Spearman's rank correlation coefficient, usually denoted as $\rho$, is a measure of concordance between two random variables.
Spearman's rho is a measure of concordance between two random variables. It is the linear (Pearson) correlation of the probability transformed random variables.
Let $r_{i,j}$ be the rank of $y_{i,j}$ among responses $\{ y_{1,j}, ..., y_{n,j}\}$ for $i = \{1, ..., n\}, j \in {1,2}$
$$\hat{\rho} = \text{Cor}[(r_{1,1},...,r_{n,1}),(r_{1,2},...r_{n,2})]$$
This measure is between -1 and +1 and depends only on the rank of the data values and so is invariant to monotonic transformations (unlike usual moment correlation).
It can also be expressed as a measure of concordance based on ranks, and has many properties in common with Kendall's tau.
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English psychologist Charles Spearman is best known for the Spearman rank correlation coefficient, or Spearman's rho. He also worked in factor analysis and is known for his work on models for human intelligence.
His best known work, the Spearman rank correlation coefficient, or Spearman's rho, is simply a Pearson correlation coefficient computed on the ranks of the data. It is a widely used measure of monotonic association between variables. It is unaffected by monotonic increasing transformation of the variables.
The Spearman correlation has good efficiency properties for measuring linear correlation at the normal and has much better robustness than the Pearson coefficient in the presence of outliers.
