Question

Find the coefficient of Rank Correlation :

$\begin{array}{cccccccccc}\text{Marks in Statistics}& 15& 10& 20& 28& 12& 10& 16& 18& \text{N= 8}\\ \text{Marks in Economics}& 16& 14& 10& 12& 11& 15& 18& 20& \text{N= 8}\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Marks in Statistics}& R_1& \text{Marks in Economics}& R_2& D(=R_1-R_2)& D^2\\ 15& 5& 16& 3& 2& 4\\ 10& 7.5& 14& 5& 2.5& 6.25\\ 20& 2& 10& 8& -6& 36\\ 28& 1& 12& 6& -5& 25\\ 12& 6& 11& 7& -1& 1\\ 10& 7.5& 15& 4& 3.5& 12.25\\ 16& 4& 18& 2& 2& 4\\ 18& 3& 20& 1& 2& 4\\ N=8& & N=8& & & \sum D^2=92.5\end{array}$

$R=1-\frac{6[\sum D^2+\frac{1}{12}(m^3-m)+.....]}{N^3-N}$ (when ranks are repeated)
where D= difference between the ranks of the two series and
N=number of individuals in each series.
$R=1-\frac{6[92.5+\frac{1}{12}(2^3-2\left)\right]}{8^3-8}=1-\frac{6\left[93\right]}{504}$
= 1-1.107 = -.107 (Negative low degree correlation)