Kendall Tau-b Tied Pairs

Kendall rank correlation coefficient, specifically Tau-b, is a non-parametric measure of strength and direction of association that exists between two variables measured on at least an ordinal scale. Unlike Tau-a, Tau-b makes adjustments for ties. It computes the concordance by distinguishing single-axis ties from joint ties in rank association.

Experiment

You can interact with the Kendall Tau-b module to explore how different data configurations and dataset sizes affect the correlation coefficient.

1. Locate the Data select control and choose Increasing.
2. Set the Prefix control to 4. Observe that all 6 pairs are concordant and Tau-b is exactly 1.0.
3. Change the Data select to Joint ties and see how it affects the counts of joint ties versus single-axis ties. Note that joint ties do not contribute to the denominator in the Tau-b calculation.
4. Finally, select Constant for the Data control. Notice that all pairs become ties in X, resulting in a zero denominator. The module correctly displays "Unavailable" for Tau-b in this edge case.