Notched Violin Plots for Circular Data

Visualizing circular data is challenging due to their periodic nature. The circular boxplot provides compact summaries of location and dispersion, but may not suffice for capturing other important distribu-tional features. The recently proposed circular violin plot addresses this limitation by superposing the estimated data density. Here we introduce the notched circular violin plot, a novel display that integrates distributional and inferential information. The method produces a notch around the median direction, constructed by a bootstrap procedure based on angular distances, to capture uncertainty and allow visual comparison across groups. The notched violin plot is implemented in R, and illustrated through applications to wind analysis and photobiology.