<P> In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter ρ (\ displaystyle \ rho) (rho) or as r s (\ displaystyle r_ (s)), is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function . </P> <P> The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). If there are no repeated data values, a perfect Spearman correlation of + 1 or − 1 occurs when each of the variables is a perfect monotone function of the other . </P> <P> Intuitively, the Spearman correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc .) between the two variables, and low when observations have a dissimilar (or fully opposed for a correlation of − 1) rank between the two variables . </P>

The interpretation of the spearman correlation coefficient is identical to that for the