Category:Kendall's Rank Correlation Coefficient
This category contains results about Kendall's Rank Correlation Coefficient.
Definitions specific to this category can be found in Definitions/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 $\sequence b_n$.
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