Abstract
It is an ongoing debate, what properties of visualizations increase people’s performance when solving Bayesian reasoning tasks. In the discussion of the properties of two visualizations, i.e., the tree diagram and the unit square, we emphasize how both visualizations make relevant subset relations transparent. Actually, the unit square with natural frequencies reveals the subset relation that is essential for the Bayes’ rule in a numerical and geometrical way whereas the tree diagram with natural frequencies does it only in a numerical way. Accordingly, in a first experiment with 148 university students, the unit square outperformed the tree diagram when referring to the students’ ability to quantify the subset relation that must be applied in Bayes’ rule. As hypothesized, in a second experiment with 143 students, the unit square was significantly more effective when the students’ performance in tasks based on Bayes’ rule was regarded. Our results could inform the debate referring to Bayesian reasoning since we found that the graphical transparency of nested sets could explain these visualizations’ effect.
Highlights
As a part of Bayesian reasoning, the Bayes’ rule plays an important role in decision making under uncertainty
For the accumulated score referring to these four items (Cronbach’s α = 0.739) a t-test yielded no significant difference between the tree diagram (M = 3.46, SD = 1.023) and the unit square (M = 3.46, SD = 1.036), t(146) = 0.000, p = 1.000
We had the following research question with the following hypothesis: Question 2: Do unit squares and tree diagrams differ with respect to performance in Bayesian reasoning tasks? Hypothesis 2: The unit square is more effective than the tree diagram with respect to performance in Bayesian reasoning tasks
Summary
As a part of Bayesian reasoning, the Bayes’ rule plays an important role in decision making under uncertainty. In many areas, such as medicine or law, critical decisions can depend on appropriately applying the Bayes’ rule, e.g., a medical diagnosis can depend on the probability of having a disease given a positive test result. 20% of women without the disease will test positive.” In this situation, the probability that a woman who was selected at random and who received a positive test result has the disease can be calculated according to the Bayes’ rule. The resulting posterior probability P(H|D) where H is the hypothesis (having the disease) and D is the data (testing positive) is: P(H|D) =. Most people, including physicians (Eddy, 1982), would expect a higher result
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