  We present an application of mosaic diagrams to the visualisation of set
relations. Venn and Euler diagrams are the best known visual representations of
sets and their relationships (intersections, containment or subsets, exclusion
or disjointness). In recent years, alternative forms of visualisation have been
proposed. Among them, linear diagrams have been shown to compare favourably to
Venn and Euler diagrams, in supporting non-interactive assessment of set
relationships. Recent studies that compared several variants of linear diagrams
have demonstrated that users perform best at tasks involving identification of
intersections, disjointness and subsets when using a horizontally drawn linear
diagram with thin lines representing sets, and employing vertical lines as
guide lines. The essential visual task the user needs to perform in order to
interpret this kind of diagram is vertical alignment of parallel lines and
detection of overlaps. Space-filling mosaic diagrams which support this same
visual task have been used in other applications, such as the visualization of
schedules of activities, where they have been shown to be superior to linear
Gantt charts. In this paper, we present an application of mosaic diagrams for
visualization of set relationships, and compare it to linear diagrams in terms
of accuracy, time-to-answer, and subjective ratings of perceived task
difficulty. The study participants exhibited similar performance on both
visualisations, suggesting that mosaic diagrams are a good alternative to Venn
and Euler diagrams, and that the choice between linear diagrams and mosaics may
be solely guided by visual design considerations.
