Which Correlation Coefficient Is More Resistant to Outliers?

Spearman’s rank correlation coefficient, $r_s$, is generally more resistant to outliers than Pearson’s product-moment correlation coefficient, $r$. This is because Spearman’s coefficient uses the ranks of observations rather than their original numerical values.

Why Spearman’s Coefficient Is More Resistant

To calculate $r_s$, each value is replaced by its position in an ordered list. Therefore, an extremely large observation usually changes ranks by only a limited amount.

For example, suppose the largest value in a data set changes from $20$ to $2000$. It remains ranked first, so its effect on $r_s$ may be very small. However, Pearson’s $r$ uses the actual distances of points from the means, so the value $2000$ can substantially change the coefficient.

A monotonic relationship consistently increases or consistently decreases, but it does not have to follow a straight line. This means $r_s$ may be more appropriate when the scatter plot shows a curved but consistently increasing or decreasing pattern.

The common misconception is that Spearman’s coefficient is completely unaffected by outliers. It is only more resistant, not immune: an outlier can still change the ordering of several observations and therefore alter $r_s$.

IB Exam Technique

This is assessed in SL 4.10: Spearman’s rank correlation coefficient. If asked which coefficient is more appropriate when outliers are present, identify $r_s$ and justify the choice by stating that ranks reduce the influence of extreme numerical values. Also inspect the scatter plot: use Pearson’s $r$ for linear association and Spearman’s $r_s$ for monotonic association, rather than choosing solely because an outlier exists.