info prev up next book cdrom email home

Fisher's z'-Transformation

Let $r$ be the Correlation Coefficient. Then defining

\begin{displaymath}
z'\equiv\tanh^{-1} r
\end{displaymath} (1)


\begin{displaymath}
\zeta\equiv \tanh^{-1}\rho,
\end{displaymath} (2)

gives
$\displaystyle \sigma_{z'}$ $\textstyle =$ $\displaystyle (N-3)^{-1/2}$ (3)
$\displaystyle \mathop{\rm var}\nolimits (z')$ $\textstyle =$ $\displaystyle {1\over n}+{4-\rho^2\over 2n^2}+\ldots$ (4)
$\displaystyle \gamma_1$ $\textstyle =$ $\displaystyle {\rho\left\vert{\rho^2-{\textstyle{9\over 16}}}\right\vert\over n^{3/2}}$ (5)
$\displaystyle \gamma_2$ $\textstyle =$ $\displaystyle {32-3\rho^4\over 16N},$ (6)

where $n\equiv N-1$.

See also Correlation Coefficient




© 1996-9 Eric W. Weisstein
1999-05-26