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Fisher's z^'-Transformation

Let r be the correlation coefficient. Then defining

z^'=tanh^(-1)r
(1)
zeta=tanh^(-1)rho,
(2)

gives

sigma_(z^')=(N-3)^(-1/2)
(3)
var(z^')=1/n+(4-rho^2)/(2n^2)+...
(4)
gamma_1=(rho|rho^2-9/(16)|)/(n^(3/2))
(5)
gamma_2=(32-3rho^4)/(16N),
(6)

where n=N-1.

See also

Correlation Coefficient

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References

David, F. N. "The Moments of the z and F Distributions." Biometrika 36, 394-403, 1949.

Cite this as:

Weisstein, Eric W. "Fisher's z^'-Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Fishersz-Transformation.html

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