Why we need to calculate the z-score of each variable while calculating Pearson's r

#1

I am currently studying about how to find a correlation between two variable while studying I came to know that the Pearson’s r is the value which tells about the strength and the direction of the correlation between two variable.

In the formula, I want to ask why we are needed to calculate the z-score of the variable we can also calculate standard deviation or variance for knowing direction and strength of correlation between two variable.

#2

hello @sid100158,

The formula for correlation is:

The ones in the brackets corresponds to the z-statistics for the variables.
As you can see this uses the standard deviation of the individual variables to compute the correlation coefficient.
If you use only sd it will give you the measure of dispersion for only one variable,to relate one to the other we need to measure their distributions in a combined way which is achieved by the 'r’

Hope this helps!!

#3

@sid100158 - We use z-score for the calculation of Pearson’s r because we want to standardize the value so that the value of Pearson’s r can lie between -1 to +1.

Hope this helps!

Regards,
Hinduja