Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five visualizations: a 2×2-table, a unit (...) square, an icon array, a tree diagram, and a double-tree diagram. In an experiment with 688 undergraduate students, we empirically investigated the effectiveness of three graphical properties of visualizations: area-proportionality, use of discrete and countable statistical entities, and graphical transparency of the nested-sets structure. We found no additional beneficial effect of area-proportionality. In contrast, the representation of discrete objects seems to be beneficial. Furthermore, our results show a strong facilitating effect of making the nested-sets structure of a Bayesian situation graphically transparent. Our results contribute to answering the questions of how and why a visualization could facilitate judgment and decision making in situations of uncertainty. (shrink)

People often struggle with Bayesian reasoning. However, research showed that people’s performance (and rationality) can be supported by the way of representing the statistical information. First, research showed that using natural frequencies instead of probabilities as format of statistical information increases people’s performance in Bayesian situations thoroughly. Second, research also yielded that people’s performance increases through using visualization. We build our paper on existing research in this field. The main aim is to analyse people’s strategies in Bayesian situations that are (...) still erroneous although statistical information is represented by natural frequencies and visualizations. In particular, we compare two pairs of visualization with similar numerical information (tree diagram vs. unit square and double-tree diagram vs. 2x2-table) concerning their impact on people’s erroneous strategies in Bayesian situations. For this aim, we conducted an experiment with 540 university students. The students were randomly assigned to four conditions that are defined by the four different visualizations of statistical information. The students were asked to indicate a fraction as response in four Bayesian situations. We documented the numerator and the denominator of the students’ responses representing a basic set and a subset in a Bayesian situation. Our results show that people’s erroneous strategies are highly dependent on the visualization. A central finding is that the visualization’s characteristic of making the nested-sets structure of a Bayesian situation transparent has a facilitating effect on people’s Bayesian reasoning. For example, compared to the unit square, a tree diagram does not explicitly visualize the set-subset relations that are relevant in a Bayesian situation. Accordingly, compared to a unit square, a tree diagram partly hinders people to find the correct denominator in a Bayesian situation, and, in particular, triggers to select a wrong numerator. By analyzing people’s erroneous strategies in Bayesian situations, we contribute to investigating approaches to facilitate Bayesian reasoning and to further develop the teaching of Bayesian reasoning. (shrink)