Pearson vs Spearman vs Kendall: Choosing a Correlation
"Correlation" is not a single number. The three workhorse coefficients — Pearson's r, Spearman's ρ, and Kendall's τ — measure different things and assume different things, so the right choice depends on your data.
Pearson measures linear association between interval variables. Spearman measures monotonic association using ranks. Kendall's tau also works on ranks but is based on concordant vs discordant pairs, and is preferred for small samples or many tied values.
Decision guide
| Coefficient | Measures | Best when |
|---|---|---|
| Pearson r | Linear | Interval data, roughly bivariate normal |
| Spearman ρ | Monotonic | Ordinal, or non-linear monotonic |
| Kendall τ | Concordance | Small n, many ties |
When Pearson misleads
Pearson is sensitive to outliers and only captures linear structure — a strong curved relationship can show a near-zero r. Always plot the scatter first.
Spearman vs Kendall
They usually agree on the conclusion; Kendall's τ has a cleaner probabilistic interpretation and is more robust with small samples.
Reporting
Report the coefficient, its CI, n, and the p-value — and state which coefficient you used and why.
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