Using Tree Diagrams without Numerical Values in Addition to Relative Numbers Improves Students’ Numeracy Skills

Friederichs, Hendrik; Ligges, Sandra; Weissenstein, Anne

doi:10.1177/0272989x13504499

Cited by 21 publications

(15 citation statements)

References 22 publications

(32 reference statements)

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“…With visualizations that contain numbers (i.e., tree diagrams or Eikosograms), the format of these numbers can make a difference in how participants understand the statistical information. For instance, it must be noted that in the 1-test case, only tree diagrams containing natural frequencies in the nodes, not tree diagrams with probabilities at the branches [ 14 , 23 ] or without any numerical information [ 43 ], significantly foster insight into Bayesian reasoning problems.…”

Section: The Medical 1-test Casementioning

confidence: 99%

Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making

et al. 2018

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In medicine, diagnoses based on medical test results are probabilistic by nature. Unfortunately, cognitive illusions regarding the statistical meaning of test results are well documented among patients, medical students, and even physicians. There are two effective strategies that can foster insight into what is known as Bayesian reasoning situations: (1) translating the statistical information on the prevalence of a disease and the sensitivity and the false-alarm rate of a specific test for that disease from probabilities into natural frequencies, and (2) illustrating the statistical information with tree diagrams, for instance, or with other pictorial representation. So far, such strategies have only been empirically tested in combination for “1-test cases”, where one binary hypothesis (“disease” vs. “no disease”) has to be diagnosed based on one binary test result (“positive” vs. “negative”). However, in reality, often more than one medical test is conducted to derive a diagnosis. In two studies, we examined a total of 388 medical students from the University of Regensburg (Germany) with medical “2-test scenarios”. Each student had to work on two problems: diagnosing breast cancer with mammography and sonography test results, and diagnosing HIV infection with the ELISA and Western Blot tests. In Study 1 (N = 190 participants), we systematically varied the presentation of statistical information (“only textual information” vs. “only tree diagram” vs. “text and tree diagram in combination”), whereas in Study 2 (N = 198 participants), we varied the kinds of tree diagrams (“complete tree” vs. “highlighted tree” vs. “pruned tree”). All versions were implemented in probability format (including probability trees) and in natural frequency format (including frequency trees). We found that natural frequency trees, especially when the question-related branches were highlighted, improved performance, but that none of the corresponding probabilistic visualizations did.

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Section: The Medical 1-test Casementioning

confidence: 99%

Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making

et al. 2018

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“…Various types of visualizations have been tested, including Euler diagrams [1,25,29], frequency grids or icon arrays [16,25,29,32,35], decision trees [13,35,37], "beam cut" diagrams [17], probability curves [7], contingency tables [7,8] and interactive designs [38]. While some researchers have compared several visualization designs [1,29,32], many of these visualizations were proposed and tested separately.…”

Section: Related Workmentioning

confidence: 99%

“…For example, results from Brase [1] and work by Garcia-Retamero and Hoffrage [16] suggest that visual aids such as Euler diagrams and icon arrays hold promise. Researchers have also explored visualizations such as decision trees [13,28], contingency tables [7], "beam cut" diagrams [17] and probability curves [7], and have shown improvements over textonly representations. However, when researchers in the visualization community extended this work to a more diverse sampling of the general population, they found that adding visualizations to existing text representations did not significantly increase accuracy [29,32].…”

Section: Introductionmentioning

confidence: 99%

Improving Bayesian Reasoning: The Effects of Phrasing, Visualization, and Spatial Ability

Ottley

Peck

Harrison

et al. 2016

IEEE Trans. Visual. Comput. Graphics

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Abstract-Decades of research have repeatedly shown that people perform poorly at estimating and understanding conditional probabilities that are inherent in Bayesian reasoning problems. Yet in the medical domain, both physicians and patients make daily, life-critical judgments based on conditional probability. Although there have been a number of attempts to develop more effective ways to facilitate Bayesian reasoning, reports of these findings tend to be inconsistent and sometimes even contradictory. For instance, the reported accuracies for individuals being able to correctly estimate conditional probability range from 6% to 62%. In this work, we show that problem representation can significantly affect accuracies. By controlling the amount of information presented to the user, we demonstrate how text and visualization designs can increase overall accuracies to as high as 77%. Additionally, we found that for users with high spatial ability, our designs can further improve their accuracies to as high as 100%. By and large, our findings provide explanations for the inconsistent reports on accuracy in Bayesian reasoning tasks and show a significant improvement over existing methods. We believe that these findings can have immediate impact on risk communication in health-related fields.

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“…However, the additional representation of a roulette wheel diagram causes only a very small or even no improvement in performance compared to versions without any visual aid ( Brase, 2014 ). Friederichs et al (2014) investigated tree diagrams without numerical values (except an imaginary sample size). In their studies, performance in probability versions with tree diagrams was similar to the performance in natural frequency versions without visualization.…”

Section: Introductionmentioning

confidence: 99%

Effects of visualizing statistical information – an empirical study on tree diagrams and 2 × 2 tables

2015

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In their research articles, scholars often use 2 × 2 tables or tree diagrams including natural frequencies in order to illustrate Bayesian reasoning situations to their peers. Interestingly, the effect of these visualizations on participants’ performance has not been tested empirically so far (apart from explicit training studies). In the present article, we report on an empirical study (3 × 2 × 2 design) in which we systematically vary visualization (no visualization vs. 2 × 2 table vs. tree diagram) and information format (probabilities vs. natural frequencies) for two contexts (medical vs. economical context; not a factor of interest). Each of N = 259 participants (students of age 16–18) had to solve two typical Bayesian reasoning tasks (“mammography problem” and “economics problem”). The hypothesis is that 2 × 2 tables and tree diagrams – especially when natural frequencies are included – can foster insight into the notoriously difficult structure of Bayesian reasoning situations. In contrast to many other visualizations (e.g., icon arrays, Euler diagrams), 2 × 2 tables and tree diagrams have the advantage that they can be constructed easily. The implications of our findings for teaching Bayesian reasoning will be discussed.

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Using Tree Diagrams without Numerical Values in Addition to Relative Numbers Improves Students’ Numeracy Skills

Abstract: We suggest the use of a tree diagram as a visual aid when dealing with diagnostic tests expressed in conditional probabilities.

Cited by 21 publications

References 22 publications

Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making

Visualizing the Bayesian 2-test case: The effect of tree diagrams on medical decision making

Improving Bayesian Reasoning: The Effects of Phrasing, Visualization, and Spatial Ability

Effects of visualizing statistical information – an empirical study on tree diagrams and 2 × 2 tables

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