3 In a beauty contest, the ranks provided by three different judges to 10 competitors are given in following table. Find out which pair of judges are more associated in term of same pattern for ranking
3 In a beauty contest, the ranks provided by three different judges to 10 competitors are given in following table. Find out which pair of judges are more associated in term of same pattern for ranking
| Competitors | A | B | C | D | E | F | G | H | I | J |
| Judge 1 | 3 | 4 | 6 | 7 | 9 | 8 | 2 | 10 | 1 | 5 |
| Judge 2 | 4 | 5 | 6 | 8 | 7 | 10 | 1 | 9 | 2 | 3 |
| Judge 3 | 5 | 7 | 9 | 8 | 10 | 6 | 3 | 4 | 1 | 2 |
- A Calculation of Rank Correlation
- Interpretation
Answer: With a view to find out the Rank Correlation between all the 3 judges we will have to find the correlation between the following:
| Comp | R1 | R2 | R3 | D12=
r1-r2 |
D23=r2-r3 | D13=r1-r3 | D2
12 |
D2
23 |
D2
13 |
| A | 3 | 4 | 5 | -1 | -1 | -2 | 1 | 1 | 4 |
| B | 4 | 5 | 7 | -1 | -2 | -3 | 1 | 4 | 9 |
| C | 6 | 6 | 9 | 0 | -3 | -3 | 0 | 9 | 9 |
| D | 7 | 8 | 8 | -1 | 0 | -1 | 1 | 0 | 1 |
| E | 9 | 7 | 10 | 2 | -3 | -1 | 4 | 9 | 1 |
| F | 8 | 10 | 6 | -2 | 4 | 2 | 4 | 16 | 4 |
| G | 2 | 1 | 3 | 1 | -2 | -1 | 1 | 4 | 1 |
| H | 10 | 9 | 4 | 1 | 5 | 6 | 1 | 25 | 36 |
| I | 1 | 2 | 1 | -1 | 1 | 0 | 1 | 1 | 0 |
| j | 5 | 3 | 2 | 2 | 1 | 3 | 4 | 1 | 9 |
| N=10 | ∑D2
12= 18 |
∑D2
23=70 |
∑D2
13=74 |
Rank correlation = 1 – (6 ∑d2)/(n(n^2-1))
Correlation coefficient between first and second judge
Rk1,2= 1- 6∑D2 1,2/n3-n
=1- 6×18/10*3-10
= 1- 108/990
=1- 0.109
= 0.89
Correlation coefficient between second and third judge
Rk2,3=1- 6∑D2 1,2/n3-n
=1- 6×70/10*3-10
= 1- 414/990
=1-0.4242
=0.58
Correlation coefficient between first and third judge
Rk1,3=1- 6∑D2 1,2/n3-n
=1- 6×74/10*3-10
= 1- 444/990
=1-0.448
=0.55
Interpretation:
Correlation between all the judges are positive and opinions of all the judges are of similar type, (their correlation is positive) i.e., their liking’s and disliking’s are very much common.
