Question

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​

Answer 1

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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