Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot displays of distributions of groups of angular data. The use of concentric boxplots brings challenges of visual perception, so we set the boxwidths to be inversely proportional to the square root of their distance from the centre. A perception survey supports this scaled boxwidth choice. For a large number of groups, we propose circular quartile plots. A three-dimensional toroidal display is also implemented for periodic angular distributions. We illustrate our methods on datasets in (1) psychology, to display motor resonance under different conditions, (2) genomics, to understand the distribution of peak phases for ancillary clock genes, and (3) meteorology and wind turbine power generation, to study the changing and periodic distribution of wind direction over the course of a year.

翻译：角度观测值，即位于单位圆上的观测值，广泛出现于多个学科领域，其描述、分析、解释与可视化均需特别处理。本文提供了构建分组角度数据分布同心圆箱线图的方法。同心箱线图的使用带来了视觉感知上的挑战，因此我们将箱体宽度设置为与其到中心距离的平方根成反比。一项感知调查支持这种缩放箱宽的选择。对于大量分组，我们提出了圆形四分位图。此外，我们还为周期性角度分布实现了三维环形显示。我们通过以下数据集中的实例展示了所提方法：(1) 心理学领域，用于展示不同条件下的运动共振；(2) 基因组学领域，用于理解辅助时钟基因峰值相位的分布；(3) 气象学与风力涡轮机发电领域，用于研究一年中风向的变化与周期性分布。