Abstract
This paper presents the first empirical investigation that compares Euler and linear diagrams when they are used to represent set cardinality. A common approach is to use area-proportional Euler diagrams but linear diagrams can exploit length-proportional straight-lines for the same purpose. Another common approach is to use numerical annotations. We first conducted two empirical studies, one on Euler diagrams and the other on linear diagrams. These suggest that area-proportional Euler diagrams with numerical annotations and length-proportional linear diagrams without numerical annotations support significantly better task performance. We then conducted a third study to investigate which of these two notations should be used in practice. This suggests that area-proportional Euler diagrams with numerical annotations most effectively supports task performance and so should be used to visualize set cardinalities. However, these studies focused on data that can be visualized reasonably accurately using circles and the results should be taken as valid within that context. Future work needs to determine whether the results generalize both to when circles cannot be used and for other ways of encoding cardinality information.
Highlights
This paper sets out to shed light on how to represent sets and their cardinalities in a manner most effective for users
An overarching goal is to ensure practical impact of the research, so we evaluated selected state-of-the-art visualization methods that exist for data of this kind: venneuler [41], iCircles [37], and the linear diagram generator in [34]
In terms of effect sizes, the odds of providing j or fewer correct answers overall with Euler Diagrams—Proportional (ED-P) was 1.4839 times that of ED-P&N, which increased to 1.5950 for set cardinality tasks and reduced to 1.4706 for intersection cardinality tasks; in all cases, there is a clear accuracy improvement with ED-P&N. This is at the expense of time, where we estimated that ED-P tasks were, overall, completed in 85.57% of the time of ED-P&N tasks; this decreased to 78.16% of the time for set cardinality tasks and increased to 93.69% of the time for intersection cardinality tasks
Summary
This paper sets out to shed light on how to represent sets and their cardinalities in a manner most effective for users. This is of particular significance because there are enormous amounts of set-based data available in a wide variety of application areas [2]. Set visualization techniques often exploit closed curves (or variations thereof) [9, 11, 25, 32, 36] or lines [1, 8, 15, 34]. This paper focuses on such methods by evaluating extensions of Euler diagrams (closed curves) [39, 41] and linear diagrams (lines) [34] that represent cardinality information. We consider two common ways of representing cardinality: proportions (of areas or lengths) and numerical annotations.
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