The Weighted Average Illusion: Biases in Perceived Mean Position in Scatterplots
This work addresses a specific visualization issue for data analysts and designers, highlighting how design choices can lead to perceptual biases, but it is incremental in nature as it builds on existing knowledge in visual perception and ensemble processing.
The paper tackles the problem of misinterpretation in trivariate scatterplots, where viewers systematically overestimate the mean position of data points due to larger or darker points being weighted more heavily, and quantifies this bias across different visual encoding ranges and data correlations.
Scatterplots can encode a third dimension by using additional channels like size or color (e.g. bubble charts). We explore a potential misinterpretation of trivariate scatterplots, which we call the weighted average illusion, where locations of larger and darker points are given more weight toward x- and y-mean estimates. This systematic bias is sensitive to a designer's choice of size or lightness ranges mapped onto the data. In this paper, we quantify this bias against varying size/lightness ranges and data correlations. We discuss possible explanations for its cause by measuring attention given to individual data points using a vision science technique called the centroid method. Our work illustrates how ensemble processing mechanisms and mental shortcuts can significantly distort visual summaries of data, and can lead to misconceptions like the demonstrated weighted average illusion.