Study on how to train Bayesian reasoning
Experts within various disciplines have to evaluate a situation based on evidence that is not 100% reliable. Medical science and law are two important examples of domains in which this is part of the experts' daily routine. Physicians and judges can use one of the pivotal equations in probability theory, Bayes' theorem, in order to reason about many of their decisions.
Bayes' theorem determines how the probability of a hypothesis (such as the medical condition of a patient or guilt of an accused person) changes when new data (such as the test results of a medical test or forensic evidence) becomes known.
Nevertheless, Bayesian reasoning in the sense of updating one's hypothesis on the basis of relevant data can be of considerable difficulty not only for lay people but also for experts. Practitioners in the medical field and judiciary system have to make decisions with significant consequences (e. g. about further medical treatment or about criminal sanctions) despite lacking unconditional certainty. Yet, within these two domains especially, a multitude of false judgements with tragic consequences have been documented.
Thus, given the relevance of Bayesian reasoning, there is an abundance of research in psychology as well as mathematical pedagogy on potentially successful strategies to foster Bayesian reasoning. So far, two of these strategies, the first being the representation of statistical information in form of natural frequencies, and the second being certain visualizations which display the statistical information, proved to support Bayesian reasoning.
This research project intends to systematically combine the strategies already developed (natural frequencies, visualizations) into a training course and to experimentally test it on students in the fields of medicine and law. Thereby, two ideal training courses (both with natural frequencies and either a unit square or a double-tree as a visualization) and two control training courses (only natural frequencies or the standard curriculum training) are implemented and compared to each other and a control group without any training in a pre-post-follow up study design. The effects of the training courses are measured in (1) the performance of Bayesian tasks, (2) the ability to estimate the effects of variations in the given parameters (covariation) and (3) the ability to evaluate expert-layperson-communication. With this study the research group aims to identify domain dependant and domain independent factors which promote Bayesian reasoning.
This approach to study Bayesian reasoning is innovative in the sense of expanding the components of Bayesian reasoning by also recognizing covariation and communication as elements of Bayesian thinking. Moreover, this research is unprecedented as it does not only test performance and understanding of covariation as results (product) but also determines the cognitive strategies (processes) which induces the outcome by applying the write-aloud method and by analysing the (non-Bayesian) interim results and mistakes.
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Project leadership:
Prof. Dr. Andreas Eichler
eichler@mathematik.uni-kassel.de
Prof. Dr. Stefan Krauss
Stefan.Krauss@mathematik.uni-regensburg.de
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