We tested variants of 2 different representations for showing the cardinality of sets and set intersections. The two representations were Euler Diagrams and Linear diagrams. The variants were non-proportional with numbers, proportional with numbers and proportional without numbers. We took the best Euler diagram representation and the best Linear Diagram representation and compared them. Proportions means varying circle and intersection sizes for Euler diagrams and varying line segment length for Linear diagrams. Overall, area proporational Euler Diagrams with numbers were best. We note that we restricted the data so that only accurate Euler diagrams were produced. In many cases, accurate Euler diagrams could not be generated and so for that data, another method must be used.
Software used to generate the diagrams
non-area proportional Euler diagrams: iCircles
area proportional Euler diagrams: venneuler
Linear diagrams: Linear diagram generator
The studies as performed by the participants are here:
Euler diagrams: Study 1
Linear diagrams: Study 2
Euler vs Linear: Study 3
The first 4 pages were training, and were always presented in the same order. There were 2 inattentive paritipant test questions. The text of these requires the participant to click on all the available options. The intention is to ensure the participant reads the questions rather than clicks as quickly as possible through them. They were always on pages 14 and 28. The 32 data generating questions were presented in a random order.
Details of diagrams, questions, statistical models and tests can be can be found here: Additional Material
The data from the three studies:
Euler diagrams: Study 1
Linear diagrams: Study 2
Euler vs Linear: Study 3
The investigators for this cardinality study are:
Gem Stapleton
Peter Chapman
Peter Rodgers
Anestis Touloumis
Andrew Blake
Aidan Delaney