Question

Calculate coefficient of rank correlation, given the following data set.

X	20	11	72	65	43	29	50
Y	60	63	26	35	43	51	37

Answer 1

X	Rank (R1)	Y	Rank (R2)	D = R1 − R2	D2
20 11 72 65 43 29 50	2 1 7 6 4 3 5	60 63 26 35 43 51 37	6 7 1 2 4 5 3	−4 −6 6 4 0 −2 2	16 36 36 16 0 4 4
N = 7					ΣD2 = 112

$$\begin{gathered} r_k=1-\frac{6{\mathrm{\Sigma D}}^2}{{\mathrm{N}}^3-\mathrm{N}} \\ \mathrm{or},r_k=1-\frac{6\left(112\right)}{7^3-7} \\ \mathrm{or},r_k=1-\frac{672}{343-7} \\ \mathrm{or},r_k=1-\frac{672}{336} \\ \mathrm{or},r_k=1-2 \\ \Rightarrow r_k=-1 \end{gathered}$$
Hence, coefficient of rank correlation = −1