Z is calculated by applying an inverse hyperbolic tangent function to r. Conversely, r is calculated by applying a hyperbolic tangent function to Z.
Unlike similar tools which transform one value at a time, our tool applies Fisher Transformations to an entire set of values, saving users time and effort.
WARNING: Contrary to popular opinions, Fisher Transformations should not be applied arbitrarily to (x, y) paired data, but only when both (x, y) random variables are approximately normally distributed; i.e., both variables must describe bell-shaped curves (Garcia, 2016; 2017). If the variables are bivariate normal, the sampling distribution of Z is approximately normally distributed with mean as described by the r-to-Z transformation (Anderson, 2007).
Ignoring the requisite of bivariate normality can introduce non-trivial errors and induce researchers to draw misleading conclusions (Zimmerman, Zumbo, & Williams, 2003). This is particularly true when Fisher Transformations are used to find confidence intervals for r, or as workarounds for averaging correlation coefficients. Before applying Fisher Transformations, be sure that you understand