# 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.

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.

Code to add this calci to your website

#### Formula:

Z_{r} = ( 1 / 2 ) [ ln ( 1 + r ) - ln ( 1 - r ) ]
SE_{zr} = ( 1 / √( n - 3 ) )
**Where,**
Z_{r} = Z Score
SE_{zr} = 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:

Z_{r} = ( 1 / 2 ) [ ln ( 1 + 0.5 ) - ln ( 1 - 0.5 ) ]

= 0.5493

SE_{0.5493} = ( 1 / sqrt ( 5 - 3 ) )

= 0.7071