Nonparametric alternative to Pearson's r.

• A. Kendall's tau
• B. Spearman rho
• C. Phi coefficient
• D. Gini index

Answer: (B)

When data don’t meet Pearson’s assumptions, look for a measure of association that doesn’t rely on normality or linearity. Spearman’s rho does this by using the ranks of the data rather than their raw values. It’s effectively the Pearson correlation calculated on the ranked values, so it captures monotonic relationships—where one variable tends to increase as the other does, though not necessarily in a straight line.

Because it relies on ranks, Spearman’s rho is robust to outliers and skewed distributions, and it doesn’t require the relationship to be linear. The value ranges from -1 to 1: a strong positive value means a strong monotonic increase, a strong negative value means a strong monotonic decrease, and values near zero indicate little monotonic association.

Kendall’s tau is another nonparametric measure of association, based on concordant and discordant pairs, and it serves a similar purpose but is computed a bit differently and can behave differently in small samples. The Phi coefficient is for associations between two dichotomous variables, not a general correlation measure, and the Gini index is a measure of inequality, not a correlation coefficient.