Spearmans rank correlation coefficient r s is defined as follows: r s = 1 6 d

Spearman’s rank correlation coefficient r_s is defined as follows:

r_s = 1 – 6 Σd² / n(n² – 1)

Where d = difference in the ranks assigned to the same individual or phenomenon and n = number of individuals or phenomena ranked. Derive r_s from r defined in Eq. (3.5.13). Rank the X and Y values from 1 to n. Note that the sum of X and Y ranks is n(n + 1)/2 each and therefore their means are (n + 1)/2.