Category:Definitions/Kendall's Rank Correlation Coefficient

This category contains definitions related to Kendall's Rank Correlation Coefficient.
Related results can be found in Category:Kendall's Rank Correlation Coefficient.

Kendall's rank correlation coefficient is a test for consistency of $2$ sets of rankings $\sequence a_n$ and $\sequence b_n$ on a set $S$ of $n$ objects.

The set $R$ of ordered pairs $\tuple {a_i, b_i}$ is assembled:

$R = \set {\tuple {a_i, b_i}: i \in \set {1, 2, \ldots, n} }$

and ordered according to $\sequence a$.

The number $Q$ of elements of $S$ out of ranking order from $\sequence b$ is counted.

Kendall's rank correlation coefficient is then formed:

$K = 1 - \dfrac {4 Q} {n \paren {n + 1} }$

which takes values between $-1$ (complete disagreement) and $+1$ (complete agreement).

Complete disagreement happens when $\sequence a_n$ is in reverse order to $\sequence b_n$.