Robust Kendall's Tau Rank Correlation
Also known as: robust tau, skipped Kendall's tau, Winsorized Kendall's tau, outlier-resistant rank correlation
Robust Kendall's tau estimates the monotone association between two variables using rank-based concordance counts, but augments the standard procedure with outlier detection or Winsorization so that a small number of extreme observations cannot distort the result. It is appropriate when data are ordinal or continuous and bivariate outliers are plausible.
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When to use it
Use robust Kendall's tau when you need to quantify the monotone relationship between two ordinal or continuous variables and suspect the data contain bivariate outliers or influential pairs. It is especially valuable with small to moderate samples where a single outlying pair can move the classical tau by a practically meaningful amount. Do not use it as a shortcut to avoid assumption checking when data are actually clean — standard Kendall's tau or Spearman rho is more powerful in outlier-free data. It is also less appropriate when ties are very frequent relative to sample size, as robust tie-breaking rules are implementation-dependent.
Strengths & limitations
- Resists the distorting influence of bivariate outliers that can heavily distort classical rank correlations.
- Makes no parametric distributional assumption; suitable for ordinal, skewed, or bounded data.
- Inference via bootstrap is valid even when the asymptotic normal approximation for classical tau is questionable.
- Interpretable on the same -1 to 1 scale as standard Kendall's tau, facilitating direct comparison.
- Detects monotone (not just linear) associations, making it more general than Pearson correlation.
- More computationally intensive than classical Kendall's tau, particularly when bootstrap inference is used.
- Multiple robust variants exist (skipped, Winsorized, MCD-based) and their results may differ; choice must be justified.
- Lower statistical power than standard Kendall's tau when the data are truly outlier-free.
- Handling of ties in the robust framework is not uniformly standardized across software implementations.
Frequently asked
How does robust Kendall's tau differ from standard Kendall's tau?
Standard Kendall's tau counts concordant and discordant pairs over all observations. Robust variants first screen or Winsorize bivariate outliers so those pairs do not dominate the concordance count. The result is a tau estimate that better represents the majority of the data.
Should I use the skipped or the Winsorized version?
The skipped (outlier-removal) version is conceptually cleaner and is recommended by Wilcox; it detects outliers via a projection method and removes them entirely. Winsorization replaces extremes with boundary values and retains all n observations. Both are defensible; report which you used and why.
Can I use robust Kendall's tau with ordinal data?
Yes. Like classical Kendall's tau, the robust version requires only that the data be at least ordinal, and ties are handled with the standard adjustment to the denominator. However, very coarse ordinal scales with many ties reduce the power of any tau-based statistic.
Do I still need to check assumptions?
Yes. Robust methods reduce sensitivity to outliers but they do not eliminate the need for thoughtful data examination. You should still inspect a scatter plot, verify that the outliers flagged are plausible errors or genuine extreme cases rather than meaningful data, and consider whether a monotone relationship is a sensible model.
Which software supports robust Kendall's tau?
Wilcox's WRS2 package in R provides the skipped tau (via the scor or ktaub functions). The robustcor and DescTools packages offer additional variants. SPSS and Stata do not natively implement robust tau; bootstrapped confidence intervals for classical tau are available in both.
Sources
- Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press. ISBN: 978-0123869838
- Croux, C., & Dehon, C. (2010). Influence functions of the Spearman and Kendall correlation measures. Statistical Methods & Applications, 19(4), 497–515. DOI: 10.1007/s10260-010-0142-z ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Kendall's Tau Rank Correlation. ScholarGate. https://scholargate.app/en/statistics/robust-kendalls-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.
- Kendall's tauStatistics↔ compare
- Robust Mann-Whitney U testStatistics↔ compare
- Robust Pearson correlationStatistics↔ compare
- Robust Spearman CorrelationStatistics↔ compare
- Spearman CorrelationStatistics↔ compare