# What are the alternatives to Bayesian thinking

## Bayesian thinking - step by step - enable insights into complex problems with frequencies and tree diagrams

Show me more biostatistics! pp 87-99 | Cite as

- Karin Binder
- Jörg Marienhagen

### Summary

Bayesian tasks represent a special cognitive challenge for students in medicine. Because both patients and medical students and doctors have difficulty calculating a positive or negative predictive value if the prevalence of the disease is with the sensitivity and false-positive rate of a diagnostic test must be combined.

A look at the common medical textbooks from biometrics shows that Bayesian tasks are predominantly introduced conventionally via the concept of conditional probabilities and that new didactic approaches are not yet adequately used. Often the introduction remains too closely linked to Bayes' formula, or percentages are used to clarify the facts. However, these approaches are not suitable for explaining Bayesian tasks in an understandable way.

As part of this article, we would like to present a didactic concept for the introduction of Bayesian tasks, which is to be further developed into an online course. The concept is based on three essential steps, which we consider important to optimally explain Bayesian tasks: The first step consists in translating the probabilities - which are often shown as percentages (e.g. 80%) - into so-called "natural frequencies" (e.g. 8 out of 10). The second step is the additional presentation of a tree diagram, which also contains natural frequencies, in order to visualize the complicated facts of Bayesian tasks. The third step is to highlight those branches of the tree diagram that are essential for answering the question. The correct result of the task can then be read off directly.

Using concrete sample tasks, it should be illustrated how Bayesian tasks can be introduced easily and clearly using these three steps.

Additional teaching material for easy application of the submitted teaching ideas is available on the Springer homepage http://www.springer.com/978-3-662-54824-0.

### attachment

Exercise sheet on the subject of HIV test,

Solution sketch of the exercise sheet on the subject of HIV testing.

### literature

- Binder K, Krauss S, Bruckmaier G (2015) Effects of visualizing statistical information - an empirical study on tree diagrams and 2 × 2 tables. Front Psychol. 6: 1186Google Scholar
- Eddy DM (1982) Probabilistic reasoning in clinical medicine: problems and opportunities. In Kahneman D, Slovic P, Tversky A (Eds) Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, New York pp. 249-267 CrossRefGoogle Scholar
- Garcia-Retamero R, Hoffrage U (2013) Visual representation of statistical information improves diagnostic inferences in doctors and their patients. Soc Sci Med 83: 27-33 CrossRefGoogle Scholar
- Gigerenzer G, Hoffrage U (1995) How to improve Bayesian reasoning without instruction: frequency formats. Psychol Rev 102: 684-704 CrossRefGoogle Scholar
- Hoffrage U, Gigerenzer G (1998) Using natural frequencies to improve diagnostic inferences. Acad Med 73: 538-540 CrossRefGoogle Scholar
- Sedlmeier P, Gigerenzer G (2001) Teaching Bayesian reasoning in less than two hours. J Exp Psychol Gen. 130: 380-400 Google Scholar
- Siegrist M, Keller C (2011) Natural frequencies and Bayesian reasoning: the impact of formal education and problem context. J. Risk Res 14: 1039-1055 CrossRefGoogle Scholar
- Wassner C, Martignon L, Biehler R (2004) Bayesian thinking in schools. Educational Science 32: 58–96Google Scholar

### Copyright information

### Authors and Affiliations

- 1. Didactics of the Mathematics University of RegensburgRegensburgGermany
- 2.Universitätsklinikum RegensburgRegensburgGermany

- What are positions in stocks
- How does a pressure gauge work
- What does rational order mean
- What is the greatest mistake in science
- Requires ICWA mathematics
- Recognizes Turnitin research that has been purchased
- How safe are Indian uranium reserves
- What is Gentle Giants' most successful song
- How many bighas are there in a morning
- What is the thad system
- Does Allah know our future sins
- Should I trust recruiters
- Who is your childhood hero
- What breed of dog is the best
- Are rice beetles problems for farmers
- What is the importance of the delivery of food
- What would you change in human biology?
- How intelligent is Quora's AI
- What do the interest rates relate to
- What is the mission statement of National Trusts
- What is Greta Thunberg's next project
- Is Kakashi stronger and smarter than Tobirama
- Is it satisfying to be a pilot?
- How is Obama seen in Sweden?