Kendall Tau-b Correlation Calculator
Calculate descriptive Kendall tau-b with separate concordant, discordant and tied-pair counts.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Compare every unordered pair and use the tau-b normalization that accounts for ties in each variable.
Tau-b=(P−Q)/sqrt[(P+Q+T)(P+Q+U)]
Worked example
Pairs (1,1), (2,3), (3,2), (4,4) have five concordant pairs and one discordant pair without ties, giving tau-b 2/3.
Assumptions and input details
2–200 paired finite observations. T and U count ties in only one variable; pairs tied in both are separate. A zero denominator is undefined. This page reports a descriptive coefficient and pair counts, not a p-value, confidence interval, causal relationship or missing-data imputation.
References: SciPy: Kendall tau-b definition and tie conventions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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