More About Significance of the Correlation Coefficient

The sample correlation \(r\) is an statistics that estimates the population correlation, \(\rho\). On typical statistical test consists of assessing whether or not the correlation coefficient is significantly different from zero.

There are least two methods to assess the significance of the sample correlation coefficient: One of them is based on the critical correlation. Such approach is based upon on the idea that if the sample correlation \(r\)is large enough, then the population correlation \(\rho\) is different from zero.

How big must the sample correlation \(r\) be in order to be entitled to claim that the population correlation \(\rho\) is different from zero? That is where we use the critical correlation \(r_c\).

The value of \(r_c\) is used to assess the significance of the sample correlation coefficient \(r\). These critical correlation values are usually found in specific correlation tables.