Question

In a contest, the competitors are awarded marks out of 20 by two judges. The scores of the 10 competitors are given below. Calculate Spearman's rank correlation.

Competitors	A	B	C	D	E	F	G	H	I	J
Judge A	2	11	11	18	6	5	8	16	13	15
Judge B	6	11	16	9	14	20	4	3	13	17

Answer 1

Judge A	`R_1`	Judge B	`R_2`	`D = R_1 - R_2`	`D^2`
2	10	6	8	2	4
11	5.5	11	6	0.5	0.25
11	5.5	16	3	2.5	6.25
18	1	9	7	-6	36
6	8	14	4	4	4
5	9	20	1	8	64
8	7	4	9	-2	4
16	2	3	10	-6	64
13	4	13	5	-1	1
15	3	17	2	1	1

C.F = `1/12 {(m_1^3 - m_1)} = 1/2 {8 -2} = 6/12 = 1/2`

`R = 1 - (6[sumd^2 + cf])/(m(n^2 -1))`

`= 1 - 6 [(184.5 + 1/2)]/(10(10^2 - 1))`

`= 1 - (6xx 185)/(10 xx 99)`

= 1 - 1.12

= - 0.12