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Kendall Tau Calculator

Calculate Kendall’s tau rank correlation from concordant and discordant pairs.

About Kendall Tau Calculator

Kendall’s tau counts how often pairs agree in ordering, giving it a direct probabilistic interpretation. It is more robust than Spearman for small samples and handles ties better. Tau values are systematically smaller than Spearman’s rho for the same data, so the two must not be compared against the same thresholds.

Formula

Kendall Tau

τ = (concordant − discordant) ÷ (n(n−1)/2)

concordant pair
Two observations ordered the same way on both variables

Worked example

With the default values below, Kendall Tau Calculator returns Kendall’s Tau of 0.530303. Change any input above and every figure here is recalculated in your browser.

Inputs used

Concordant pairsminimum 0
45
Discordant pairsminimum 0
10
Number of observationsminimum 3
12

Results

Kendall’s Tau
0.530303
Total Pairs
66
Z Statistic
2.40004
Strength of Association
Strong
Significance
Statistically significant

Step by step

  1. 1Values used
  2. 2Kendall Tau
  3. 3Kendall’s Tau= 0.530303
  4. 4Total Pairs= 66
  5. 5Z Statistic= 2.40004
  6. 6Strength of Association= Strong
  7. 7Significance= Statistically significant

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Kendall Tau calculated?

τ = (concordant − discordant) ÷ (n(n−1)/2) Kendall’s tau counts how often pairs agree in ordering, giving it a direct probabilistic interpretation. It is more robust than Spearman for small samples and handles ties better.

Why does Kendall Tau matter?

Tau values are systematically smaller than Spearman’s rho for the same data, so the two must not be compared against the same thresholds.

What values do I need to enter?

This calculator takes 3 inputs: Concordant pairs, Discordant pairs, Number of observations. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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