Bivariate Correlation

Bivariate correlation analytical methods are fundamental techniques used by educational researchers to quantify the degree of association between two variables measured on the interval or ratio scale. Imagine, for example, that you are interested in exploring the relationship between undergraduate entrance exam scores and final undergraduate grade point average. How could we quantify, interpret, and statistically evaluate this relationship, should one exist? While there exist many methods for addressing questions such as these, Pearson’s Product Moment Correlation Coefficient (or Pearson’s r) and Spearman’s rho are two widely used and common approaches (Conover, 1999; Cohen et al., 2022). Both techniques help researchers quantify the strength and direction of the association between two variables with the former being most optimum in exploring linear relationships between normally distributed interval or ratio variables and the latter being most optimum in exploring monotonic relationships between non-normal variables measured on at least an ordinal scale (Havlicek & Peterson, 1976; Conover, 1999, p. 314). This chapter will discuss these techniques at a foundational level, including understanding the assumptions underlying each technique, and then provide the reader with a step-by-step guide for implementing these techniques using R.