Robust Correlation (Spearman, Kendall, and Biweight)
Also known as: Spearman correlation, Kendall tau, biweight midcorrelation, rank correlation, Robust Korelasyon (Spearman & Kendall & Biweight)
Robust Correlation is a family of association measures that resist outliers, covering Spearman's rank correlation, Kendall's tau, and the biweight midcorrelation. Drawing on the robust-statistics tradition described by Wilcox (2012) and Shevlyakov & Oja (2016), it measures how strongly two variables move together without being distorted by a few extreme points.
Key highlights
- Resistant to outliers and heavy-tailed distributions, so a few extreme points do not dominate the result.
- Does not require the data to be normally distributed and works for continuous or ordinal variables.
- Spearman and Kendall capture any monotone relationship, not only strictly linear ones.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use robust correlation when you want the strength of association between two continuous or ordinal variables but suspect outliers, heavy tails, or a relationship that is monotone rather than strictly linear. It is well suited to data that are not normally distributed, and a sample of at least about 20 observations is recommended. Spearman assumes the relationship is monotone, and Kendall works best when there are few tied values. When outliers are extreme, the biweight midcorrelation is the safest choice within the family.
Strengths & limitations
- Resistant to outliers and heavy-tailed distributions, so a few extreme points do not dominate the result.
- Does not require the data to be normally distributed and works for continuous or ordinal variables.
- Spearman and Kendall capture any monotone relationship, not only strictly linear ones.
- With very small samples (n < 10) the coefficients become unreliable; a permutation-based test is preferable.
- When the outlier ratio is very high (above about 25%) even Spearman and Kendall can be affected, and only the biweight midcorrelation may survive.
- Rank-based measures describe monotone association, not the size of a linear effect, so they are not a drop-in replacement for a regression slope.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What is the difference between Spearman and Kendall?
Both are rank-based, but Spearman correlates the ranks of the values, while Kendall's tau counts concordant minus discordant pairs. Kendall tends to be more interpretable as a probability of agreement and is more stable with small samples, though it is more affected by many tied values.
When should I use the biweight midcorrelation instead of Spearman or Kendall?
When the proportion of outliers is very high — above roughly a quarter of the data — even rank correlations can be distorted. The biweight midcorrelation down-weights points far from the median and remains stable in that situation, making it the most resistant choice in the family.
How is robust correlation different from Pearson correlation?
Pearson's coefficient measures linear association and a single extreme value can pull it far from the true pattern. Robust correlations use ranks or down-weighting so that outliers and non-normal, heavy-tailed data have far less influence, and they capture monotone rather than strictly linear association.
What sample size do I need?
A sample of at least about 20 observations is recommended. Below roughly 10 observations the coefficients become unreliable and a permutation-based test of association is preferable.
Sources
- 1.Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing. Academic Press.ISBN 978-0123869838
- 2.Shevlyakov, G. & Oja, H. (2016). Robust Correlation: Theory and Applications. Wiley.ISBN 978-1118493458
You have read it. What now?
Cite this page
ScholarGate. (2026, June 1). Robust Correlation. ScholarGate. https://scholargate.app/statistics/robust-correlation