Confirmed that you’re not supposed to square it, see this comment for a more detailed derivation. (My post might or might not have been the indirect source for that mistake. Oops. In my defense, yes I squared it, but I also hedged, right from the start, that I was very unsure about the squaring.)
(If you had a correlation between a noisy measurement and a noiseless ground truth, then that would get squared. But the test-retest correlation between two noisy measurements does not get squared.)
Confirmed that you’re not supposed to square it, see this comment for a more detailed derivation. (My post might or might not have been the indirect source for that mistake. Oops. In my defense, yes I squared it, but I also hedged, right from the start, that I was very unsure about the squaring.)
(If you had a correlation between a noisy measurement and a noiseless ground truth, then that would get squared. But the test-retest correlation between two noisy measurements does not get squared.)