Data can be visually represented using visual channels like position, length or luminance. An existing ranking of these visual channels is based on how accurately participants could report the ratio between two depicted values. There is an assumption that this ranking should hold for different tasks and for different numbers of marks. However, there is surprisingly little existing work that tests this assumption, especially given that visually computing ratios is relatively unimportant in real-world visualizations, compared to seeing, remembering, and comparing trends and motifs, across displays that almost universally depict more than two values. To simulate the information extracted from a glance at a visualization, we instead asked participants to immediately reproduce a set of values from memory after they were shown the visualization. These values could be shown in a bar graph (position (bar)), line graph (position (line)), heat map (luminance), bubble chart (area), misaligned bar graph (length), or 'wind map' (angle). With a Bayesian multilevel modeling approach, we show how the rank positions of visual channels shift across different numbers of marks (2, 4 or 8) and for bias, precision, and error measures. The ranking did not hold, even for reproductions of only 2 marks, and the new probabilistic ranking was highly inconsistent for reproductions of different numbers of marks. Other factors besides channel choice had an order of magnitude more influence on performance, such as the number of values in the series (e.g., more marks led to larger errors), or the value of each mark (e.g., small values were systematically overestimated). Every visual channel was worse for displays with 8 marks than 4, consistent with established limits on visual memory. These results point to the need for a body of empirical studies that move beyond two-value ratio judgments as a baseline for reliably ranking the quality of a visual channel, including testing new tasks (detection of trends or motifs), timescales (immediate computation, or later comparison), and the number of values (from a handful, to thousands).

Bar charts are among the most frequently used visualizations, in part because their position encoding leads them to convey data values precisely. Yet reproductions of single bars or groups of bars within a graph can be biased. Curiously, some previous work found that this bias resulted in an overestimation of reproduced data values, while other work found an underestimation. Across three empirical studies, we offer an explanation for these conflicting findings: this discrepancy is a consequence of the differing aspect ratios of the tested bar marks. Viewers are biased to remember a bar mark as being more similar to a prototypical square, leading to an overestimation of bars with a wide aspect ratio, and an underestimation of bars with a tall aspect ratio. Experiments 1 and 2 showed that the aspect ratio of the bar marks indeed influenced the direction of this bias. Experiment 3 confirmed that this pattern of misestimation bias was present for reproductions from memory, suggesting that this bias may arise when comparing values across sequential displays or views. We describe additional visualization designs that might be prone to this bias beyond bar charts (e.g., Mekko charts and treemaps), and speculate that other visual channels might hold similar biases toward prototypical values.

Data visualization is powerful in large part because it facilitates visual extraction of values. Yet, existing measures of perceptual precision for data channels (e.g., position, length, orientation, etc.) are based largely on verbal reports of ratio judgments between two values (e.g., [7]). Verbal report conflates multiple sources of error beyond actual visual precision, introducing a ratio computation between these values and a requirement to translate that ratio to a verbal number. Here we observe raw measures of precision by eliminating both ratio computations and verbal reports; we simply ask participants to reproduce marks (a single bar or dot) to match a previously seen one. We manipulated whether the mark was initially presented (and later drawn) alone, paired with a reference (e.g. a second '100%' bar also present at test, or a y-axis for the dot), or integrated with the reference (merging that reference bar into a stacked bar graph, or placing the dot directly on the axis). Reproductions of smaller values were overestimated, and larger values were underestimated, suggesting systematic memory biases. Average reproduction error was around 10% of the actual value, regardless of whether the reproduction was done on a common baseline with the original. In the reference and (especially) the integrated conditions, responses were repulsed from an implicit midpoint of the reference mark, such that values above 50% were overestimated, and values below 50% were underestimated. This reproduction paradigm may serve within a new suite of more fundamental measures of the precision of graphical perception.