# Rank correlation

In statistics, **rank correlation** is the study of relationships between different rankings on the same set of items. It deals with measuring correspondence between two rankings, and assessing the significance of this correspondence.

## Correlation coefficients

Two of the more popular rank correlation statistics are

- Spearman's rank correlation coefficient (Spearman's ρ)
- Kendall's tau rank correlation coefficient (Kendall's τ)

A rank correlation coefficient is in the interval [-1,1] where:

- If the agreement between the two rankings is perfect (i.e., the two rankings are the same) the coefficient has value 1.
- If the disagreement between the two rankings is perfect (i.e., one ranking is the reverse of the other) the coefficient has value -1.
- For all other arrangements the value lies between -1 and 1, and increasing values imply increasing agreement between the rankings.
- If the rankings are completely independent, the coefficient has value 0.

## See also