Fisher Z Transformation Equation

Fisher Z Transformation is used to transform the sampling distribution of Pearson’s r (i.e. the correlation coefficient) into a normally distributed variable "Z". The "z" in Fisher Z stands for a z-score. It was developed by Fisher and so it is named as Fisher's Z transformation. Substitute the values of r and size in the Fisher z transformation equation for transforming the Pearson product-moment correlation coefficient into z' (Zr) and to find the standard error (SEzr).


Zr = ( 1 / 2 ) [ ln ( 1 + r ) - ln ( 1 - r ) ]
SEzr = ( 1 / √( n - 3 ) )


Zr = Z Score
SEzr = Standard Error
r = Correlation Coefficient
n = Size

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Fisher's z' is used to find confidence intervals for both r and differences between correlations. Use the above Fisher z transformation equation to test the significance of the difference between two correlation coefficients, r1 and r2 from independent samples.

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