Question

From the following data calculate coefficient of correlation by the method of rank differences.

X	:	75	68	95	70	60	80	81	50
Y	:	120	134	150	115	110	140	142	100

Answer 1

X	R1	Y	R2	(R1 − R2) D	D2
75	5	120	4	1	1
68	3	134	5	−2	4
95	8	150	8	0	0
70	4	115	3	1	1
60	2	110	2	0	0
80	6	140	6	0	0
81	7	142	7	0	0
50	1	100	1	0	0
					$\sum D^2=6$

Given:
N = 8
Now,
$$\begin{gathered} r_k=1-\frac{6\mathrm{\Sigma }{D}^2}{N^3-N} \\ =1-\frac{6\times 6}{512-8} \\ =1-\frac{36}{504}=1-0.0714 \\ =0.928\mathrm{or}0.93(\mathrm{approx}.) \end{gathered}$$
Thus, the coefficient of rank correlation is 0.93.