The Weighted Average Illusion: Biases in Perceived Mean Position in Scatterplots

TL;DR

This paper investigates the weighted average illusion in scatterplots, revealing how size and color encoding can bias perceived data means, influenced by design choices and attention distribution, leading to potential misconceptions.

Contribution

It introduces the weighted average illusion, quantifies its bias across different visual encodings, and explores underlying attention mechanisms causing this distortion.

Findings

Bias increases with larger size and darker points.

Bias varies with data correlation levels.

Attention focus correlates with perceived mean distortions.

Abstract

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.