Two graphs walk into a bar: Readout-based measurement reveals the Bar-Tip Limit error, a common, categorical misinterpretation of mean bar graphs

Abstract

How do viewers interpret graphs that abstract away from individual-level data to present only summaries of data such as means, intervals, distribution shapes, or effect sizes? Here, focusing on the mean bar graph as a prototypical example of such an abstracted presentation, we contribute three advances to the study of graph interpretation. First, we distill principles for Measurement of Abstract Graph Interpretation (MAGI principles) to guide the collection of valid interpretation data from viewers who may vary in expertise. Second, using these principles, we create the Draw Datapoints on Graphs (DDoG) measure, which collects drawn readouts (concrete, detailed, visuospatial records of thought) as a revealing window into each person's interpretation of a given graph. Third, using this new measure, we discover a common, categorical error in the interpretation of mean bar graphs: the Bar-Tip Limit (BTL) error. The BTL error is an apparent conflation of mean bar graphs with count bar graphs. It occurs when the raw data are assumed to be limited by the bar-tip, as in a count bar graph, rather than distributed across the bar-tip, as in a mean bar graph. In a large, demographically diverse sample, we observe the BTL error in about one in five persons; across educational levels, ages, and genders; and despite thoughtful responding and relevant foundational knowledge. The BTL error provides a case-in-point that simplification via abstraction in graph design can risk severe, high-prevalence misinterpretation. The ease with which our readout-based DDoG measure reveals the nature and likely cognitive mechanisms of the BTL error speaks to the value of both its readout-based approach and the MAGI principles that guided its creation. We conclude that mean bar graphs may be misinterpreted by a large portion of the population, and that enhanced measurement tools and strategies, like those introduced here, can fuel progress in the scientific study of graph interpretation.

Replacing bar graphs of continuous data with more informative graphics: are we making progress?

“…The present study extends these findings to many other fields, while showing that this pattern was consistently observed from 2010 to 2020. Recent research indicates that some readers conflate bar graphs that show counts or proportions with bar graphs that show means of continuous data [ 21 ], even though these two data types have very different properties. When examining a bar graph of continuous data, one in five people incorrectly interpret the bar end as the maximum of the underlying data points, rather than the center of the data points [ 21 ].…”

“…Recent research indicates that some readers conflate bar graphs that show counts or proportions with bar graphs that show means of continuous data [ 21 ], even though these two data types have very different properties. When examining a bar graph of continuous data, one in five people incorrectly interpret the bar end as the maximum of the underlying data points, rather than the center of the data points [ 21 ]. This misinterpretation was found across general education levels [ 21 ].…”

“…When examining a bar graph of continuous data, one in five people incorrectly interpret the bar end as the maximum of the underlying data points, rather than the center of the data points [ 21 ]. This misinterpretation was found across general education levels [ 21 ]. An earlier study found that when comparing equidistant data points above and below the bar tip, viewers rated points within the bar as being more likely than points above the bar [ 22 ].…”