How is the statistical significance of Pearson’s correlation coefficient tested?

It is important to clarify that while Pearson’s correlation coefficient (r) quantifies the strength of a linear relationship, it does not inherently measure the statistical significance of that association.12

To determine the statistical significance of the observed correlation, researchers must conduct a separate analysis using a t-test. This test evaluates the difference between the observed correlation coefficient (r) and the expected correlation under the null hypothesis (which typically posits that there is no linear relationship, or r = 0).12

By performing this test, analysts can determine whether the observed association is statistically meaningful or likely the result of random variation within the sample data. It is essential to remember that even a significant correlation does not establish a cause-and-effect relationship; it only indicates the extent to which variables are associated.12