# International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

# Kendall’s Tau

Reference work entry
DOI: https://doi.org/10.1007/978-3-642-04898-2_324

Kendall’s Tau is a nonparametric measure of the degree of correlation. It was introduced by Maurice Kendall in 1938 (Kendall 1938).

Kendall’s Tau measures the strength of the relationship between two ordinal level variables. Together with Spearman’s rank correlation coefficient, they are two widely accepted measures of rank correlations and more popular rank correlation statistics.

It is required that the two variables, X and Y, are paired observations. Then, provided both variables are at least ordinal, it would be possible to calculate the correlation between them. In general, application of the product-moment correlation coefficient is limited by the requirement that the trend must be linear. A less restrictive measure of correlation is based on the probabilistic notion that the correlation between variables X and Y is strong if on average, there is a high probability that an increase in X will be accompanied by an increase in Y (or decrease in Y). Then the only limitation imposed...

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## References and Further Reading

1. Abdi H (2007) The Kendall rank correlation coefficient. In: Salkin NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand OaksGoogle Scholar
2. Burr EJ (1960) The distribution of Kendall’s score S for a pair of tied rankings. Biometrika 47:151–171
3. Daniel WW (1990) Applied nonparametric statistics, 2nd edn. PWS-KENT Publishing Company, BostonGoogle Scholar
4. Hollander M, Wolfe DA (1998) Nonparametric statistical methods, 2nd edn. Wiley, New YorkGoogle Scholar
5. Kendall M (1938) A new measure of rank correlation. Biometrika 30:81–89
6. Noether GE (1967) Elements of nonparametric statistics. Wiley, New York
7. Sillitto GP (1947) The distribution of Kendall’s coefficient of rank correlation in rankings containing ties. Biometrika 34:36–40

## Copyright information

© Springer-Verlag Berlin Heidelberg 2011

## Authors and Affiliations

1. 1.University of TiranaTiranaAlbania