Abstract: The natural frequency hypothesis proposed by Gigerenzer & Hoffrage (1995) assumed that the cognitive fallacy in Bayesian inference would be diminished when the problem was presented in frequency format instead of in probability format. The nested-sets hypothesis proposed by Mellers et al. (1999), however, thought that the natural frequency format facilitated the problem-solving because this format made the visualization of the nested relation among sets. Sloman (2003) and Gigerenzer & Hoffrage (1999) explained the facilitating effect of frequency format on problem-solving from the point of view of the concept of set. On the basis of the findings above, this study aimed to evaluate the effects of different external representation on transparent nested-sets relation, and to discuss the facilitating effect of transparent nested-sets relations on Bayesian inference. In addition, this study investigated if transparent nested-sets relations could diminish the difference on reasoning results from participants who are majored in arts or science. The present study also discussed if narrating reason could enhance participants’ meta-cognition monitoring and understanding of the nested relation in classic Bayesian inference, thereby improve their reasoning results.
Two experiments were collectively conducted with totally 336 arts and science students, among whom 82 students were majored in mathematics and 86 in Chinese in the first experiment, and 83 students majored in mathematics and 85 in Chinese in the second experiment. All participants were not familiar with Bayesian inference rule. A total of 329 questionnaires were collected. A analysis of variance of the absolute value of difference between posterior probability and normal value was performed.
The results indicated that: (1) there was no significant effect of one-by-one-question; (2) facilitating effect of completed tree diagram and uncompleted one on Bayesian reasoning was found by framing problem’s nested-sets relations in terms, but the effect of simple tree diagram was not significant. (3) narrating reasons inspired meta-cognition so that participants could effectively sense internal nested-sets relations by mobilizing their knowledge and schema and improved their Bayesian reasoning performances. (4) there was no significant difference between arts and science students.
The results of this study supported the hypothesis that transparent nested-sets relations in task representation could improve Bayesian reasoning. It also suggests that the meta-cognition monitoring by narrating reason could mobilize foregone logic knowledge and scheme knowledge in mind and make thinking more transparent. These findings offered psychological evidence to reduce students’ short-time memory burden so as to improve teaching efficiency and students’ performance

Key words: Bayesian reasoning, nested-sets relation, metacognition, tree diagram representation