Kendall Tau

Definition

Kendall Tau is a non-parametric statistical method used to measure the strength and direction of association that exists between two numerical features. It's a measure of rank correlation, which means it compares the order or ranking of data points in one feature to the order or ranking of data points in another feature.

Range of score: -1 to 1

A value of 1 indicates that the ranks of corresponding values in the features are always in the same order, implying a perfect positive association. A value of -1 indicates that the ranks are always in the opposite order, implying a perfect negative association. A value of 0 indicates that there is no association between the ranks.

How it works

Kendall Tau is calculated by comparing pairs of data points. For each pair of data points in your dataset, the calculation determines whether they are concordant or discordant. Concordant pairs are pairs in which the ranks for both features increase together or decrease together. Discordant pairs are pairs in which one rank increases while the other decreases.

(In the figure above, Points in the grey segments are concordant while all points in white segments are discordant)

The difference between the number of concordant pairs and the number of discordant pairs is calculated and divided by the total number of pairs.

This method of calculation makes Kendall Tau a robust measure of correlation, as it does not make any assumptions about the distribution of the data and is less sensitive to outliers than some other correlation measures.