Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

Abstract

People often struggle with Bayesian reasoning. However, previous research showed that people's performance (and rationality) can be supported by the way the statistical information is represented. First, research showed that using natural frequencies instead of probabilities as the format of statistical information significantly increases people's performance in Bayesian situations. Second, research also revealed that people's performance increases through using visualization. We have built our paper on existing research in this field. Our main aim was to analyze people's strategies in Bayesian situations that are erroneous even though statistical information is represented as natural frequencies and visualizations. In particular, we compared two pairs of visualization with similar numerical information (tree diagram vs. unit square, and double-tree diagram vs. 2 × 2-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 defined by the four different visualizations of statistical information. The students were asked to indicate a fraction in response to four Bayesian situations. We documented the numerator and denominator of the students' responses representing a basic set and a subset in a Bayesian situation. Our results showed that people's erroneous strategies are highly dependent on visualization. A central finding was 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 in finding the correct denominator in a Bayesian situation, and, in particular, triggers selecting 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.

Perspectives on the 2 × 2 Matrix: Solving Semantically Distinct Problems Based on a Shared Structure of Binary Contingencies

“…Using a matrix-based framework for structuring our analysis primarily provides us with a methodological tool. Thus, rather than claiming that the 2 × 2 matrix provides a superior type of visualization (see e.g., Binder et al, 2020 ; Eichler et al, 2020 , for comparisons between alternatives), we use its geometric potential for distinguishing between locations and directions.…”

“…While most people agree that most presentations of scientific findings benefit from clear and transparent visualizations (e.g., Tufte, 2001 ), precisely explaining why visualization help remains challenging (see Streeb et al, 2020 , for a systematic review). A full-fledged theory of visualizing metrics derived from 2 × 2 matrices is still lacking (though see, e.g., Micallef et al, 2012 ; Binder et al, 2015 , 2020 ; Khan et al, 2015 ; Böcherer-Linder and Eichler, 2017 , 2019 ; Eichler et al, 2020 , for studies contrasting specific types of visualizations). But as we began this article with Simon's ( 1981 ) notion that a problem's solution lies in its transparent representation, we owe an account of what renders representations transparent.…”

“…Although such icons seem suitable for expressing frequencies, probabilities, and conditional probabilities in a compact fashion, they assume a framed 2 × 2 matrix and reach their limits for more complex measures (e.g., the aggregate scores of Figure 6 or Table 3 ). Additional options for visually explicating particular perspectives on tasks involving probabilistic measures include icon arrays, unit squares, tables, tree diagrams , and frequency nets (see Neth et al, 2018 , for generating different visualizations from a shared representation, and Binder et al, 2015 , 2020 , and Böcherer-Linder at al., 2019 , 2020 for empirical comparisons).…”

“…In addition to the theoretical challenge of explaining people's poor performance, researchers in applied psychology, clinical diagnostics, and information visualization face the practical challenge of improving it. In numerous attempts to train people (e.g., Sedlmeier and Gigerenzer, 2001 ; Ruscio, 2003 ; Sirota et al, 2015 ) or support their performance by visual aids (e.g., Brase, 2008 ; Moro et al, 2011 ; Garcia-Retamero and Hoffrage, 2013 ; Binder et al, 2015 , 2020 ; Böcherer-Linder and Eichler, 2017 ; Eichler et al, 2020 ), solutions rates remained frustratingly low (e.g., Micallef et al, 2012 ; Khan et al, 2015 ; Weber et al, 2018 ). Thus, despite considerable progress, it is still controversial to what extent humans are able to solve such problems, how they perform the required calculations, and which aspects of the task, person, or task environment help or hinder their performance (see Navarrete and Mandel, 2016 ; McDowell and Jacobs, 2017 , for reviews).…”

Improving Diagnostic Efficiency with Frequency Double-Trees and Frequency Nets in Bayesian Reasoning

“… 2 Presenting natural frequencies in Bayesian tasks leads to significantly more correct results. 17 – 19 The thyroid cancer problem with natural frequencies reads as follows:…”