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:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“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)