How to test correlation coefficients can look like a daunting process. But once you have figured out the correlation coefficient it’s an easy process that only takes a couple of steps. If you can read a table–you can test for correlation coefficient.
Sample problem: test the significance of the correlation coefficient r = 0.565 (How to calculate a correlation coefficient) using the critical values for PPMC table. Test at α = 0.01 for a sample size of 9.
Step 1: Subtract two from the sample size to get df, degrees of freedom.
Step 2: Look the values up in the PPMC Table. With df = 7 and α = 0.01, the table value is = 0.798
r = 0.565 does not fall into the “reject” region (above 0.798), so there isn’t enough evidence to state a strong linear relationship exists in the data.