Definition:Kendall's Rank Correlation Coefficient

Definition

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 $\sequence b_n$.

Also see

• Definition:Kendall's Coefficient of Concordance: used when more than $2$ sets of rankings need to be assessed

• Results about Kendall's rank correlation coefficient can be found here.

Source of Name

This entry was named for Maurice George Kendall.

Historical Note

Kendall's rank correlation coefficient was devised by Maurice George Kendall in $1938$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): correlation coefficient: 3.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correlation coefficient: 3.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rank correlation coefficient