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:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“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)