The table contains critical values for two-tail tests. For one-tail tests, multiply α by 2.
If the absolute value of Kendall’s tau is greater than the critical value from the table, then reject the null hypothesis that there is no correlation.
See Kendall’s Tau for details.
Download Table
Click here to download the Excel workbook with the above table.
Reference
van Belle, G., Fisher, L., Heagerty, P. J., Lumley, T. (2004) Biostatistics: A methodology for the health sciences 2nd Ed. Wiley
http://faculty.washington.edu/heagerty/Books/Biostatistics/TABLES/Kendall.pdf
Is it the absolute value that should be greater?
Hi Michal,
Yes, your are correct. Thanks for catching this error. I have just corrected the webpage.
I appreciate your diligence in improving the quality of the Real Statistics website.
Charles
Hello! A colleague pointed me to this table, and i’m glad to have it as a validation against some others. However, to obtain critical values for one-sided tests, should we not divide alpha by 2 rather than multiply? (The same critical value, used to lop off only one side of the symmetric distribution, will result in only half as much being lost.) Thank you for the resource.
Cory,
To calculate the p-value for the two-sided test you halve the alpha value for the one-sided test. To get the critical value for the one-sided test you double the alpha value for the two-sided test.
Charles
How is this table caculAted
Larry,
I don’t know how the values in this table were calculated. Usually such values are calculated by Monte Carlo simulation.
Charles
No need for MC. It’s explained in the book by Kendall. For small n you can count the possibilities of the orderings. For random pairs then each ordering is equally possible. Then you can obtain a distribution of the taus under the null-hypothesis, i.e. all pairs are random. Its a bit cumbersome of a calculation. For large n (say > 30) the distribution becomes approximately normal and its variance is given by var(tau) = (4n+10)/9n(n+1).
Hello Christian,
Thank you very much for your comment.
1. I am not familiar with the abbreviation MC. Are you saying that the table is not needed?
2. Are you referencing “An Introduction To The Theory Of Statistics”? If so, where in the book is this explained? Is it different from the description at https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-tau-correlation-detailed/ ?
3. I believe that the normal approximation variance is (4n+10)/(9n(n-1)) with n-1 instead of n+1. Are you sure that it should be n+1?
Charles