Visualizing Kendall’s τ and Hidden Structures in Ranked Data

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 τ coefficient, a nonparametric 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 τ is well-established, there are relatively few graphing methods available to visualize the results. Here, we describe several alternative and complementary visualization methods and provide an interactive app for graphing Kendall’s τ. The resulting graphs provide a visualization of rank correlation which helps display the proportion of concordant and discordant pairs. Moreover, these methods highlight other key features of the data which are not represented by Kendall’s τ alone but may nevertheless be meaningful, such as longer monotonic chains and the relationship between discrete pairs of observations. We demonstrate the utility of these approaches through several examples and compare our results to other visualization methods.