Statistical Methods

9. Correlation and Regression

9.4.Testing the Significance of the correlation coefficient
Let r be the observed correlation coefficient in a sample of n pairs of observations from a bivariate normal population. To test the hypothesis H_o: = 0, i.e., population correlation coefficient is zero, the following test procedure is used:
(i) Hypothesis
H_o : =0 H₁: ≠ 0
(ii) Test statistic
Compute :

Which is distributed as t with (n-2) df.
(iii) Statistical decision
If the calculated value of t is greater than the table value of t with n-2 degrees of freedom at the desired level of significance, the correlation between the variables is significant.
However, it is to be noted that the significance of r is not an indication of the strength of relationship. It is simply a test to see whether is equal to zero or not. The degree of the relationship between two variables can be measured by the square of the correlation coefficient r (which is called the coefficient of determination). Unless r² very high, one variable should not be used to predict the other.