title: Effects of visualizing statistical information - an empirical study on tree diagrams and 2 × 2 tables.
abstract: In their research articles, scholars often use 2 × 2 tables or tree diagrams including natural frequencies in order to illustrate Bayesian reasoning situations to their peers. Interestingly, the effect of these visualizations on participants' performance has not been tested empirically so far (apart from explicit training studies). In the present article, we report on an empirical study (3 × 2 × 2 design) in which we systematically vary visualization (no visualization vs. 2 × 2 table vs. tree diagram) and information format (probabilities vs. natural frequencies) for two contexts (medical vs. economical context; not a factor of interest). Each of N = 259 participants (students of age 16-18) had to solve two typical Bayesian reasoning tasks ("mammography problem" and "economics problem"). The hypothesis is that 2 × 2 tables and tree diagrams - especially when natural frequencies are included - can foster insight into the notoriously difficult structure of Bayesian reasoning situations. In contrast to many other visualizations (e.g., icon arrays, Euler diagrams), 2 × 2 tables and tree diagrams have the advantage that they can be constructed easily. The implications of our findings for teaching Bayesian reasoning will be discussed.
authors.affiliation: Mathematics Education, Faculty of Mathematics, University of Regensburg Regensburg, Germany.
authors.forename: Karin
authors.initials: K
authors.lastname: Binder
authors.affiliation: Mathematics Education, Faculty of Mathematics, University of Regensburg Regensburg, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Krauss
authors.affiliation: Mathematics Education, Faculty of Mathematics, University of Regensburg Regensburg, Germany.
authors.forename: Georg
authors.initials: G
authors.lastname: Bruckmaier
keywords: 2 × 2 table; Bayesian reasoning; natural frequencies; natural sampling tree; visual representation