Question

Calculate Spearman's rank correlation from the following data:

X	:	10	12	8	15	20	25	40
Y	:	15	10	6	25	16	12	8

Answer 1

X	R1	Y	R2	(R1 − R2) D	D2
10	2	15	5	−3	9
12	3	10	3	0	0
8	1	6	1	0	0
15	4	25	7	−3	9
20	5	16	6	−1	1
25	6	12	4	2	4
40	7	8	2	5	25
					$\sum D^2=48$

Given:
N = 7
Now,
$$\begin{gathered} r_k=1-\frac{6\mathrm{\Sigma }{D}^2}{N^3-N}=1-\frac{6\times 48}{343-7} \\ =1-0.857 \\ =0.143 \end{gathered}$$
Thus, the rank coefficient of correlation is 0.143.