's q but am unsure of how to do this. Could anyone help me with this please?
Question 2:
Is it okay to use the same procedure with Spearman's correlation coefficients (i.e. Fisher's zr transformation and then calculate the difference)?
Update:
I have just seen that the R package cocor includes Zou's (2007) confidence interval of the difference between two correlation coefficients. Obviously, this might be helpful as some sort of workaround. If the CI does not include 0, the difference is significant, and at the same time it gives an estimate of the CI of this difference. Cocor can also be used to test whether two correlation coefficients are significantly different from each other based on Fisher's zr transformation. More information can be found here.
However I would still be highly interested in any suggestions/answers concerning the two questions above.
Best Answer
I think I have found out how to calculate the 95% CI for Cohen's q. The approach is based on the fact that Cohen's q is a z-score because of the r-to-z transformation.
Cohen's $q=z_1-z_2$
$\mathrm{SE}(q)=\sqrt{\dfrac{1}{N_1-3}+\dfrac{1}{N_2-3}}$
For 95% CI: z = 1.96
Upper and lower 95% CI for Cohen's q is calculated as
$q\pm 1.96\cdot \mathrm{SE}(q)$