Question

In a baby competition, two judges accorded following to 12 competitors. Find the coefficient of rank correlation.

Entry	A	B	C	D	E	F	G	H	I	J	K	L
jJudge X	1	2	3	4	5	6	7	8	9	10	11	12
Judge Y	12	9	6	10	3	5	4	7	8	2	11	1

Answer 1

Entry	Ranks by Judge X (RX)	Ranks by Judge Y (RY)	D = RX – RY	D2
A B C D E F G H I J K L	1 2 3 4 5 6 7 8 9 10 11 12	12 9 6 10 3 5 4 7 8 2 11 1	–11 –7 –3 –6 2 1 3 1 1 8 0 11	121 49 9 36 4 1 9 1 1 64 0 121
N = 12				${\sum }_{}{D}^2=416$

$$\begin{gathered} r_k=1-\frac{6{\sum }_{}{D}^2}{N^3-N} \\ \mathrm{or},r_k=1-\frac{6\times 416}{1728-12}=1-\frac{2496}{1716}=-0.455 \\ \mathrm{Hence},r_k=-0.455 \end{gathered}$$