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
Famous quotes containing the word definition:
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)