Editing Fisher transformation (section)

{{short description|Statistical transformation}}
{{Redirect-distinguish|Fisher z-transformation|Fisher's z-distribution}}
[[Image:fisher transformation.svg|300px|right|thumb|A graph of the transformation (in orange). The untransformed sample correlation coefficient is plotted on the horizontal axis, and the transformed coefficient is plotted on the vertical axis. The identity function (gray) is also shown for comparison.]]

In [[statistics]], the '''Fisher transformation''' (or '''Fisher ''z''-transformation''') of a [[Pearson correlation coefficient]]  is its [[inverse hyperbolic tangent]] (artanh). 
When the sample correlation coefficient ''r'' is near 1 or -1, its distribution is highly [[Skewness|skewed]], which makes it difficult to estimate [[confidence intervals]] and apply [[tests of significance]] for the population correlation coefficient ρ.<ref>{{cite journal| last=Fisher | first= R. A. | year=1915 | title= Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population | journal=Biometrika | volume=10 | pages=507–521 | jstor=2331838| issue=4| doi=10.2307/2331838| hdl= 2440/15166 | hdl-access=free }}</ref><ref>{{cite journal|authorlink=Ronald Fisher | last=Fisher | first= R. A. | year=1921 | title=On the 'probable error' of a coefficient of correlation deduced from a small sample | journal=Metron | volume=1 | pages=3–32|url=http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15169/1/14.pdf}}</ref><ref>Rick Wicklin. Fisher's transformation of the correlation coefficient. September 20, 2017. https://blogs.sas.com/content/iml/2017/09/20/fishers-transformation-correlation.html. Accessed Feb 15,2022.</ref> 
The Fisher transformation solves this problem by yielding a variable whose distribution is approximately [[normally distributed]], with a variance that is stable over different values of ''r''.