Question

Calculate rank coefficient of correlation between years of service and efficiency rating.

Persons	:	A	B	C	D	E	F	G	H	I	J
Years of Service	:	24	30	12	25	29	19	16	10	11	7
Efficiency rating	:	66	51	84	66	45	81	72	97	92	70

Answer 1

Persons	Years of Service	R1	Efficiency Rating	R2	(R1 − R2) D	D2
A	24	7	66	3.5	3.5	12.25
B	30	10	51	2	8	64
C	12	4	84	8	−4	16
D	25	8	66	3.5	4.5	20.25
E	29	9	45	1	8	64
F	19	6	81	7	−1	1
G	16	5	72	6	−1	1
H	10	2	97	10	−8	64
I	11	3	92	9	−6	36
J	7	1	70	5	−4	16
						$\sum D^2=294.5$

Given:
N = 10
When ranks are repeated more than once, the following formula is used to calculate rank coefficient of correlation.
$$\begin{gathered} r_k=1-\frac{6\left[\mathrm{\Sigma }{D}^2+{\displaystyle \frac{1}{12}}\left(m^3-m\right)\right]}{N^3-N} \\ =1-\frac{6\left[294.5+{\displaystyle \frac{1}{12}}\left(2^3-2\right)\right]}{1000-10} \\ =1-\frac{6\left[294.5+0.5\right]}{990} \\ =1-\frac{1770}{990} \\ =1-1.787 \\ =-0.787 \end{gathered}$$
Thus, the rank coefficient of correlation is $-$0.787.