A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net

Binder, Karin; Krauss, Stefan; Wiesner, Patrick

doi:10.3389/fpsyg.2020.00750

Cited by 21 publications

(45 citation statements)

References 65 publications

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“…This result agrees with the findings of Bruckmaier et al (2019) regarding the analysis of people’s ability to identify conjoint probabilities in a tree diagram and a 2 × 2-table. Our results concur with the findings of Binder et al (2020) , who found that a 2 × 2-table facilitates identifying conjoint events compared to a double tree diagram. The result also goes along with our own finding in Böcherer-Linder et al (2018) that people’s performance can be increased by making the subset H ∩ D as intersection set, graphically transparent.…”

Section: Discussionsupporting

confidence: 92%

“…Nevertheless, there are some studies that did not find a facilitating effect of visualization (e.g., icon arrays in Sirota et al, 2014 ; Euler-diagrams in Brase, 2009 ). For this reason, and congruent with the research of Binder et al (2015) and Binder et al (2020) , we found that visualization in combination with natural frequencies strongly impacted people’s performance in Bayesian situations. We have analyzed differences in people’s performance concerning visualization before ( Böcherer-Linder and Eichler, 2019 ).…”

Section: Discussionsupporting

confidence: 90%

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Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

2020

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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.

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Section: Discussionsupporting

confidence: 92%

Section: Discussionsupporting

confidence: 90%

Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

2020

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“…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.…”

Section: The Matrix Lens Modelmentioning

confidence: 99%

“…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.…”

Section: The Matrix Lens Modelmentioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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Cognition is both empowered and limited by representations. The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such tasks, the model links several problems and semantic domains and provides a new perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems. The shared structural construct of a 2 × 2 matrix supports a set of generic tasks and semantic mappings that provide a unifying framework for understanding problems and defining scientific measures. Our model's key explanatory mechanism is the adoption of particular perspectives on a 2 × 2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization. As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation. To demonstrate the explanatory scope of our model, we use it to clarify theoretical debates on biases and facilitation effects in Bayesian reasoning and to integrate the scientific measures from various semantic domains within a unifying framework. A better understanding of problem structures, representational transparency, and the role of perspectives in the scientific process yields both theoretical insights and practical applications.

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Stochastik: Leitidee Daten und Zufall

Biehler,

Engel,

Frischemeier

2023

Handbuch Der Mathematikdidaktik

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A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net

Cited by 21 publications

References 65 publications

Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

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

Stochastik: Leitidee Daten und Zufall

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