Question

12 entries in a painting competition were ranked by two judges , Judge I : 5, 2, 3, 4, 1, 6, 8, 7, 10, 9, 12, 11 and byJudge II: 4, 5, 2, 1, 6, 7, 10, 9, 11, 12, 3, 8. Calculate Spearman's rank correlation coefficient.

Answer 1

Rank Correlation Coefficient, $r_s=1-\frac {6\sum \rho_i^2} {n(n^2-1)}$

where, $\rho_i=$ Difference between two ranks of each observation.

Here, n=12

$r_s=1-\frac {6(1+9+1+9+25+1+4+4+1+9+81+9)}{12(144-1)}=1-\frac {924} {1716}=1-0.538=0.462$