Kendall's Tau Correlation Calculator
This Kendall's Tau calculator computes both Tau-a and Tau-b coefficients, showing the number of concordant and discordant pairs, and provides significance testing.
Further Information
Kendall's Tau is a non-parametric measure of the strength and direction of association between two ranked variables. Like Spearman's rho, it is useful when data violate the assumptions of Pearson's correlation.
Requirements
- Two variables measured at least at the ordinal scale
- Monotonic relationship between variables
- No assumption of normality required
- At least 3 pairs of observations
Tau-a vs Tau-b
Tau-a (simple formula):
Tau-a = (C - D) / [n(n-1)/2]
Tau-b (corrects for ties):
Tau-b = (C - D) / sqrt[(n0-n1)(n0-n2)]
Where C = concordant pairs, D = discordant pairs, n0 = total pairs, n1 = pairs tied on X, n2 = pairs tied on Y.
Concordant and Discordant Pairs
- Concordant: Both variables change in the same direction
- Discordant: Variables change in opposite directions
- Tied: One or both variables have the same value
When to Use Kendall's Tau vs Spearman's Rho
Prefer Kendall's Tau when:
- Sample size is small
- There are many tied ranks
- You want a more robust measure
- Interpretation in terms of probability is preferred
Interpretation
- Tau = +1: Perfect agreement (all pairs concordant)
- Tau = 0: No association
- Tau = -1: Perfect disagreement (all pairs discordant)
Note: Kendall's Tau values are typically lower than Spearman's rho for the same data.
