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arXiv · 2208.05070

Fisher transformation via Edgeworth expansion

Jan Vrbik
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Abstract

We show how to calculate individual terms of the Edgeworth series to approximate the distribution of the Pearson correlation coefficient with the help of a simple Mathematica program. We also demonstrate how to eliminate the corresponding skewness, thus making the approximation substantially more accurate. This leads, in a rather natural way, to deriving a superior (in terms of its accuracy) version of Fisher's z transformation. The code can be easily modified to deal with any sample statistics defined as a function of several sample means, based on a random independent sample from a multivariate distribution.

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Jan Vrbik. 2022-08-09. Fisher transformation via Edgeworth expansion. https://arxiv.org/abs/2208.05070

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