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Analysis of erroneous strategies in Bayesian Reasoning

Bayes‘ formula is a fundamental model for estimating risks. It is of essence in probability theory and in various professions such as medicine and law. Yet, multiple research results from cognitive psychology and mathematics education suggest that learners as well as experts struggle immensely when judging Bayesian situations (we thereby understand situations in which Bayes’ formula can be applied). Based on the relevance of adequately judging Bayesian situations, much empirical research is carried out in order to detect influences on the performance of participants in studies about Bayesian situations. Two strategies are particularly relevant for increasing performance, first the format of the statistical information in a Bayesian situation in so-called natural frequencies (e.g., “80 out of 100 people” instead of probabilities such as “80%”) and second the visualization of the statistical information. So far, it has been shown that depending on the support the performance of Bayesian situation varies between 5% without any support, 25% if the statistical information is given in natural frequencies and 60-75% for comprehensive support in form of a visualization in combination with natural frequencies. Despite all different strategies, which may be used in Bayesian situations, a considerable proportion of erroneous strategies is still observed in all samples. Yet, so far studies on identifying the erroneous strategies are rare. However, empirical results on typical erroneous strategies are central as they are part of every learning process. Moreover, to know about erroneous strategies is important for regulating the learning process and therefore for successful learning. After all, it can also be useful to know about erroneous strategies in the sense of “error-knowledge”. The few contributions on erroneous strategies in Bayesian situations have shown that different typical strategies are used by the participants of the studies. However, some of the studies find partially contrasting results. The differences may be based on different contexts of the Bayesian situation, the format of the statistical information, the visualization or the question type. Therefore, it is a central interest of this project to systematize and broaden the knowledge on erroneous strategies in Bayesian situations. For that, we plan to systematically vary the format of the statistical information (natural frequencies vs. probabilities), the kind of visualization and the question type for the first time. The results should contribute to the understanding of the construct of Bayesian Reasoning, which goes beyond simply measuring the performance of participants.

 

Projektleitung:
Prof. Dr. Karin Binder
karin.binder@math.lmu.de
Prof. Dr. Andreas Eichler
eichler@mathematik.uni-kassel.de