Definition
The transformation is defined by:
where "ln" is the natural logarithm function and "artanh" is the inverse hyperbolic function.
If (X, Y) has a bivariate normal distribution, and if the (Xi, Yi) pairs used to form r are independent for i = 1, ..., n, then z is approximately normally distributed with mean
and standard error
where N is the sample size.
This transformation, and its inverse,
can be used to construct a confidence interval for ρ.
Read more about this topic: Fisher Transformation
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