Measures of the Benefit of Direct Encoding of Data Deltas for Data Pair Relation Perception

The power of data visualization is not to convey absolute values of individual data points, but to allow the exploration of relations (increases or decreases in a data value) among them. One approach to highlighting these relations is to explicitly encode the numeric differences (deltas) between data values. Because this approach removes the context of the individual data values, it is important to measure how much of a performance improvement it actually offers, especially across differences in encodings and tasks, to ensure that it is worth adding to a visualization design. Across 3 different tasks, we measured the increase in visual processing efficiency for judging the relations between pairs of data values, from when only the values were shown, to when the deltas between the values were explicitly encoded, across position and length visual feature encodings (and slope encodings in Experiments 1 & 2). In Experiment 1, the participant's task was to locate a pair of data values with a given relation (e.g., Find the `small bar to the left of a tall bar' pair) among pairs of the opposite relation, and we measured processing efficiency from the increase in response times as the number of pairs increased. In Experiment 2, the task was to judge which of two relation types was more prevalent in a briefly presented display of 10 data pairs (e.g., Are there more `small bar to the left of a tall bar' pairs or more `tall bar to the left of a small bar' pairs?). In the final experiment, the task was to estimate the average delta within a briefly presented display of 6 data pairs (e.g., What is the average bar height difference across all `small bar to the left of a tall bar' pairs?). Across all three experiments, visual processing of relations between data value pairs was significantly better when directly encoded as deltas rather than implicitly between individual data points, and varied substantially depending on the task (improvement ranged from 25% to 95%). Considering the ubiquity of bar charts and dot plots, relation perception for individual data values is highly inefficient, and confirms the need for alternative designs that provide not only absolute values, but also direct encoding of critical relationships between those values.