About Kendall Tau Correlation Calculator
This Kendall tau calculator compares every pair of observations. A pair is concordant when both variables move the same way and discordant when they move opposite ways. It opens on two judges ranking eight contestants. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Kendall τ-b is the surplus of concordant over discordant pairs, scaled so that ties in either variable are handled fairly. It reads as a difference of probabilities: τ of 0.7 means a randomly chosen pair is 70 percentage points more likely to agree than to disagree.
It suits small samples, many tied ranks and agreement between raters. Its values are usually smaller than Spearman ρ on the same data, which is normal and not a sign of weaker evidence.
How to use Kendall Tau Correlation Calculator
- Paste your data as two columns from a spreadsheet, or type one x, y pair per line. Use the "Two columns" tab if your x and y values are in separate lists.
- Pick the headline coefficient: Pearson r, Spearman ρ or Kendall τ-b. All three are always shown in the table.
- Choose a confidence level for the interval of r. 95% is the usual choice.
- Read the strength and direction sentence, the p-value and the confidence interval. A small p-value means the correlation is unlikely to be zero in the population.
- Check the scatter plot for curves, clusters or outliers, because one number can hide them.
- Open the step-by-step panel to see the means, the sums of squares, r, the t statistic and the Fisher z interval.
Features
- Pearson r with a t test for H0: ρ = 0 and a Fisher z confidence interval.
- Spearman rank correlation with tied values given their average rank.
- Kendall τ-b, corrected for ties, with a normal approximation for p.
- Paste from Excel or Google Sheets: tab, comma, semicolon and space separated pairs all work, and decimal commas are understood.
- Scatter plot with a least squares trend line, a values table for screen readers and a PNG download.
- Strength and direction in plain words, plus r² for Pearson.
- Worked Pearson steps in KaTeX that you can copy as LaTeX.
- Four bundled examples, including Anscombe set I and a data set with an outlier.
Kendall tau-b
Let C be the concordant pairs, D the discordant pairs, and n1 and n2 the number of tied pairs in x and in y.
tau-b = (C − D) / sqrt((n0 − n1)(n0 − n2))
n0 = n(n − 1) / 2Worked examples
Two judges ranking 8 contestants, four neighbouring swaps gives τ-b = 0.7143, Spearman ρ = 0.9048
24 pairs agree and 4 disagree out of 28.
Privacy: how it works
- Everything is calculated by code running in your browser tab. Your data is not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Always look at the scatter plot. A curve, two clusters or one outlier can make r misleading.
- If r is near zero but the plot shows a clear curve, the relationship is real but not linear.
- With many pairs, even a tiny r can be significant. Judge the size of r, not only the p-value.
- Do not include totals or averages of the same variable twice. Repeated measures break the independence that the p-value assumes.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your pairs are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your pairs are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is the difference between tau-a and tau-b?
Tau-a ignores ties. Tau-b corrects the denominator for tied values in either variable, which is why it is the version most software and this calculator report.
Why is tau smaller than Spearman rho?
They are on different scales. For the same data tau is typically about two thirds of rho, so compare each coefficient with its own guidelines.
When is Kendall better than Spearman?
With small samples or many ties, Kendall has a more accurate sampling distribution and a direct meaning as a probability difference.
More Correlation Coefficient Calculator pages
- Correlation Coefficient CalculatorPaste two columns or x, y pairs to get Pearson r, Spearman ρ and Kendall τ with a scatter plot and the working.
- Pearson Correlation CalculatorPaste x, y pairs to get Pearson r, r², a p-value and a confidence interval.
- Spearman Rank Correlation CalculatorPaste x, y pairs to get Spearman ρ, which resists outliers and measures any steady rise or fall.