Track 9 · Correlation and Regression · Lesson 2 of 15
Rank correlation
Calculate and interpret Spearman's and Kendall's rank correlations, and choose between them and Pearson's r for monotone, curved or outlier-prone data.
Race organisers want to know whether runners who train more finish faster. The relationship is clearly downhill but curved — the first extra kilometres help much more than the fiftieth — and some training figures are rough self-reports. Rank correlations ask a simpler, more robust question: do higher values of one variable go with higher (or lower) values of the other?
Pearson's measures linear association. Many relationships are monotone instead: as increases, keeps moving in one direction, but not at a constant rate. A rank correlation replaces each value by its rank (1 for the smallest, 2 for the next…) and measures how consistently the two orderings agree. Because only the order matters, rank correlations ignore curvature and are barely moved by one extreme value.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute Spearman's correlation from ranks and Kendall's tau from concordant and discordant pairs
- Explain the difference between linear and monotone association
- Choose between Pearson and a rank correlation for curved, ordinal or outlier-prone data
- Interpret tau on its own scale rather than comparing it with r