Bayesian Reasoning To Complete The Characteristics And Influencing Factors

In this paper, two experiments were designed to examine the Bayesian reasoning's performance features and effective factors of high school students who were in Grade One.Experiment 1 had a 2×2×2 between-participant design. The three factors were data structure (partitioned versus unpartitioned), question form (single-step versus two-step) and problem content (disease versus writer). The results showed that: 1) The participants' estimates were largely affected by problem content while there was no effect of data structure or question form. 2) Nearly 5% of the participants got correct answer, 73% of who used frequency to rewrite the information. 3) Among the divided steps in Bayesian inference, division was the most difficult, P(-H) and addition were less difficult and multiplication was the easiest. 4) 50% of the participants could apply one or several of the four concepts: probability of "not the event", multiplication rule, addition rule and condition probability. 5) P(H)×P(D|H) and P(D|H) were two major non-Bayesian algorithms. 6) Less than 25% of the participants used frequency. In those who got other results except P(H|D), much more people used probability.Experiment 2 had a randomized multigroup posttest design. There was only one factor named implied condition which had five levels: not imply, imply P(-H), imply addition, imply division and imply all. The results showed that: 1) All the implied conditions significantly improved the participants' performance. When under the condition of implying division, the participants derived the best results. 2) 31.9% of the participants got correct answer, 73% of who used frequency to rewrite the information. 3) 78% of the participants could apply one or several of the four concepts: probability of "not the event", multiplication rule, addition rule and condition probability. 4) 40% of the participants used frequency. In those who got other results except P(H|D) , much more people used proportion. 5) Two kinds of misunderstanding should be considered.From the two experiments, the author drew five main conclusions: 1) No matter the high school students in Grade One participated the experiment 1 or experiment 2, when they used frequency they could get the correct answer more probably than when they used probability. 2) In experiment 1 and experiment 2, nearly 5% and 32% of the students got the correct answer respectively; 50% and 78% of the students could apply one or several of the four concepts respectively: probability of "not the event", multiplication rule, addition rule and condition probability. 3) To the high school students in Grade One, division was the most difficult among the divided steps in Bayesian inference, P(-H) and addition were less difficult and multiplication was the easiest. 4) The participants' estimates were largely affected by problem content. 5) All the implied conditions significantly improved the participants' performance, among which the condition of implying division caused the best results. The statements of implied conditions needed further improved.