Why can only 24% solve Bayesian reasoning problems in natural frequencies: Frequency phobia in spite of probability blindness

For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer & Hoffrage, 1995). In a recent meta-analysis, McDowell & Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in probability format. Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a task in frequency format. In this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect).

二十余年来，诸多研究已证实自然频数（natural frequencies）在解决贝叶斯推理任务（Bayesian reasoning tasks）时的正向效用（Gigerenzer & Hoffrage, 1995）。近期一项元分析（meta-analysis）研究显示，McDowell与Jacobs（2017）发现，以自然频数格式呈现任务时，受试者的正确作答率可达24%；而同一任务以概率格式呈现时，正确作答率仅为4%。尽管如此，该元分析中仍有平均四分之三的受试者未能正确解答该自然频数格式的任务。本研究针对受试者面对自然频数时的典型错误行为开展了一项实证研究。我们发现，多数受试者并未实际使用自然频数进行计算，反而将其转换为更为复杂的概率形式。这种从直观呈现格式转向非直观计算格式的现象，将在心理学理论框架（如心向效应（Einstellung effect））下展开探讨。