Visualizing and comparing distributions with half-disk density strips

TL;DR

The paper introduces the half-disk density strip (HDDS), a graphical tool that visually compares probability densities in univariate and multivariate settings, aiding interpretation and analysis.

Contribution

It presents the HDDS method and its extension to multivariate data, providing an intuitive visualization for density comparison and analysis.

Findings

Effective visualization of density features like symmetry and multi-modality.

Facilitates comparison of pairs of densities in complex data.

Applied to income and life-satisfaction data with positive results.

Abstract

We propose a user-friendly graphical tool, the half-disk density strip (HDDS), for visualizing and comparing probability density functions. The HDDS exploits color shading for representing a distribution in an intuitive way. In univariate settings, the half-disk density strip allows to immediately discern the key characteristics of a density, such as symmetry, dispersion, and multi-modality. In the multivariate settings, we define HDDS tables to generalize the concept of contingency tables. It is an array of half-disk density strips, which compactly displays the univariate marginal and conditional densities of a variable of interest, together with the joint and marginal densities of the conditioning variables. Moreover, HDDSs are by construction well suited to easily compare pairs of densities. To highlight the concrete benefits of the proposed methods, we show how to use HDDSs for analyzing income distribution and life-satisfaction, conditionally on continuous and categorical controls, from survey data. The code for implementing HDDS methods is made available through a dedicated R package.