Beyond Log Scales: Toward Cognitively Informed Bar Charts for Orders of Magnitude Values

Keywords

orders of magnitude, comparisons, exponent, mantissa, logarithmic scale, bar charts

Abstract

In this work, we challenge the dominant use of logarithmic scales to communicate values spanning multiple orders of magnitude—Orders of Magnitude Values (OMVs)—to the general public. Focusing on bar charts, we incorporate cognitive insights into visualization design to better align with how humans perceive OMVs. Studies in cognitive psychology suggest that, for large numerical ranges such as millions and billions, people do not think logarithmically. Instead, they perceive numbers in a piecewise linear manner, grouping values into scale words (e.g., millions) and applying linear reasoning within each group. We build upon a recently introduced piecewise linear scale, EplusM, and validate its use in bar charts, which we refer to as EplusM bar charts. We also introduce two novel variants of the EplusM bar chart informed by findings in numerical perception: Bricks, which builds on the concepts of round numbers and subitizing, and Multi-Magnitude, which leverages categorical perception of large numbers. In a crowdsourced experiment, we evaluate four bar chart designs: 1) Log, 2) EplusM, 3) Bricks, and 4) Multi-Magnitude, across value retrieval and quantitative comparison tasks. Our results show that EplusM bar charts are significantly preferred over logarithmic designs, increase user confidence, and reduce perceived mental demand, while maintaining task performance. These findings suggest that EplusM bar charts can serve as effective alternatives to logarithmic ones when visualizing OMVs for general audiences.