Calculator
Example Data Table
| Observation | X | Y |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 2 | 1 |
| 3 | 2 | 2 |
| 4 | 3 | 3 |
| 5 | 4 | 4 |
| 6 | 4 | 5 |
| 7 | 5 | 4 |
| 8 | 6 | 6 |
Formula Used
Tau-a = (C - D) / n0
Tau-b = (C - D) / √[(n0 - n1)(n0 - n2)]
Tau-c = 2m(C - D) / [n²(m - 1)]
Here, C is the count of concordant pairs and D is the count of discordant pairs.
n0 = n(n - 1) / 2 is the total number of pair comparisons.
n1 is the number of tied pairs in X. n2 is the number of tied pairs in Y.
m is the smaller number of distinct categories across X and Y.
The z test shown here uses an asymptotic variance approximation for the S statistic, with optional continuity correction.
How to Use This Calculator
- Enter your paired observations in the text area or upload a CSV file.
- Select the tau variant that fits your data. Tau-b is usually best when ties exist.
- Choose alpha and decimal settings.
- Enable continuity correction if you want the adjusted z statistic.
- Click the calculation button.
- Review the result box above the form for tau, p value, ties, and interpretation.
- Use the CSV buttons to export summaries or cleaned pairs.
- Use the PDF button to download a compact result report.
FAQs
1) What does Kendall tau measure?
Kendall tau measures the strength and direction of ranked association between two variables. It checks how often paired observations agree or disagree in ordering.
2) When should I use tau-b?
Use tau-b when tied values are present in either variable. It adjusts the denominator for ties, making it the most common choice for practical ranked data.
3) What is the difference between tau-a and tau-c?
Tau-a ignores tie adjustment. Tau-c is often used with rectangular tables or ordinal categories. Tau-b usually gives the most balanced result for general tied samples.
4) Can I paste data with headers?
Yes. A simple header row is accepted. The parser skips nonnumeric header text and then reads the first two numeric columns or values it finds.
5) What does a negative tau mean?
A negative tau means higher values of one variable tend to pair with lower values of the other. That indicates an inverse ranked relationship.
6) Is the p value exact?
No. This tool reports an asymptotic p value based on the z approximation. It is very useful for moderate and larger samples.
7) Why are ties reported separately?
Ties affect Kendall calculations and interpretation. Reporting ties in X, Y, and both variables helps explain why tau-a, tau-b, and tau-c can differ.
8) What file format should my CSV use?
A standard CSV with two numeric columns works well. Delimiters such as commas, tabs, semicolons, and pipes are supported by the parser.