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’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)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)