How do statisticians choose a measure of association for two variables?

Statisticians choose a measure of association based primarily on the characteristics and measurement scales of the variables involved. These scales are generally categorized as interval/ratio (continuous), ordinal/rank (integer), or nominal/categorical (qualitative).1

Common selection criteria include:

• Interval/Ratio Data: When both variables are measured on a continuous scale, Pearson’s correlation coefficient is typically used to quantify the strength of their linear relationship.1
• Ordinal/Rank Data: For variables measured on an ordinal or ranked scale, statisticians often use the Spearman rank-order correlation coefficient or Kendall tau to measure monotonic associations.1
• Categorical Data: The chi-square test is a standard method for assessing the significance of an association between two categorical variables. In fields like epidemiology, researchers may also use relative risk or odds ratio to quantify associations.1
• Mixed Data Types: Specialized methods, such as the point-biserial correlation coefficient, are applied when variables have differing measurement scales, such as one interval variable and one dichotomous variable.1

It is essential to note that these measures quantify association rather than establishing cause-and-effect, and analysts must exercise careful judgment when interpreting results.213