Fisher transformation

In statistics, hypotheses about the value of r, the correlation coefficient between variables x and y of the underlying population, can be tested using the Fisher transformation applied to r.

Definition of the Fisher transformation

Let N be the sample size. The transformation is defined by:

z = ½ log((1+r)/(1-r)

Here z is approximately normally distributed with mean r, and standard error

1/((N-3)^0.5).

This is a common way of testing whether a correlation coefficient is significantly different from 0, and hence ascribing a p-value.

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