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Spearman's ρ ○◂｜Definition｜1st｜20261014173609-00-⌔

Spearman’s rank correlation coefficient - Wikipedia

Spearman’s rank correlation coefficient

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In statistics, Spearman’s rank correlation coefficient or Spearman’s ρ is a number ranging from −1 to 1 that indicates how strongly two sets of ranks are correlated. It is used in situations where the ranking of a dataset is important, for instance in sports. If a statistician wanted to know whether people who are high ranking in sprinting are also high ranking in long-distance running, they would use a Spearman rank correlation coefficient.

The coefficient is named after Charles Spearman¹ and often denoted by the Greek letter $\rho$ (rho) or as $r_s$. It 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.

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.

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.

Spearman’s coefficient is appropriate for both continuous and discrete ordinal variables.²³ Both Spearman’s $\rho$ and Kendall’s $\tau$ can be formulated as special cases of a more general correlation coefficient.

Printed 2026-10-14.

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Footnotes

1. Spearman, C. (January 1904). “The Proof and Measurement of Association between Two Things” (PDF). The American Journal of Psychology. 15 (1): 72–101. doi:10.2307/1412159. JSTOR 1412159. ↩

2. Scale types. ↩

3. Lehman, Ann (2005). Jmp For Basic Univariate And Multivariate Statistics: A Step-by-step Guide. Cary, NC: SAS Press. p. 123. ISBN 978-1-59047-576-8. ↩

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