Kendall's Tau Correlation Calculator
Rank correlation with Kendall’s tau-b — concordant and discordant pairs, tie handling, z-score and p-value for two paired lists.
How it works
τ_b = (C − D) ÷ √[(n₀ − T_x)(n₀ − T_y)], n₀ = n(n−1)/2; z = (C − D) ÷ √[n(n−1)(2n+5)/18]
Kendall's tau looks at every pair of observations and counts whether the two variables move in the same direction (concordant) or opposite directions (discordant). It is a probability-scale statistic — τ = 0.4 means concordant pairs outnumber discordant by 40 points — which makes it easier to interpret than Spearman's rho, and it is more robust with small samples and many ties. Tau-b corrects the denominator for tied pairs.
Worked example
Ten paired ranks: 26 concordant, 14 discordant, one tie on each variable — τ_b = 0.28, z = 1.07, p = 0.28.
Frequently asked questions
Kendall or Spearman?
They agree on direction and significance; tau is usually smaller in magnitude and has a cleaner interpretation. Spearman is more common in older literature.
Is the p-value exact?
It uses the normal approximation, adequate from about 10 pairs; for fewer pairs exact tables are preferable.
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