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

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.

Posted Date: 2/16/2013 7:07:54 AM | Location : United States







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