"Fisher z-transformation" redirects here. Not to be confused with Fisher's z-distribution.
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 skewed, which makes it difficult to estimate confidence intervals and apply tests of significance for the population correlation coefficient ρ.[1][2][3]
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.
^Fisher, R. A. (1915). "Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population". Biometrika. 10 (4): 507–521. doi:10.2307/2331838. hdl:2440/15166. JSTOR 2331838.
^Fisher, R. A. (1921). "On the 'probable error' of a coefficient of correlation deduced from a small sample" (PDF). Metron. 1: 3–32.
^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.
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