Rank Correlation - Correlation Coefficients

Correlation Coefficients

Some of the more popular rank correlation statistics include

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 and assumes the value:

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

Following Diaconis (1988), a ranking can be seen as a permutation of a set of objects. Thus we can look at observed rankings as data obtained when the sample space is (identified with) a symmetric group. We can then introduce a metric, making the symmetric group into a metric space. Different metrics will correspond to different rank correlations.