Question

Two ladies were asked to rank ten different types of cell phones. The ranks given by them are given below :

$\begin{array}{ccccccccccc}\text{Cell Phone}& \text{A}& \text{B}& \text{C}& \text{D}& \text{E}& \text{F}& \text{G}& \text{H}& \text{I}& \text{J}\\ \text{Tina}& 1& 6& 3& 9& 5& 2& 7& 10& 8& 4\\ \text{Rita}& 6& 8& 3& 7& 2& 1& 5& 9& 4& 10\end{array}$

Calculate Spearman's rank correlation coefficient.

Answer 1

$\begin{array}{cccc}\text{Rank}& \text{Rank}& D=R_1-R_2& D^2\\ R_1& R_2& & \\ 1& 6& -5& 25\\ 6& 8& -2& 4\\ 3& 3& 0& 0\\ 9& 7& 2& 4\\ 5& 2& 3& 9\\ 2& 1& 1& 1\\ 7& 5& 2& 4\\ 10& 9& 1& 1\\ 8& 4& 4& 16\\ 4& 10& -6& 36\\ N=10& & \sum D=0& \sum D^2=100\end{array}$
Spearman's rank coefficient = $r_k=1-\frac{6\sum D^2}{N^3-N}$
$r_k=1-\frac{6\times 100}{{10}^3-10}$ $=1-\frac{600}{990}\Rightarrow 1-0.606=0.394$