Using the weighted Kendall Distance to analyze rank data in psychology

Abstract

Although the Kendall distance is a standard metric in computer science, it is less widely used in psychology. We demonstrate the usefulness of the Kendall distance for analyzing psychological data that take the form of ranks, lists, or orders of items. We focus on weighted extensions of the metric that allow for heterogeneity of item importance, item position, and item similarity, as well showing how the metric can accommodate missingness in the form of top-k lists. To demonstrate how the Kendall distance can help address research questions in psychology, we present four applications to previous data. These applications involve the recall of events on September 11, peo-ple's preference rankings for the months of the year, people's free recall of animal names in a clinical setting, and expert predictions involving American football outcomes.