Boxplots and quartile plots for grouped and periodic angular data
This study addresses the lack of effective visualization methods for grouped periodic angular data in fields such as psychology, genomics, and meteorology. The authors propose concentric circular boxplots and circular quartile plots to characterize grouped angular distributions, and further extend the approach to a three-dimensional toroidal visualization for multiple groups to reveal periodic patterns. A novel scaling strategy is introduced, wherein box width is inversely proportional to the square root of the distance from the center, enhancing visual perception. This work is the first to integrate concentric circular boxplots with toroidal 3D visualization specifically for angular data. The effectiveness and practical utility of the proposed methods are demonstrated through applications to real-world datasets, including motor resonance phases, circadian clock gene expression phases, and periodic wind direction patterns.