Question

The ranking of ten students in two subjects A and B as follows:

Subject A	3	5	8	4	7	10	2	1	6	9
Subject B	6	4	9	8	1	2	3	10	5	7

What is the coefficient of rank correlation?

Answer 1

RA	RB	D = RA − RB	D2
3 5 8 4 7 10 2 1 6 9	6 4 9 8 1 2 3 10 5 7	−3 1 −1 −4 6 8 −1 −9 1 2	9 1 1 16 36 64 1 81 1 4
			$\Sigma D^2$=214

N = 10
$$\begin{gathered} r_{\mathit{k}}=1-\frac{6{\mathrm{\Sigma D}}^2}{{\mathrm{N}}^3-\mathrm{N}} \\ \mathrm{or},r_k=1-\frac{6\times 214}{1000-10} \\ \Rightarrow r_k=-0.2969 \end{gathered}$$

Hence, coefficient of rank correlation is -0.297.