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A Common, Categorical Misinterpretation of Bar Graphs: Readout-based Measurement Reveals the Bar-tip Limit Error

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Abstract

Here, we make three contributions to the study of graph cognition. First, we introduce a framework for measuring graph comprehension via the elicitation of a readout: a relatively concrete and detailed record of thought. Second, we create a flexible new readout-based measure, called Draw Datapoints on Graphs (DDoG), to assess the comprehension of graphs that abstract away from their raw, underlying data. Third, using this new measure, we identify a common error in the interpretation of bar graphs of means. The error we identify is an apparent conflation of bar graphs of means with bar graphs of counts. It occurs when the raw underlying data is assumed to be limited by, rather than spread across, the bar-tip. We therefore call it the Bar-Tip Limit Error (BTLE). In a large, demographically diverse sample, we observe BTLE in about one in five persons, across educational levels, ages, and genders, and despite thoughtful responding and relevant foundational knowledge. The identification of BTLE provides a case-in-point that simplification via abstraction can risk severe, high-prevalence misinterpretation. DDoG reveals the nature and likely cognitive mechanisms of BTLE with an ease that speaks both to DDoG’s value as a measure of graph comprehension and, more broadly, to the efficacy of our readout-focused framework. We conclude that bar graphs of means may be misinterpreted by a large proportion of the population, and that readout-focused measurement holds promise for accelerating the study of graph cognition.

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