Question

Give the formula to calculate rank correlation coefficient with
(i) non-repeated ranks and
(ii) repeated ranks

Answer 1

(i) When ranks are not repeated
$r_k=1-\frac{6\sum D^2}{N^3-N}$
(ii) When ranks are repeated
$r_k=1-\frac{6[\sum D^2+\frac{1}{12}(m^3-m)+...]}{N^3-N}$

where,
$r_k=$ rank correlation
$\sum D^2=$ the total of squares of the differences of corresponding ranks
$N=$ the number of pairs of observations
$m=$ the number of times the ranks are repeated