Measuring Association for Scaled Data: Pearson’s Correlation Coefficient

Abstract

This chapter introduces the linear correlation coefficient, a widely used descriptive statistic that enables the researcher to describe the relationship between two interval- or ratio-level measures that can be either discrete or continuous in nature. Pearson’s r is a widely used linear correlation coefficient. It examines the placement of subjects on both variables relative to the mean and estimates how strongly the scores move together or in opposite directions relative to the mean. Pearson’s r is a standardized coefficient that varies between −1 (perfect negative relationship) and +1 (perfect positive relationship). Outliers have a strong impact on Pearson’s r. Spearman’s r is a nonparametric alternative to Person’s r and may provide a less misleading result when outliers are present. The t distribution may be used to test significance for Pearson’s and Spearman’s correlation coefficients.