ABSTRACT
Previous research on Bayesian inference, reporting poor performance by students and experts alike, has often led to the conclusion that the mind lacks the appropriate cognitive algorithm. We argue that this conclusion is unjustified because it does not take into account the information format in which this cognitive algorithm is designed to operate. We demonstrate that a Bayesian algorithm is computationally simpler when the information is represented in a frequency rather than a probability format that has been used in previous research. A frequency format corresponds to the way information is acquired in natural sampling–sequentially and without constraints on which observations will be included in the sample. Based on the assumption that performance will reflect computational complexity, we predict that a frequency format yields more Bayesian solutions than a probability format. We tested this prediction in a study conducted with 48 physicians. Using outcome and process analysis, we categorized their individual solutions as Bayesian or non-Bayesian. When information was presented in the frequency format, 46% of their inferences were obtained by a Bayesian algorithm, as compared to only 10% when the problems were presented in the probability format. We discuss the impact of our results on teaching statistical reasoning.
Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, who equated probability theory with the common sense of educated people, would have said the answer is no. And when Ward Edwards and his colleagues (Edwards, 1968) started to test experimentally whether human inference follows Bayes' theorem, they gave the same answer: although "conservative," inferences were usually proportional to those calculated from Bayes' theorem. Kahneman and Tversky (1972, p. 450), however, arrived at the opposite conclusion: "In his evaluation of evidence, man is apparently not a conservative Bayesian: he is not a Bayesian at all." In the 1970s and '80s, proponents of their "heuristics-and-biases" program amassed an apparently damning body of evidence that people systematically neglect base rates in Bayesian inference problems. This could be shown not only with students, but also with experts in their fields, for instance, with physicians (Casscells, Schoenberger, & Grayboys, 1978; Eddy, 1982).
Thus, there are two contradictory claims as to whether people naturally reason according to Bayesian inference. In this paper we argue that both views are based on an incomplete analysis: They focus on cognitive processes, Bayesian or otherwise, without making the connection between what we will call a cognitive algorithm and an information format. We (a) provide a theoretical framework (based on Gigerenzer and Hoffrage, 1995) that specifies why a frequency format should improve Bayesian reasoning and (b) present a study that tests this hypothesis.
