Which statistic is a parametric measure of the strength and direction of the linear relationship between two interval-level variables?

• A. Pearson's r
• B. Spearman's rho
• C. Kendall's tau
• D. Regression coefficient

Answer: (A)

Tracking how two interval-level variables move together in a straight line is best captured by Pearson's correlation coefficient. It’s a parametric statistic, meaning it uses the actual values and relies on assumptions about the data (continuous interval/ratio scales, a linear relationship, and roughly normal distribution). The result ranges from -1 to 1, where the sign shows the direction of the relationship and the magnitude indicates how strong that linear association is. A value near 0 suggests little linear relationship, while values near ±1 indicate a strong linear link.

Nonparametric alternatives like Spearman's rho and Kendall's tau use ranks and assess monotonic relationships rather than strictly linear ones, and they don’t require the same normality assumptions. The regression coefficient, on the other hand, describes the slope of a line in a regression model and depends on the units of measurement, so it’s not a standardized measure of the strength and direction of the linear relationship in the same way Pearson’s r is.