# Analyzing and supporting mental representations and strategies in solving Bayesian problems

## TL;DR

This study shows that visualizing Bayesian problems improves learning success and reduces cognitive load compared to using formulas.

## Contribution

The study compares the effectiveness of different visualization methods for solving Bayesian problems and their impact on cognitive load.

## Key findings

- Learning success is significantly higher with the unit square and 2 × 2 table than with the formula.
- No significant differences were found between the unit square and 2 × 2 table in learning success or cognitive load.
- Creating and explaining visualizations improves solution performance and reduces effort.

## Abstract

Solving Bayesian problems poses many challenges, such as identifying relevant numerical information, classifying and translating it into mathematical formula language, and forming a mental representation. This triggers research on how to support the solving of Bayesian problems. The facilitating effect of using numerical data in frequency format instead of probabilities is well documented, as is the facilitating effect of given visualizations of statistical data. Accordingly, this study examines the differences, in learning success and cognitive load, between the formula, the 2 × 2 table, and the unit square. The visualizations are additionally explained in a descriptive way and created by the participants themselves. The results confirm the hypothesis of the study that learning success is significantly higher when using the unit square and the 2 × 2 table than when using the formula. A contrasting pattern emerged for passive and active load. Significant differences between the unit square and the 2 × 2 table could not be found for learning success and passive and active load. Consequently, the visualization of Bayesian problems, which are explicitly explained and created by the participants, increase solution performance and reduce the effort that the solution of a task requires from the learners.