Perceptual proxies for extracting averages in data visualizations

Across science, education, and business, we process and communicate data visually. One bedrock finding in data visualization research is a hierarchy of precision for perceptual encodings of data (e.g., that encoding data with Cartesian positions allows more precise comparisons than encoding with sizes). But this hierarchy has only been tested for single-value comparisons, under the assumption that those lessons would extrapolate to multivalue comparisons. We show that when comparing averages across multiple data points, even for pairs of data points, these differences vanish. Viewers instead compare values using surprisingly primitive perceptual cues (e.g., the summed area of bars in a bar graph). These results highlight a critical need to study a broader constellation of visual cues that mediate the patterns that we can see in data, across visualization types and tasks.