Illustration of Rank Correlation Coefficient
In a beauty competition two assessors were asked to rank the 10 contestants by using the professional assessment skills. The results obtained were described as shown in the table below as:
Contestants
1^{st} assessor
2^{nd} assessor
A
6
5
B
1
3
C
4
D
7
E
8
F
2
G
H
J
10
9
K
REQUIRED
Compute the rank correlation coefficient and thus comment briefly on the value acquired
d
d2
-2
-1
-4
16
+1
Σd^{2} = 36
∴ The rank correlation coefficient R
R = 1 - {(6Σd^{2})/(n(n^{2} -1))}
= 1 - {(6(36))/(10(10^{2} -1))}
= 1 - (216/990)
= 1 - 0.22
= 0.78
Comment: because the correlation is 0.78 it implies that there is high positive correlation among the ranks awarded to the contestants. 0.78 > 0 and 0.78 > 0.5.