title: The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares.
abstract: It is an ongoing debate, what properties of visualizations increase people's performance when solving Bayesian reasoning tasks. In the discussion of the properties of two visualizations, i.e., the tree diagram and the unit square, we emphasize how both visualizations make relevant subset relations transparent. Actually, the unit square with natural frequencies reveals the subset relation that is essential for the Bayes' rule in a numerical and geometrical way whereas the tree diagram with natural frequencies does it only in a numerical way. Accordingly, in a first experiment with 148 university students, the unit square outperformed the tree diagram when referring to the students' ability to quantify the subset relation that must be applied in Bayes' rule. As hypothesized, in a second experiment with 143 students, the unit square was significantly more effective when the students' performance in tasks based on Bayes' rule was regarded. Our results could inform the debate referring to Bayesian reasoning since we found that the graphical transparency of nested sets could explain these visualizations' effect.
authors.affiliation: Institute of Mathematics Education, University of Education, Freiburg Freiburg, Germany.
authors.forename: Katharina
authors.initials: K
authors.lastname: Böcherer-Linder
authors.affiliation: Institute of Mathematics, University of Kassel Kassel, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Eichler
keywords: Bayesian reasoning; nested sets; tree diagram; unit square; visualization