### 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.

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.

Original language | English |
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Article number | e0211234 |

Journal | PLoS ONE |

Volume | 14 |

Issue number | 3 |

DOIs | |

Publication status | Published - 28 Mar 2019 |

### Bibliographical note

© 2019 Stapleton et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.### Cite this

Stapleton, G., Chapman, P., Rodgers, P., Touloumis, A., Blake, A., & Delaney, A. (2019). The efficacy of Euler diagrams and linear diagrams for visualizing set cardinality using proportions and numbers.

*PLoS ONE*,*14*(3), [e0211234]. https://doi.org/10.1371/journal.pone.0211234