Question

Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result: 

X	35	54	80	95	73	73	35	91	83	81
Y	40	60	75	90	70	75	38	95	75	70

Answer 1

To determine Spearman’s Rank Correlation:

X	Y	R1	R2	d = R1 - R2	d2
35	40	9.5	9	0.5	0.25
54	60	8	8	0	0
80	75	5	4	1	1
95	90	1	2	-1	1
73	70	6.5	6.5	0	0
73	75	6.5	4	2.5	6.25
35	38	9.5	10	-0.5	0.25
91	95	2	1	1	1
83	75	3	4	-1	1
81	70	4	6.5	-2.5	6.25
Total					∑d2 = 17

r = 1 - `(6[sum"d"^2 + sum (("t"^3 - "t")/12)])/("N"("N"^2 - 1))`

where t is the number of individual involved in a tie.

Here, ∑d² = 17, N = 10 , t = 3,2,2,2

`sum("t"^3-"t")/12 = ((3)^2 - 3)/12 + 3 xx ((2)^3 - 2)/12`

`= (27-3)/12 + 3 xx (8 - 2)/12`

 

`= 24/12 + 18/12 = 42/12 =7/2 = 3.5` 

r = `1 - (6[17 + 3.5])/(10(100 - 1))`

`=1 - 123/990`

`= (990-123)/990`

`= 867/990 = 0.876`