Fisher's z'-Transformation

Let $r$ be the Correlation Coefficient. Then defining

$$z'\equiv\tanh^{-1} r$$ (1)

$$\zeta\equiv \tanh^{-1}\rho,$$ (2)

gives

$$\sigma_{z'} = (N-3)^{-1/2}$$ (3)

$$\mathop{\rm var}\nolimits (z') = {1\over n}+{4-\rho^2\over 2n^2}+\ldots$$ (4)

$$\gamma_1 = {\rho\left\vert{\rho^2-{\textstyle{9\over 16}}}\right\vert\over n^{3/2}}$$ (5)

$$\gamma_2 = {32-3\rho^4\over 16N},$$ (6)

where $n\equiv N-1$.

See also Correlation Coefficient