Abstract
For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer and Hoffrage, 1995). In a recent meta-analysis, McDowell and 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).
Highlights
Many professionals, such as medical doctors and judges in court, are expected to make momentous decisions based on statistical information
In an empirical study with N = 180 students from the University of Regensburg, we found that the majority of participants do not actively use natural frequencies in Bayesian reasoning tasks
Even if the task is presented in the intuitive natural frequency format, about half of the participants still prefer calculating with probabilities instead
Summary
Many professionals, such as medical doctors and judges in court, are expected to make momentous decisions based on statistical information. Insufficient knowledge of statistics in general and incorrect Bayesian reasoning in particular can result in false convictions or acquittals made by juries in court, for example when they have to evaluate evidence based on a fragmentary DNA sample. These faults bear the risk of destroying innocent people’s lives, too, as happened, for instance, in the famous case of Sally Clark (Schneps and Colmez, 2013; Barker, 2017). If one of these people is not addicted to heroin, the probability is 0.19% that he or she will have fresh needle pricks
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