Visualizing Statistical Mix Effects and Simpson's Paradox
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Updated: Apr 4, 2026

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
Published on: October 13, 2018
Abstract:
We discuss how "mix effects" can surprise users of visualizations and potentially lead them to incorrect conclusions. This statistical issue (also known as "omitted variable bias" or, in extreme cases, as "Simpson's paradox") is widespread and can affect any visualization in which the quantity of interest is an aggregated value such as a weighted sum or average. Our first contribution is to document how mix effects can be a serious issue for visualizations, and we analyze how mix effects can cause problems in a variety of popular visualization techniques, from bar charts to treemaps. Our second contribution is a new technique, the "comet chart," that is meant to ameliorate some of these issues.
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