Statistical correlation coefficients tau [f] introduced by Kutzelnigg [Phys. Rev. 172, 49 (1968)] provide overall measures of the difference between the electron-pair density and the product of single-electron densities, where f=f(r) is a probe function. It is shown that the angular correlation coefficient tau [r], a particular case of tau [f] for f(r)=r, is simply expressible in terms of the generalized electron-pair moments ((a,b)) with two real-valued parameters a and b. Especially, the relation for a=b=1 means that tau [r] is nothing but the difference between the center-of-mass motion and relative motion contributions in the second electron-pair moments. Conversely, the electron-pair moments ((a,b)) are obtained from the single-electron moment < Sigma (i)r(i)(2)> and the correlation coefficient tau [r]. The same is also true in momentum space.