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In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter ρ {\displaystyle \rho } or as r s {\displaystyle r_{s}} , is a nonparametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function.
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. 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.
Intuitively, the Spearman correlation between two variables will be high when observations have a similar rank between the two variables, and low when observations have a dissimilar rank between the two variables.
Spearman's coefficient is appropriate for both continuous and discrete ordinal variables. Both Spearman's ρ {\displaystyle \rho } and Kendall's τ {\displaystyle \tau } can be formulated as special cases of a more general correlation coefficient.