Question

Two judges in a beautry competition rank the 12 entries as follows :

X	:	1	2	3	4	5	6	7	8	9	10	11	12
Y	:	12	9	6	10	3	5	4	7	8	2	11	1

Calculate rank coefficient of correlation.

Answer 1

X (R1)	Y (R2)	(R1 − R2) D	D2
1	12	−11	121
2	9	−7	49
3	6	−3	9
4	10	−6	36
5	3	2	4
6	5	1	1
7	4	3	9
8	7	1	1
9	8	1	1
10	2	8	64
11	11	0	0
12	1	11	121
			$\sum D^2=416$

Given,
N = 12
Now,
$$\begin{gathered} r_k=1-\frac{6\mathrm{\Sigma }{D}^2}{N^3-N} \\ =1-\frac{6\times 416}{1728-12}=1-\frac{2496}{1716} \\ =1-1.4545 \\ =-0.454 \end{gathered}$$
Thus, the rank coefficient of correlation is $-$0.454.