Project Details
Projekt
Error analyses for Bayesian reasoning
Subject Area
General and Domain-Specific Teaching and Learning
General, Cognitive and Mathematical Psychology
General, Cognitive and Mathematical Psychology
Term
since 2022
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 499726865
The formula of Bayes is a central model for the assessment of situations under uncertainty and it is of fundamental importance in many professions such as medicine. However, there are numerous findings from the fields of cognitive psychology and mathematics education that show that even experts have difficulties and struggle in judging Bayesian situations - i.e., situations in which the formula of Bayes can be applied. Due to the importance of correct judgements in Bayesian situations, there are many studies investigating possible effects on the performance of participants in Bayesian situations. In particular, the format of the statistical information in a Bayesian situation as "natural frequencies" ("80 out of 100 people" instead of probabilities "80%") and the visualization of the statistical information have been shown to increase performance. So far, solution rates have been reported dependent on the supportive tools, namely 5% in the textual format in probabilities, 25% when natural frequencies are used instead, and 60-75% when natural frequencies are used in combination with a supportive visualization. Despite all strategies to increase participants’ performance in Bayesian situations, there remains a high rate of erroneous solutions in all populations studied. Nevertheless, studies investigating erroneous solutions are very rare so far. However, empirical findings on error patterns are central, as they are a part of any learning process. Errors are also important for successful learning and are effective learning material in the sense of "error knowledge." The limited work on errors in Bayesian situations has shown that typical error patterns can be distinguished in participants’ responses. However, different studies have shown partly contradictory results, which might be due to different contexts in Bayesian situations, different formats of statistical information, varying visualizations, or different formats of the question. Therefore, the main focus of the present project is to systematize and extend the existing knowledge on error patterns in Bayesian situations. For this purpose, the format of statistical information (natural frequencies vs. probabilities), the type of a supporting visualization, and the format of the question will be systematically varied for the first time in Bayesian situations. The thus varied Bayesian situations will be incorporated into a test instrument that will be used with different populations of students. The results are expected to contribute to an understanding of the construct of Bayesian reasoning that goes beyond simply measuring the performance of participants.
DFG Programme
Research Grants
