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
|
1st assessor
|
2nd assessor
|
A
|
6
|
5
|
B
|
1
|
3
|
C
|
3
|
4
|
D
|
7
|
6
|
E
|
8
|
7
|
F
|
2
|
1
|
G
|
4
|
8
|
H
|
5
|
2
|
J
|
10
|
9
|
K
|
9
|
10
|
REQUIRED
Compute the rank correlation coefficient and thus comment briefly on the value acquired
|
|
|
d
|
d2
|
A
|
6
|
5
|
1
|
1
|
B
|
1
|
3
|
-2
|
4
|
C
|
3
|
4
|
-1
|
1
|
D
|
7
|
6
|
1
|
1
|
E
|
8
|
7
|
1
|
1
|
F
|
2
|
1
|
1
|
1
|
G
|
4
|
8
|
-4
|
16
|
H
|
5
|
2
|
3
|
9
|
J
|
10
|
9
|
+1
|
1
|
K
|
9
|
10
|
-1
|
1
|
|
|
|
|
Σd2 = 36
|
∴ The rank correlation coefficient R
R = 1 - {(6Σd2)/(n(n2 -1))}
= 1 - {(6(36))/(10(102 -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.