Rank correlation

A rank correlation is any statistic that measures the relationship between rankings. A "ranking" is the assignment of "first", "second", "third", etc. to different observations of a variable. (In general, to place things in an order) A rank correlation coefficient measures the degree of similarity between two rankings.

One might test for do colleges with a higher-ranked basketball program tend to have a higher-ranked football program? A quite important question is do people with higher-ranked education tend to get higher levels of income?

Some of the most used rank correlation statistics are

1. Spearman's ρ
2. Kendall's τ
3. Goodman and Kruskal's γ

An increasing rank correlation coefficient implies increasing agreement between rankings. The coefficient is inside the interval [−1, 1] and assumes the value:

• 1 if the agreement between the two rankings is perfect; the two rankings are the same.
• 0 if the rankings are completely independent.
• −1 if the disagreement between the two rankings is perfect; one ranking is the reverse of the other.