Kendall's Coefficient of Concordance/Examples
Examples of Kendall's Coefficient of Concordance
Arbitrary Example 1
Consider the $3$ competitors $\text {Xavier}$, $\text {Yuri}$ and $\text {Zal}$, who are demonstrating their skills to the $4$ judges $\text {Araminta}$, $\text {Boecluvius}$, $\text {Coriolanius}$ and $\text {Derek}$.
The following table shows the ranking afforded the competitors by each judge, with the row summations per competitor:
| $\textit {Judge}$ | ||
| $\textit {Competitor}$ | $\begin{array} {r {{|}} cccc {{|}} c} & \text A & \text B & \text C & \text D & s_i \\ \hline \text X & 1 & 1 & 2 & 3 & 7 \\ \text Y & 3 & 2 & 3 & 1 & 9 \\ \text Z & 2 & 3 & 1 & 2 & 8 \\ \hline \end{array}$ |
Kendall's coefficient of concordance is $\dfrac 1 {16}$.
Arbitrary Example 2
Consider the $4$ competitors $\text {Wilhelmina}$, $\text {Xanthippe}$, $\text {Yondalla}$ and $\text {Zena}$, who are demonstrating their skills to the $4$ judges $\text {Ariadne}$, $\text {Boudicca}$, $\text {Constantine}$ and $\text {Donald}$.
The following table shows the ranking afforded the competitors by each judge, with the row summations per competitor:
| $\textit {Judge}$ | ||
| $\textit {Competitor}$ | $\begin{array} {r {{|}} cccc {{|}} c} & \text A & \text B & \text C & \text D & s_i \\ \hline \text X & 1 & 1 & 4 & 4 & 10 \\ \text Y & 2 & 2 & 3 & 3 & 10 \\ \text Z & 3 & 3 & 2 & 2 & 10 \\ \text Z & 4 & 4 & 1 & 1 & 10 \\ \hline \end{array}$ |