A visualization technique for Bayesian reasoning

Bayesian versus diagnostic information in physician-patient communication: Effects of direction of statistical information and presentation of visualization

BACKGROUND

Communicating well with patients is a competence central to everyday clinical practice, and communicating statistical information, especially in Bayesian reasoning tasks, can be challenging. In Bayesian reasoning tasks, information can be communicated in two different ways (which we call directions of information): The direction of Bayesian information (e.g., proportion of people tested positive among those with the disease) and the direction of diagnostic information (e.g., the proportion of people having the disease among those tested positive). The purpose of this study was to analyze the impact of both the direction of the information presented and whether a visualization (frequency net) is presented with it on patient's ability to quantify a positive predictive value.

MATERIAL AND METHODS

109 participants completed four different medical cases (2⨯2⨯4 design) that were presented in a video; a physician communicated frequencies using different directions of information (Bayesian information vs. diagnostic information). In half of the cases for each direction, participants were given a frequency net. After watching the video, participants stated a positive predictive value. Accuracy and speed of response were analyzed.

RESULTS

Communicating with Bayesian information led to participant performance of only 10% (without frequency net) and 37% (with frequency net) accuracy. The tasks communicated with diagnostic information but without a frequency net were correctly solved by 72% of participants, but accuracy rate decreased to 61% when participants were given a frequency net. Participants with correct responses in the Bayesian information version without visualization took longest to complete the tasks (median of 106 seconds; median of 13.5, 14.0, and 14.5 seconds in other versions).

DISCUSSION

Communicating with diagnostic information rather than Bayesian information helps patients to understand specific information better and more quickly. Patients' understanding of the relevance of test results is strongly dependent on the way the information is presented.

The Use of Visualizations to Improve Bayesian Reasoning: A Literature Review

Decisions are often made under uncertainty. The most that one can do is use prior knowledge (e.g., base rates, prior probabilities, etc.) and make the most probable choice given the information we have. Unfortunately, most people struggle with Bayesian reasoning. Poor performance within Bayesian reasoning problems has led researchers to investigate ways to improve Bayesian reasoning. Many have found success in using natural frequencies instead of probabilities to frame problems. Beyond the quantitative format, there is growing literature on the use of visualizations or visual representations to improve Bayesian reasoning, which will be the focus of this review. In this review, we discuss studies that have found visualizations to be effective for improving Bayesian reasoning in a lab or classroom setting and discuss the considerations for using visualizations, paying special attention to individual differences. In addition, we will review the factors that influence Bayesian reasoning, such as natural frequencies vs. probabilities, problem format, individual differences, and interactivity. We also provide general and specific suggestions for future research.

How to Train Novices in Bayesian Reasoning

Bayesian Reasoning is both a fundamental idea of probability and a key model in applied sciences for evaluating situations of uncertainty. Bayesian Reasoning may be defined as the dealing with, and understanding of, Bayesian situations. This includes various aspects such as calculating a conditional probability (performance), assessing the effects of changes to the parameters of a formula on the result (covariation) and adequately interpreting and explaining the results of a formula (communication). Bayesian Reasoning is crucial in several non-mathematical disciplines such as medicine and law. However, even experts from these domains struggle to reason in a Bayesian manner. Therefore, it is desirable to develop a training course for this specific audience regarding the different aspects of Bayesian Reasoning. In this paper, we present an evidence-based development of such training courses by considering relevant prior research on successful strategies for Bayesian Reasoning (e.g., natural frequencies and adequate visualizations) and on the 4C/ID model as a promising instructional approach. The results of a formative evaluation are described, which show that students from the target audience (i.e., medicine or law) increased their Bayesian Reasoning skills and found taking part in the training courses to be relevant and fruitful for their professional expertise.

Applying Insights on Categorisation, Communication, and Dynamic Decision-Making: A Case Study of a ‘Simple’ Maritime Military Decision

A complete understanding of decision-making in military domains requires gathering insights from several fields of study. To make the task tractable, here we consider a specific example of short-term tactical decisions under uncertainty made by the military at sea. Through this lens, we sketch out relevant literature from three psychological tasks each underpinned by decision-making processes: categorisation, communication and choice. From the literature, we note two general cognitive tendencies that emerge across all three stages: the effect of cognitive load and individual differences. Drawing on these tendencies, we recommend strategies, tools and future research that could improve performance in military domains – but, by extension, would also generalise to other high-stakes contexts. In so doing, we show the extent to which domain general properties of high order cognition are sufficient in explaining behaviours in domain specific contexts.

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

Background. Medical students often have problems with Bayesian reasoning situations. Representing statistical information as natural frequencies (instead of probabilities) and visualizing them (e.g., with double-trees or net diagrams) leads to higher accuracy in solving these tasks. However, double-trees and net diagrams (which already contain the correct solution of the task, so that the solution could be read of the diagrams) have not yet been studied in medical education. This study examined the influence of information format (probabilities v. frequencies) and visualization (double-tree v. net diagram) on the accuracy and speed of Bayesian judgments. Methods. A total of 142 medical students at different university medical schools (Munich, Kiel, Goettingen, Erlangen, Nuremberg, Berlin, Regensburg) in Germany predicted posterior probabilities in 4 different medical Bayesian reasoning tasks, resulting in a 3-factorial 2 × 2 × 4 design. The diagnostic efficiency for the different versions was represented as the median time divided by the percentage of correct inferences. Results. Frequency visualizations led to a significantly higher accuracy and faster judgments than did probability visualizations. Participants solved 80% of the tasks correctly in the frequency double-tree and the frequency net diagram. Visualizations with probabilities also led to relatively high performance rates: 73% in the probability double-tree and 70% in the probability net diagram. The median time for a correct inference was fastest with the frequency double tree (2:08 min) followed by the frequency net diagram and the probability double-tree (both 2:26 min) and probability net diagram (2:33 min). The type of visualization did not result in a significant difference. Discussion. Frequency double-trees and frequency net diagrams help answer Bayesian tasks more accurately and also more quickly than the respective probability visualizations. Surprisingly, the effect of information format (probabilities v. frequencies) on performance was higher in previous studies: medical students seem also quite capable of identifying the correct solution to the Bayesian task, among other probabilities in the probability visualizations.

Different Visualizations Cause Different Strategies When Dealing With Bayesian Situations

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.

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

In teaching statistics in secondary schools and at university, two visualizations are primarily used when situations with two dichotomous characteristics are represented: 2 × 2 tables and tree diagrams. Both visualizations can be depicted either with probabilities or with frequencies. Visualizations with frequencies have been shown to help students significantly more in Bayesian reasoning problems than probability visualizations do. Because tree diagrams or double-trees (which are largely unknown in school) are node-branch structures, these two visualizations (in contrast to the 2 × 2 table) can even simultaneously display probabilities on branches and frequencies inside the nodes. This is a teaching advantage as it allows the frequency concept to be used to better understand probabilities. However, 2 × 2 tables and (double-)trees have a decisive disadvantage: While joint probabilities [e.g., P(A∩B)] are represented in 2 × 2 tables but no conditional probabilities [e.g., P(A|B)], it is exactly the other way around with (double-)trees. Therefore, a visualization that is equally suitable for the representation of joint probabilities and conditional probabilities is desirable. In this article, we present a new visualization—the frequency net—in which all absolute frequencies and all types of probabilities can be depicted. In addition to a detailed theoretical analysis of the frequency net, we report the results of a study with 249 university students that shows that “net diagrams” can improve reasoning without previous instruction to a similar extent as 2 × 2 tables and double-trees. Regarding questions about conditional probabilities, frequency visualizations (2 × 2 table, double-tree, or net diagram with absolute frequencies) are consistently superior to probability visualizations, and the frequency net performs as well as the frequency double-tree. Only the 2 × 2 table with frequencies—the one visualization that participants were already familiar with—led to higher performance rates. If, on the other hand, a question about a joint probability had to be answered, all implemented visualizations clearly supported participants’ performance, but no uniform format effect becomes visible. Here, participants reached the highest performance in the versions with probability 2 × 2 tables and probability net diagrams. Furthermore, after conducting a detailed error analysis, we report interesting error shifts between the two information formats and the different visualizations and give recommendations for teaching probability.