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Exploratory data analysis of high-dimensional datasets is a crucial task for which visual analytics can be especially useful. However, the ad hoc nature of exploratory analysis can also lead users to draw incorrect causal inferences. Previous studies have demonstrated this risk and shown that integrating counterfactual concepts within visual analytics systems can improve users’ understanding of visualized data. However, effectively leveraging counterfactual concepts can be challenging, with only bespoke implementations found in prior work. Moreover, it can require expertise in both counterfactual subset analysis and visualization to implement the functionalities practically. This paper aims to help address these challenges in two ways. First, we propose an operator-based conceptual model for the use of counterfactuals that is informed by prior work in visualization research. Second, we contribute the Co-op library, an open and extensible reference implementation of this model that can support the integration of counterfactual-based subset computation with visualization systems. To evaluate the effectiveness and generalizability of Co-op, the library was used to construct two different visual analytics systems each supporting a distinct user workflow. In addition, expert interviews were conducted with professional visual analytics researchers and engineers to gain more insights regarding how Co-op could be leveraged. Finally, informed in part by these evaluation results, we distil a set of key design implications for effectively leveraging counterfactuals in future visualization systems. 

Counterfactuals – expressing what might have been true under different circumstances – have been widely applied in statistics and machine learning to help understand causal relationships. More recently, counterfactuals have begun to emerge as a technique being applied within visualization research. However, it remains unclear to what extent counterfactuals can aid with visual data communication. In this paper, we primarily focus on assessing the quality of users’ understanding of data when provided with counterfactual visualizations. We propose a preliminary model of causality comprehension by connecting theories from causal inference and visual data communication. Leveraging this model, we conducted an empirical study to explore how counterfactuals can improve users’ understanding of data in static visualizations. Our results indicate that visualizing counterfactuals had a positive impact on participants’ interpretations of causal relations within datasets. These results motivate a discussion of how to more effectively incorporate counterfactuals into data visualizations. 

Existing guidelines for categorical color selection are heuristic, often grounded in intuition rather than empirical studies of readers' abilities. While design conventions recommend palettes maximize hue differences, more recent exploratory findings indicate other factors, such as lightness, may play a role in effective categorical palette design. We conducted a crowdsourced experiment on mean value judgments in multi-class scatterplots using five color palette families-single-hue sequential, multihue sequential, perceptually-uniform multi-hue sequential, diverging, and multi-hue categorical-that differ in how they manipulate hue and lightness. Participants estimated relative mean positions in scatterplots containing 2 to 10 categories using 20 colormaps. Our results confirm heuristic guidance that hue-based categorical palettes are most effective. However, they also provide additional evidence that scalable categorical encoding relies on more than hue variance.