I am aware of this question here, which mine was listed as a duplicate of, but it does not fully answer my question. It did however help me progress a little further so thanks, I couldn't find it before. The online calculator on the above answer also disagrees (though marginally) with the vassarstats.net calculator so I think that further backs up my reasoning for not using a black box.
So I'll re-explain my problem and hope that this gets opened to answers:
I have two Pearson correlation coefficients which I would like to compare. Each comes from 2 sets of 40 genetically identical lines and are correlations between male and female trait values.
I have managed to do $z$-transformations on my correlation coefficients in
R using the function
atanh() and replicated that with a home-made function
RtoZ <- function (r) 0.5*log((1+r)/(1-r)).
The problem is what to do next: how do I actually test, in
R, whether the two correlations are different?