Hoffrage Ulrich, Krauss Stefan, Martignon Laura, Gigerenzer Gerd
Faculty of Business and Economics (HEC Lausanne), University of Lausanne Lausanne, Switzerland.
Mathematics Education, Faculty of Mathematics, University of Regensburg Regensburg, Germany.
Front Psychol. 2015 Oct 14;6:1473. doi: 10.3389/fpsyg.2015.01473. eCollection 2015.
Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true. Real-life applications, however, often involve situations where cues (e.g., medical tests) have more than one value, where more than two hypotheses (e.g., diseases) are considered, or where more than one cue is available. In Study 1, we show that natural frequencies, compared to information stated in terms of probabilities, consistently increase the proportion of Bayesian inferences made by medical students in four conditions-three cue values, three hypotheses, two cues, or three cues-by an average of 37 percentage points. In Study 2, we show that teaching natural frequencies for simple tasks with one dichotomous cue and two hypotheses leads to a transfer of learning to complex tasks with three cue values and two cues, with a proportion of 40 and 81% correct inferences, respectively. Thus, natural frequencies facilitate Bayesian reasoning in a much broader class of situations than previously thought.
用自然频率而非概率来表示统计信息，可提高贝叶斯推理任务的表现。自然频率的这种有益效果已在医学、法律和教育等多个应用领域得到证实。然而，迄今为止所有的研究和应用都局限于使用一个二分线索来推断两个假设中哪一个为真的情况。然而，实际应用中常常涉及这样的情形：线索（如医学检查）有多个值、考虑的假设不止两个（如疾病）或者有多个线索可用。在研究1中，我们发现，与用概率表述的信息相比，自然频率能持续提高医学生在四种情况下（三个线索值、三个假设、两个线索或三个线索）做出贝叶斯推断的比例，平均提高37个百分点。在研究2中，我们发现，针对有一个二分线索和两个假设的简单任务教授自然频率，能促使学生将学习迁移到有三个线索值和两个线索的复杂任务中，正确推断的比例分别为40%和81%。因此，自然频率在比先前认为的更广泛的情形中促进贝叶斯推理。
