Question

Twelve entries were submitted in a flower show competition. They were ranked by two judges as under:

Entries	:	1	2	3	4	5	6	7	8	9	10	11	12
Judge A	:	7	8	2	1	9	3	12	11	4	10	6	5
Judge B	:	6	4	1	3	11	2	12	10	5	9	7	8

Answer 1

Entries	Judge A (R1)	Judge B (R2)	(R1 − R2) D	D2
1	7	6	−1	1
2	8	4	4	16
3	2	1	1	1
4	1	3	−2	4
5	9	11	−2	4
6	3	2	1	1
7	12	12	0	0
8	11	10	1	1
9	4	5	−1	1
10	10	9	1	1
11	6	7	−1	1
12	5	8	−3	9
				$\sum D^2=40$

Given,
N = 12
To calculate Spearman's Rank correlation, the following formula is used,
$$\begin{gathered} r_k=1-\frac{6\mathrm{\Sigma }{D}^2}{N^3-N} \\ =1-\frac{6\times 40}{1728-12} \\ =1-\frac{240}{1716} \\ =1-0.139 \\ =0.860 \end{gathered}$$
Thus, the Spearman's rank correlation is 0.860.