Beyond the Cloud: A Perceptual Illusion in Overlaid Bar Charts

A general challenge in information visualization is to represent multiple datasets in a way that supports comparison. One approach is to use overlaid bar charts, in which multiple sets of bars, each representing different measures of the same categories, are layered using colors with varying opacities. One set of bars is sorted from low to high, leaving the other set(s) unsorted. Although such charts may support comparison, we observed an illusion when comparing means—the mean of unsorted bars appears higher than the mean of sorted bars when the means are equal. To study this illusion, we presented participants with overlaid bar charts representing the popularity of two flower types (two sets of bars) across 50 counties (categories), sorted by “flower 1” or “flower 2” (balancing which flower was represented by opaque/translucent bars). Participants reported which flower was more popular overall (i.e., which set of bars had a greater mean). Numerically, the mean popularity of the two flowers was the same. We varied bar color across trials; participants saw all pairs of eight bar hues controlled for lightness and chroma. Overall, participants reported the mean of the unsorted bars was higher than the mean of the sorted bars (p<.001), despite the means being equal. A potential explanation is that taller bars in the unsorted set may appear especially salient as they extend beyond the overlapping region, or “cloud,” leading participants to weight taller bars (beyond the cloud) more than shorter bars when estimating the mean. Supporting this account, making the smaller bars more salient within the “cloud” by increasing color contrast reduced the illusion (p<.001). Thus, we call the illusion the “beyond the cloud” illusion. These results emphasize the importance of understanding how low-level perceptual features influence the ability to perform accurate statistical estimates from information visualizations.