Graphing methods for Kendall's {\tau}

TL;DR

This paper introduces a novel interactive visualization method for Kendall's { au} rank correlation, enabling better understanding of concordant and discordant pairs in ranked data across various fields.

Contribution

The paper presents a new graphing technique and an interactive app for visualizing Kendall's { au} that highlights data features beyond the correlation coefficient.

Findings

The visualization effectively displays the proportion of concordant and discordant pairs.

It reveals relationships between discrete observations not captured by Kendall's { au}.

The method outperforms existing visualization approaches in clarity and insight.

Abstract

Ranked data is commonly used in research across many fields of study including medicine, biology, psychology, and economics. One common statistic used for analyzing ranked data is Kendall's {\tau} coefficient, a non-parametric measure of rank correlation which describes the strength of the association between two monotonic continuous or ordinal variables. While the mathematics involved in calculating Kendall's {\tau} is well-established, there are relatively few graphing methods available to visualize the results. Here, we describe a visualization method and provide an interactive app for graphing Kendall's {\tau} which uses a series of rigid Euclidean transformations along a Cartesian plane to map rank pairs into discrete quadrants. The resulting graph provides a visualization of rank correlation which helps display the proportion of concordant and discordant pairs. Moreover, this method highlights other key features of the data which are not represented by Kendall's {\tau} alone but may nevertheless be meaningful, such as the relationship between discrete pairs of observations. We demonstrate the effectiveness of our approach through several examples and compare our results to other visualization methods.