Kendall's tau statistics: The measures of the correlation between the two sets of rankings. Kendall's tau itself (τ) is the rank correlation coefficient based on number of inversions in one ranking as compared with another, that is on S given by

here P is the number of concordant pairs of the observations, which means pairs of observations such that their rankings on the two variables are in same direction, and Q is the number of discordant pairs for which rankings on the two variables are in reverse direction.

The coefficient τ is calculated as follows

 
The number of other versions of τ have been developed which are appropriate for measuring the association in an r×c contingency table with row and column variables both having ordered categories. (Tau itself is not suitable since it supposes no tied observations.) One instance is the coefficient, τ C given by the following formula

 

where m min r; c.