Obtain spearman’s rank correlation coefficient from the ranks allotted by 2 judges,
Paintings 1 2 3 4 5 6
Ranks (I Judge) 6 2 1 3 5 4
Ranks (II Judge) 4 1 3 5 6 2
Answers
Given :
Paintings 1 2 3 4 5 6
Ranks (I Judge) 6 2 1 3 5 4
Ranks (II Judge) 4 1 3 5 6 2
To Find : The Rank correlation coefficient
Solution :
Paintings 1 2 3 4 5 6
R1 6 2 1 3 5 4
R2 4 1 3 5 6 2
d 2 1 -2 -2 -1 2
d² 4 1 4 4 1 4
∑d² = 4 + 1 + 4 + 4 + 1 + 4= 18
rank correlation coefficient = 1 - 6 ∑ (di)² / (n(n² - 1))
n = 6
∑ (di)² = sum of squares of the differences in ranks = 18
rank correlation coefficient = 1 - 6 ( 18) / ( 6 ( 6² - 1))
= 1 - 18 / 35
= 17/35
= 0.486
The Rank correlation coefficient is 0.486
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