Question

The following are the marks obtained (out of 100) by a group of candidates in an employment interview held by two independent judges separately. Calculate the rank coefficient of correlation.

Candidates	:	A	B	C	D	E	F	G	H	I	J
Judge X	:	20	25	18	15	12	16	11	13	14	10
Judge Y	:	22	20	15	14	10	8	11	12	13	9

Answer 1

Candidate	Judge X	R1	Judge Y	R2	(R1 − R2) D	D2
A	20	9	22	10	−1	1
B	25	10	20	9	1	1
C	18	8	15	8	0	0
D	15	6	14	7	−1	1
E	12	3	10	3	0	0
F	16	7	8	1	6	36
G	11	2	11	4	−2	4
H	13	4	12	5	−1	1
I	14	5	13	6	−1	1
J	10	1	9	2	−1	1
						$\sum D^2=46$

Given:
N = 10
Now,
$$\begin{gathered} r_k=1-\frac{6\mathrm{\Sigma }{D}^2}{N^3-N} \\ =1-\frac{6\times 46}{1000-10}=1-\frac{276}{990}=1-0.278 \\ {r}_k=0.721 \end{gathered}$$
Thus, the rank coefficient of correlation is 0.721.