When is the Pearson correlation coefficient most appropriately used?

The Pearson correlation coefficient is most appropriately used when both variables being analyzed are normally distributed, making it a suitable measure for linear relationships between continuous variables. This statistical tool assumes that the data follows a normal distribution, which allows it to accurately reflect the strength and direction of the linear relationship. When both variables meet the normality assumption, the Pearson coefficient can provide valid and reliable insights into the correlation.

Using the Pearson correlation with normally distributed data ensures that the underlying mathematical properties of the correlation coefficient hold true, particularly regarding the interpretation of its values. It helps in validating hypothesis testing related to correlation, as the properties of normally distributed variables contribute to the robustness of the results derived from such analyses.

In contrast, using the Pearson correlation coefficient when the data is not normally distributed may lead to distortions in the analysis, as the correlation could either underestimate or overestimate the true relationship between the variables. Therefore, establishing normality in both variables is crucial for the appropriateness of the Pearson correlation coefficient.