Despite years of research yielding systems and guidelines to aid visualization design, practitioners still face the challenge of identifying the best visualization for a given dataset and task. One promising approach to circumvent this problem is to leverage perceptual laws to quantitatively evaluate the effectiveness of a visualization design. Following previously established methodologies, we conduct a large scale (n=1687) crowdsourced experiment to investigate whether the perception of correlation in nine commonly used visualizations can be modeled using Weber's law. The results of this experiment contribute to our understanding of information visualization by establishing that: (1) for all tested visualizations, the precision of correlation judgment could be modeled by Weber's law, (2) correlation judgment precision showed striking variation between negatively and positively correlated data, and (3) Weber models provide a concise means to quantify, compare, and rank the perceptual precision afforded by a visualization.

Figure 1: Examples of the visual explanations in our experiment-We tested two ways to represent an example instance: (a) an image or (b) a rose chart of features, and three spatial layouts to arrange the instances: (c) grid, (d) tree, and (e) graph. Three images (c-e) here show explanations of the same instances, classifier, and classification recommendation.

Recent visualization research efforts have incorporated experimental techniques and perceptual models from the vision science community. Perceptual laws such as Weber's law, for example, have been used to model the perception of correlation in scatterplots. While this thread of research has progressively refined the modeling of the perception of correlation in scatterplots, it remains unclear as to why such perception can be modeled using relatively simple functions, e.g., linear and log-linear. In this paper, we investigate a longstanding hypothesis that people use visual features in a chart as a proxy for statistical measures like correlation. For a given scatterplot, we extract 49 candidate visual features and evaluate which best align with existing models and participant judgments. The results support the hypothesis that people attend to a small number of visual features when discriminating correlation in scatterplots. We discuss how this result may account for prior conflicting findings, and how visual features provide a baseline for future model-based approaches in visualization evaluation and design.

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