Sets or frequencies? How to help people solve conditional probability problems

Moro, Rodrigo; Bodanza, Gustavo A.; Freidin, Esteban

doi:10.1080/20445911.2011.579072

Cited by 18 publications

(25 citation statements)

References 21 publications

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“…However, since the unit square is only predominant for subset relations that are not in line with the hierarchy of the tree diagram, we attribute this effect to the graphical transparency of the relevant subset relation and not to the area-proportionality. Therefore, we can argue that the measured effect is not due to a possible “frequentist reading” (Moro et al, 2011, p. 849) of the unit square.…”

Section: Resultsmentioning

confidence: 85%

The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares

Böcherer-Linder

Eichler

2017

Front. Psychol.

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It is an ongoing debate, what properties of visualizations increase people’s performance when solving Bayesian reasoning tasks. In the discussion of the properties of two visualizations, i.e., the tree diagram and the unit square, we emphasize how both visualizations make relevant subset relations transparent. Actually, the unit square with natural frequencies reveals the subset relation that is essential for the Bayes’ rule in a numerical and geometrical way whereas the tree diagram with natural frequencies does it only in a numerical way. Accordingly, in a first experiment with 148 university students, the unit square outperformed the tree diagram when referring to the students’ ability to quantify the subset relation that must be applied in Bayes’ rule. As hypothesized, in a second experiment with 143 students, the unit square was significantly more effective when the students’ performance in tasks based on Bayes’ rule was regarded. Our results could inform the debate referring to Bayesian reasoning since we found that the graphical transparency of nested sets could explain these visualizations’ effect.

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Section: Resultsmentioning

confidence: 85%

The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares

Böcherer-Linder

Eichler

2017

Front. Psychol.

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“…Furthermore, the results of the behavioural performances on the MHD show that when giving conditional feedback, the numerical representation of feedback is important. Previous research on the MHD (Aaron & Spivey-Knowlton, 1998;Krauss & Wang, 2003;Tubau, 2008) and other conditional probability problems (e.g., Gigerenzer, 1991Gigerenzer, , 1994Gigerenzer & Hoffrage, 1995;Moro et al, 2011) have shown that participants perform better when the problems are presented in frequencies rather than in percentages or proportions. In our study, we did not replicate this overall superiority of the frequency manipulation as such.…”

Section: Discussionmentioning

confidence: 96%

“…This latter manipulation is based on research indicating that people perform better on conditional probability problems when the problem is stated in frequencies rather than in percentages or probabilities (e.g., Gigerenzer, 1991Gigerenzer, , 1994Gigerenzer & Hoffrage, 1995;Moro, Bodanza, & Freidin, 2011). As already mentioned above, this has also been demonstrated for the MHD by the research of Aaron and SpiveyKnowlton (1998), Krauss and Wang (2003), and Tubau (2008).…”

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confidence: 81%

A randomised Monty Hall experiment: The positive effect of conditional frequency feedback

Saenen

Dooren

Onghena

2014

Thinking & Reasoning

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The Monty Hall dilemma (MHD) is a notorious probability problem with a counterintuitive solution. There is a strong tendency to stay with the initial choice, despite the fact that switching doubles the probability of winning. The current randomised experiment investigates whether feedback in a series of trials improves behavioural performance on the MHD and increases the level of understanding of the problem. Feedback was either conditional or non-conditional, and was given either in frequency format or in percentage format. Results show that people learn to switch most when receiving conditional feedback in frequency format. However, problem understanding does not improve as a consequence of receiving feedback. Our study confirms the dissociation between behavioural performance on the MHD, on one hand, and actual understanding of the MHD, on the other. We discuss how this dissociation can be understood.

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“…We used a numerical and graphical pictorial format of the problems, expressed by frequencies, referring to classic works in the literature on this topic Girotto & Gonzalez, 2001;Moro et al, 2011).…”

Section: Probabilistic Reasoningmentioning

confidence: 99%

What’s about the Calibration between Confidence and Accuracy? Findings in Probabilistic Problems from Italy and Spain

Agus

Peró‐Cebollero

Guàrdia‐Olmos

et al. 2019

EURASIA J MATH SCI T

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This paper reports some experiments on probabilistic reasoning designed to investigate the impact of the probabilistic problem presentation format (verbalnumerical and graphical-pictorial) on subjects' confidence in the correctness of their performance, other than the calibration between confidence and accuracy. To understand the potential effect of the format, these dimensions were assessed by monitoring contextual and individual variables: time pressure, numerical and visuospatial abilities, statistical anxiety and attitudes towards statistics. The participants included 257 Psychology students without statistical knowledge, recruited from Italian and Spanish universities, who fulfilled self-report validated measures. The students expressed their retrospective judgments of confidence item-by-item in relation to each probabilistic problem. This approach enabled the computation of two measures of calibration (the Bias Index-the Confidence-Judgment Accuracy Quotient). The results indicated that the problem presentation format did not exert a significant main effect on confidence, with the exception of when the interaction between the format and one subscale of the attitudes towards the statistics test was considered. The Bias Index, however, was significantly related to the interaction between format and time pressure. The study offers a point of reflection in relation to the potential effect exerted by the problem format and time constraint in calibration.

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Sets or frequencies? How to help people solve conditional probability problems

Cited by 18 publications

References 21 publications

The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares

The Impact of Visualizing Nested Sets. An Empirical Study on Tree Diagrams and Unit Squares

A randomised Monty Hall experiment: The positive effect of conditional frequency feedback

What’s about the Calibration between Confidence and Accuracy? Findings in Probabilistic Problems from Italy and Spain

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