Spearman's rank correlation coefficient

A Spearman correlation of results when the two variables being compared are monotonically related, even if their relationship is not linear. This means that all data points with greater values than that of a given data point will have greater values as well. In contrast, this does not give a perfect Pearson correlation.
When the data are roughly elliptically distributed and there are no prominent outliers, the Spearman correlation and Pearson correlation give similar values.
The Spearman correlation is less sensitive than the Pearson correlation to strong outliers that are in the tails of both samples. That is because Spearman's ρ limits the outlier to the value of its rank.

In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman[1] and often denoted by the Greek letter (rho) or as , 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.[2][3] Both Spearman's and Kendall's can be formulated as special cases of a more general correlation coefficient.

  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.