Kendall Tau Rank Correlation
Kendall Tau Rank Correlation Coefficient · Also known as: Kendall's tau, Kendall tau-b, tau correlation, Kendall Tau Korelasyonu
Kendall Tau is a nonparametric rank correlation coefficient introduced by Maurice G. Kendall in 1938 to measure the strength and direction of a monotone association between two ordinal or continuous variables. It is particularly suited to small samples and datasets containing many tied ranks, where the Spearman coefficient can be less stable.
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When to use it
Use Kendall Tau when you want to assess the monotone relationship between two variables measured on at least an ordinal scale and you cannot assume normality. It is especially appropriate when the sample is small (as few as 10 observations) or when there are many tied values in the data. Both variables must be ordinal or continuous; the relationship is assumed to be monotone (consistently increasing or decreasing) rather than strictly linear. If the data are continuous, approximately normal, and you expect a linear relationship, Pearson correlation is more powerful. If there are few ties and the sample is reasonably large, Spearman correlation is a close alternative and easier to compute by hand.
Strengths & limitations
- Robust to outliers and violations of normality because it uses only rank information.
- Handles many tied ranks gracefully through the tau-b correction.
- Reliable in small samples where other correlation measures become unstable.
- The coefficient has a direct probability interpretation: tau equals the probability of concordance minus the probability of discordance.
- Less statistically powerful than Pearson correlation when normality holds and the relationship is linear.
- Computationally more demanding than Spearman for large datasets, though this is negligible with modern software.
- Only captures monotone associations; it will underestimate or miss non-monotone (e.g. U-shaped) relationships.
Frequently asked
What is the difference between tau-a and tau-b?
Tau-a uses the total number of pairs in the denominator without adjusting for ties. Tau-b corrects for ties in each variable separately, yielding a coefficient that can still reach ±1 when ties are present. Most software reports tau-b by default, and it is the appropriate form for most real datasets.
How does Kendall Tau compare to Spearman's rho?
Both are nonparametric rank correlations, but they weight pair relationships differently. Tau is generally smaller in magnitude than rho for the same data and has a cleaner probability interpretation. Tau is more robust in very small samples or when ties are frequent; rho is numerically simpler to compute and slightly more powerful in large, tie-free samples.
What sample size do I need?
A minimum of 10 observations is required for asymptotic p-values to be reasonable. With fewer than 10 observations, use exact permutation p-values. Kendall Tau is one of the few correlation measures specifically recommended for samples in the range of 10–30, where Pearson is unreliable and Spearman can be unstable.
What if my p-value is significant but tau is very small?
In large samples even a trivially small tau will produce a significant p-value. Always report the tau coefficient alongside the p-value so readers can judge practical significance. A tau of 0.05 may be statistically significant yet practically meaningless.
Sources
- Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1–2), 81–93. DOI: 10.1093/biomet/30.1-2.81 ↗
How to cite this page
ScholarGate. (2026, June 1). Kendall Tau Rank Correlation Coefficient. ScholarGate. https://scholargate.app/en/statistics/kendall-tau
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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- Spearman CorrelationStatistics↔ compare
- Wilcoxon signed-rank testStatistics↔ compare