Question

Two judges in a baby competition rank the 12 entires as follows :

$\begin{array}{ccccccccccccc}\text{Entries}& \text{A}& \text{B}& \text{C}& \text{D}& \text{E}& \text{F}& \text{G}& \text{H}& \text{I}& \text{J}& \text{K}& \text{L}\\ \text{X- Judge}& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11& 12\\ \text{Y-Judge}& 12& 9& 6& 10& 3& 5& 4& 7& 8& 2& 11& 1\end{array}$
What degree of agreement is there between the judges?

Answer 1

$\begin{array}{ccccc}\text{Entry}& \text{Rank by X}\left(R_1\right)& \text{Rank by Y}\left(R_2\right)& D=R_1-R_2& D^2\\ A& 1& 12& -11& 121\\ B& 2& 9& -7& 49\\ C& 3& 6& -3& 9\\ D& 4& 10& -6& 36\\ E& 5& 3& +2& 4\\ F& 6& 5& +1& 1\\ G& 7& 4& +3& 9\\ H& 8& 7& +1& 1\\ I& 9& 8& +1& 1\\ J& 10& 2& +8& 64\\ K& 11& 11& 0& 0\\ L& 12& 1& +11& 121\\ & N=12& & \sum D=0& \sum D^2=416\end{array}$

$R=1-\frac{6\sum D^2}{N^3-N}=1-\frac{6\times 416}{{12}^3-12}=1-\frac{2496}{1716}=-0.4545$

It indicates that the judges X and Y have fairly strong divergent likes and dislikes so far as ranking of the babies is concerned.