The impact of topological and graphical choices on the perception of Euler diagrams

Abstract

This paper establishes the impact of topological and graphical properties on the comprehension of Euler diagrams. To-date, various studies have examined the impact of individual properties of Euler diagrams, such as curve shape and orientation. This has allowed us to establish guides for using these properties such as 'draw Euler diagrams with circles' and 'draw Euler diagrams without regard to orientation'. However, until the work described here, questions still remain, for example 'do these guides, when combined, make a significant difference to real-world Euler diagrams?', and if so, 'should they be used by those visualizing set data with Euler diagrams?' To answer these questions an empirical study was conducted to compare Euler diagrams that have been drawn by others for their real-world data, against versions that adhere to all of the guides in combination. The study establishes that both the accuracy and the speed with which information is derived from Euler diagrams is significantly improved when Euler diagrams adhere, where possible, to all the guides. The improvement is considerable when using the guided diagrams, with on average, the error rate being more than halved from 21.4% to 10.3%, and a 9 second improvement in the average time taken, from 34.2 seconds to 24.9 seconds. As Euler diagrams are regularly used to visualize information in a multitude of areas, ranging from crime control to social network analysis, our results indicate that applying the guides to these diagrams will improve the ability of users to accurately and quickly extract information.

The Semiotics of Spider Diagrams

“…Blake et al [7]), interpreted with reference to the above. Well matchedness and free rides are of special relevance to our discussion, both because they have been enormously influential ideas among diagram scientists and because, as we will explore, they are partial recreations of concepts first explained in detail by Peirce.…”

Presence and Absence of Individuals in Diagrammatic Logics: An Empirical Comparison

“…When drawing the diagrams, care was taken to ensure that their layouts aided cognition [3,13,29]. The following Euler diagram drawing guidelines were followed: each set was represented by a circle; each circle had a three pixel stroke width and a unique colour; their interiors had a transparent fill; the areas of the zones ensured that the individuals' names would comfortably fit in them; all set names were written in capital letters and took the same colour as their associated circle; the names were chosen so that no two names had a similar pronunciation.…”

“…For example, Figure 1 shows three semantically equivalent Euler diagrams, one of which is also a Venn diagram. The results of [2,5,32] imply that d 1 is sometimes the most effective representation from the perspective of cognition, and that the Venn diagram, d 3 , can significantly hinder cognition compared to d 1 and d 2 . Given this, we have insight into how to represent information about sets using Euler diagrams.…”

Evaluating Visualizations of Sets and Networks that Use Euler Diagrams and Graphs

“…Automated visualization techniques should aim to avoid such properties whilst ensuring an accurate visualization of the underlying data. Euler Diagram Properties Prior research has led to the identification of properties of Euler diagrams that impact their effectiveness [3], with an important category being five well-formedness properties [15]:…”