Standard Article

Rank Correlation

  1. Helena Chmura Kraemer

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15133

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Kraemer, H. C. 2005. Rank Correlation. Encyclopedia of Biostatistics. 6.

Author Information

  1. Stanford University, Stanford, CA, USA

Publication History

  1. Published Online: 15 JUL 2005


When observations on two variables are made on each of a number of units, the association between the variables is often measured by the Pearson product-moment correlation coefficient. This is inappropriate if the variables are ordinal or when their distributions are far from normal. Rank correlation coefficients are based on the ranks of the observations. Spearman's coefficient is obtained by using the ranks in the usual formula for the product-moment coefficient. Kendall's tau coefficient is expressed through comparisons between all pairs of units, noting, for each pair, whether the two variables order the units in the same or the opposite direction. Methods of inference are outlined.


  • product-moment;
  • Spearman;
  • Kendall;
  • tau;
  • tied ranks