Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung?

Binder, Karin; Steib, Nicole; Krauss, Stefan

doi:10.1007/s13138-022-00215-9

Cited by 3 publications

(4 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The tree diagram, the double tree, and the net diagram have a node-branch structure in which probabilities can be entered at the branches ( Figure 2 , left) and frequencies in the nodes ( Figure 2 , right). Nevertheless, frequencies and probabilities can, in principle, also be included simultaneously (imagine putting the left and the right visualization on top of each other), which makes it possible to depict both formats into the visualization at once ( Binder et al, 2023 ). Thereby, the net diagram is the only visualization that can display all 16 probabilities.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

How general is the natural frequency effect? The case of joint probabilities

Stegmüller,

Binder,

Krauss

2024

Front. Psychol.

Self Cite

View full text Add to dashboard Cite

Natural frequencies are known to improve performance in Bayesian reasoning. However, their impact in situations with two binary events has not yet been completely examined, as most researchers in the last 30 years focused only on conditional probabilities. Nevertheless, situations with two binary events consist of 16 elementary probabilities and so we widen the scope and focus on joint probabilities. In this article, we theoretically elaborate on the importance of joint probabilities, for example, in situations like the Linda problem. Furthermore, we implemented a study in a 2×5×2 design with the factors information format (probabilities vs. natural frequencies), visualization type (“Bayesian text” vs. tree diagram vs. double tree diagram vs. net diagram vs. 2×2 table), and context (mammography vs. economics problem). Additionally, all four “joint questions” (i.e., P(A∩B),P(A¯∩B),P(A¯∩B¯),P(A∩B¯)) were asked for. The main factor of interest was whether there is a format effect in the five visualization types named above. Surprisingly, the advantage of natural frequencies was not found for joint probabilities and, most strikingly, the format interacted with the visualization type. Specifically, while people’s understanding of joint probabilities in a double tree seems to be worse than the understanding of the corresponding natural frequencies (and, thus, the frequency effect holds true), the opposite seems to be true in the 2 × 2 table. Hence, the advantage of natural frequencies compared to probabilities in typical Bayesian tasks cannot be found in the same way when joint probability or frequency tasks are asked.

show abstract

Section: Theoretical Frameworkmentioning

confidence: 99%

How general is the natural frequency effect? The case of joint probabilities

Stegmüller,

Binder,

Krauss

2024

Front. Psychol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Typical visualizations are, for example, tree diagrams or 2 × 2 tables (for an overview of a variety of alternative visualizations such as roulette-wheel diagrams or frequency grids, see Spiegelhalter et al, 2011 or Binder et al, 2015 ). In the present study, we chose enhancements of tree diagrams and 2 × 2 tables, namely double-trees ( Binder et al, 2022 ) and unit squares ( Böcherer-Linder and Eichler, 2017 ; Pfannkuch and Budgett, 2017 ; Talboy and Schneider, 2017 ). Both visualizations are suited to calculation and covariation as well, and can, in principle, be equipped with probabilities and/or absolute frequencies.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Considering the multiple representations of covariation in 2.2, the question arises which visualization should be implemented in order to allow a understanding of the previous conventional Bayesian reasoning task. Since both the formulas and the graphical representation ( Figure 2 ) are based on probabilities (which has proven to be a disadvantageous format in many studies), we chose double-tree diagrams and unit squares (which have already proven helpful in conventional Bayesian reasoning; Böcherer-Linder and Eichler, 2017 ; Binder et al, 2022 ). The structure of the visualization was explained to participants in advance in written form using a different context ( Supplementary material 1S, 2S ).…”

Section: Research Questionsmentioning

confidence: 99%

Measuring people’s covariational reasoning in Bayesian situations

Steib,

Krauss,

Binder

et al. 2023

Front. Psychol.

Self Cite

View full text Add to dashboard Cite

Previous research on Bayesian reasoning has typically investigated people’s ability to assess a posterior probability (i.e., a positive predictive value) based on prior knowledge (i.e., base rate, true-positive rate, and false-positive rate). In this article, we systematically examine the extent to which people understand the effects of changes in the three input probabilities on the positive predictive value, that is, covariational reasoning. In this regard, two different operationalizations for measuring covariational reasoning (i.e., by single-choice vs. slider format) are investigated in an empirical study with N = 229 university students. In addition, we aim to answer the question wheter a skill in “conventional” Bayesian reasoning is a prerequisite for covariational reasoning.

show abstract

“…However, they already provide an idea of what visualisations may look like when designed according to multimedia principles (lowest row). Empirical studies have investigated a wide variety of visualisations that have been proven to support Bayesian Reasoning: tree diagrams (e.g., [13,29,39,40]), doubletrees (e.g., [15,34,41]), unit squares (e.g., [42][43][44]); 2 × 2 tables (e.g., [35,45]), icon arrays (e.g., [36,46,47]), frequency nets [34,48] and others were all found to increase performance in Bayesian Reasoning. However, there are also visualisations that provide little or no support (e.g., Euler diagrams as in [49]).…”

Section: Visualisations and Bayesian Reasoningmentioning

confidence: 99%

Designing Visualisations for Bayesian Problems According to Multimedia Principles

et al. 2022

View full text Add to dashboard Cite

Questions involving Bayesian Reasoning often arise in events of everyday life, such as assessing the results of a breathalyser test or a medical diagnostic test. Bayesian Reasoning is perceived to be difficult, but visualisations are known to support it. However, prior research on visualisations for Bayesian Reasoning has only rarely addressed the issue on how to design such visualisations in the most effective way according to research on multimedia learning. In this article, we present a concise overview on subject-didactical considerations, together with the most fundamental research of both Bayesian Reasoning and multimedia learning. Building on these aspects, we provide a step-by-step development of the design of visualisations which support Bayesian problems, particularly for so-called double-trees and unit squares.

show abstract

Von Baumdiagrammen über Doppelbäume zu Häufigkeitsnetzen – kognitive Überlastung oder didaktische Unterstützung?

Cited by 3 publications

References 34 publications

How general is the natural frequency effect? The case of joint probabilities

How general is the natural frequency effect? The case of joint probabilities

Measuring people’s covariational reasoning in Bayesian situations

Designing Visualisations for Bayesian Problems According to Multimedia Principles

Contact Info

Product

Resources

About