(Co-)Variation of parameters in a Bayesian Situation -An analysis of students' reasoning about the effect of base rate changes

Theresa Büchter (1) , Katharina Böcherer-Linder (2) , Andreas Eichler (1) , Markus Vogel (1)

1 University of Kassel
2 University of Freiburg [Freiburg]

Evaluating the risk of a hypothesis given some indicators for the hypothesis is a crucial example for conditional probability reasoning. Calculating the probability of a risk when a set of parameters (e. g. the so-called base rate, true-and false-positive rate) is given, is a task which is referred to as a Bayesian task, as it can be solved with the Bayes' formula. The conceptual understanding of a mathematical formula (and of Bayesian tasks more specifically) implies being able to reason about effects of changes in the given quantities. Based on the dimensions of the concept of functional thinking we propose to refer to this aspect as "Covariation" of Bayesian reasoning. However, hardly any studies have so far investigated Covariation in a Bayesian situation. In this paper we present a study in which participants are asked to reason about changes of the base rate and introduce a coding system with which their answers can be analyzed.

Mots clés: Bayesian reasoning; covariation in Bayesian situations; statistics education

Domaines: Mathématiques [math]

Theresa Büchter, Katharina Böcherer-Linder, Andreas Eichler, Markus Vogel. (Co-)Variation of parameters in a Bayesian Situation -An analysis of students' reasoning about the effect of base rate changes. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, Bozen-Bolzano, Italy. ⟨hal-03751813⟩