Question

A group of ten workers of a factory is ranked according to their efficiency by two different judges as follows:

Name of Worker	A	B	C	D	E	F	G	H	I	J
Rank by Judge A	4	8	6	7	1	3	2	5	10	9
Rank by Judge B	3	9	6	5	1	2	4	7	8	10

Calculate the coefficient of rank correlation.

Answer 1

Name of Worker	Rank by Judge A (RA)	Rank by Judge B (RB)	D= RA−RB	D2
A B C D E F G H I J	4 8 6 7 1 3 2 5 10 9	3 9 6 5 1 2 4 7 8 10	1 -1 0 2 0 1 -2 -2 2 -1	1 1 0 4 0 1 4 4 4 1
				$\Sigma D^2$=20

N = 10

$$\begin{gathered} r_{\mathit{k}}=1-\frac{6\Sigma D^{\mathit{2}}}{N^{\mathit{3}}\mathit{-}N} \\ or,r_k=1-\frac{6\times 20}{1000-10} \\ or,r_k=1-0.121 \\ \Rightarrow r_k=0.88 \end{gathered}$$

Hence, coefficient of rank correlation=0.88