Improving conventional and extended Bayesian reasoning

English: Conventional Bayesian reasoning as the process of updating probabilistic information based on new information (through calculation) is considered highly relevant but also counter-intuitive for professionals in domains such as medicine and law. While conventional Bayesian reasoning (in the form of calculation) is undoubtedly important, it has lately been pointed out that Bayesian reasoning entails more than calculation. As a consequence, the framework of Bayesian reasoning is extended by two aspects, i.e., covariation and communication, which go beyond the pure calculation of probabilities. The focus of the present dissertation in this extended framework of Bayesian reasoning is on calculation as the aspect of conventional Bayesian reasoning and on covariation as a particular aspect of extended Bayesian reasoning. With regard to conventional Bayesian reasoning, a low performance has frequently been observed and led to extensive research within the last three decades on how it can be improved. Thereby, natural frequencies as well as specific (but not all) visualisations have been identified as crucial strategies for improving Bayesian reasoning without instruction. However, even with these supportive strategies, performance is not satisfactory given the high relevance of correct Bayesian reasoning in the domains of medicine and law. Therefore, instruction is required. While existing training studies on conventional Bayesian reasoning provide valuable first insights for improving conventional Bayesian reasoning with instruction, they are often limited with regard to the effects of visualisations. Thus, to study the supportive effect of different visualisations is a desideratum which has not yet been addressed sufficiently for improving conventional Bayesian reasoning with instruction. Prior research about covariation as a particular aspect of extended Bayesian reasoning is very sparse. One study found that without instruction, performance is low. Another study focused on comparing two visualisations in their support for improving covariational reasoning, showing that such support differs between the two. Further research on how to improve covariational reasoning is missing and could be informative for improvement with and without instruction. This thesis is based on the work of the TrainBayes project with the aim of improving conventional and extended Bayesian reasoning with instruction. It contributes to the desiderata mentioned above with three peer-reviewed articles. Article 1 provides original empirical insights into covariational reasoning as a particular form of extended Bayesian reasoning from a preliminary study in the project. In a mixed-methods study, N = 173 future teachers responded to open-ended tasks on covariational reasoning. These responses are analysed based on the Structure of Observed Learning Outcome (SOLO) taxonomy and the resulting categories are analysed inferentially, e.g., with regard to the influence of particular visualisations. Article 2 presents evidence-based development of training courses on conventional and extended Bayesian reasoning for professionals, based on research about multimedia learning and the four-component instructional design (4C/ID) model as a promising instructional approach. It includes a formative evaluation of these training courses with n = 8 medical and n = 8 law students and presents the results of the preparation for the main study in the project. Article 3 presents the results of the main study with a quantitative design on the short- and medium-term learning results with the two developed level-2 training courses from article 2 and two additional level-1 training courses, by comparing the learning of n = 260 medical and n = 255 law students on conventional Bayesian reasoning and studying interactions with prior mathematical achievement. Surprising results are complemented by a qualitative analysis of participants’ notes.