Kendall's tau is a family of correlation coefficients for ordinal data that measure the degree of correspondence between two rankings. Unlike Spearman's rho (which uses rank differences), Kendall's tau is based on counting concordant and discordant pairs, giving it clearer probabilistic interpretation.
CrossTabs.com calculates both variants:
Based on concordant (C) and discordant (D) pairs with tie corrections:
Where T₁ = pairs tied on X only, T₂ = pairs tied on Y only
Kendall's tau has a direct probabilistic interpretation: τ = P(concordant) − P(discordant). A tau of 0.30 means that a randomly chosen pair of observations is 30 percentage points more likely to be concordant than discordant. Cohen's guidelines: |τ| < 0.10 negligible, 0.10–0.30 small, 0.30–0.50 moderate, ≥ 0.50 large.
Use tau-b for square tables (same number of row and column categories). Use tau-c for rectangular tables. If unsure, report tau-b as it is the most commonly used variant.
Both measure ordinal association, but tau is based on concordant/discordant pairs while rho uses rank differences. Tau is generally preferred for contingency tables because it handles ties naturally and has a clearer interpretation. Numerically, |τ| is typically smaller than |ρ| for the same data.
Yes, but it is most commonly used for ordinal categorical data in contingency tables. For continuous data, Spearman's rho is more conventional, though tau is equally valid.