Illustration of rank correlation coefficient, Mathematics

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	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.

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