Fisher Z Transformation Calculator

Pearson product moment correlation coefficient is also referred as Pearson's r or bivariate correlation. It is a measure of linear correlation between two variables x and y and its represented with the symbol 'r'. Pearson's r is not normally distributed, Fisher Z Transformation calculator is used to transform the sampling distribution into normally distributed variable z'. Convert r to fisher z' to find the Pearson product correlation coefficient and the standard error.

Convert r to Fisher z'

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Formula:

Zr = ( 1 / 2 ) [ ln ( 1 + r ) - ln ( 1 - r ) ] SEzr = ( 1 / √( n - 3 ) ) Where, Zr = Z Score SEzr = Standard Error r = Correlation Coefficient n = Size

Example:

Find the Z score and error of a sampling function if the correlation coefficient is 0.5 and the size is 5?

Solution:

Zr = ( 1 / 2 ) [ ln ( 1 + 0.5 ) - ln ( 1 - 0.5 ) ]
= 0.5493
SE0.5493 = ( 1 / sqrt ( 5 - 3 ) )
= 0.7071

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