Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,

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The paper examines constraints ond preferences employed by people in learning decision rules from preclossified examples. Results from four experiments with human subiects were onolyzed ond compared with ortificiol intelligence (Al) inductive learning programs. The results showed the people’s rule inductions tended lo emphosize category validity (probability of some property, given o category) more than cue validity (probability that on entity is o member of o cote-gory given that it hos some property) to o greater extent than did the Al pro-groms. Although the relative proportions of different rule types (e.g., conjunctive vs. disjunctive) changed across experiments, o single process model provided o good account of the data from each study. These observations ore used to argue for describing constraints in terms of processes embodied in models rather than in terms of products or outputs. Thus Al induction programs become condidote psychological process models ond results from inductive learning experiments con suggest new algorithms. More generally, the results show that humon induc-tive generolizotions tend toword greater specificity than would be expected if conceptual simplicity were the key constraint on inductions. This bias toword specificity moy be due lo the fact that this criterion both maximizes inferences that moy be drown from category membership ond protects rule induction sys-tems from developing over-generolizotions.

Purpose. To test whether physicians ’ diagnostic inferences can be improved by communicating information using natural frequencies instead of probabilities. Whereas probabilities and relative frequencies are normalized with respect to disease base rates, natural frequencies are not normalized. Method. The authors asked 48 physicians in Munich and Düsseldorf to determine the positive predictive values (PPVs) of four diagnostic tests. Information presented in the four problems appeared either as probabilities (the traditional way) or as natural frequencies. Results. When the information was presented as probabilities, the physicians correctly estimated the PPVs in only 10 % of cases. When the same information was presented as natural frequencies, that percentage increased to 46%. Conclusion. Representing information in natural frequencies is a fast and effective way of facilitating diagnostic insight, which in turn helps physicians to better communicate risks to patients, and patients to better understand these risks. What does a positive medical test result mean? Physicians often have diffi culty inferring the probability of a disease from statistical information relevant to positive test results. 1–5 In one study,

Much has changedsince the widespread introductionof statistics courses into the university curriculum, but the way introductory statistics courses are taught has not kept up with these changes. This article discusses the changes, and the way the introductory syllabus should change to re � ect them. In particular, seven ideas are discussed that every student who takes elementary statistics should learn and understand in order to be an educated citizen. Misunderstanding these topics leads to cynicism among the public at best, and misuse of study results by policy-makers, physicians, and others at worst.

Practitioners and teachers should be able to justify their chosen techniques by taking into account research results: This is evidence-based practice (EBP). We argue that, specifically, statistical practice and statistics education should be guided by evidence, and we propose statistical cognition (SC) as an integration of theory, research, and application to support EBP. SC is an interdisciplinary research field, and a way of thinking. We identify three facets of SC—normative, descriptive, and prescriptive— and discuss their mutual influences. Unfortunately, the three components are studied by somewhat separate groups of scholars, who publish in different journals. These separations impede the implementation of EBP. SC, however, integrates the facets and provides a basis for EBP in statistical practice and education.

Abstract. Th is study addresses the counselling of heterosexual men with low-risk behaviour who, voluntarily or involuntarily, take a HIV test. If such a man tests positive, the chance that he is infected can be as low as 50%. We study what information counsellors communicate to clients concerning the meaning of a positive test and whether they communicate this information in a way the client can understand. To get realistic data, one of us visited as a client 20 public health centres in Germany to take 20 counselling sessions and HIV tests. A majority of the counsellors explained that false positives do not occur, and half of the counsellors told the client that if he tests positive, it is 100 % certain that he is infected with the virus. Counsellors communicated numerical information in terms of probabilities rather than absolute frequencies, became confused, and were inconsistent. Based on experimental evidence, we propose a simple method that counsellors can learn to communicte risks in a more eff ective way. Former Senator Lawton Chiles of Florida reported at an AIDS conference in 1987 that of 22 blood donors in Florida who were notifi ed that they tested HIV-positive with the ELISA test, seven committed suicide. In the same medical text that reported this tragedy, the reader is informed that “even if the results of both AIDS tests, the ELISA and WB (Western blot), are positive, the chances are only 50–50 that the individual is infected ” (Stine, 1996, pp. 333, 338).

Leading accounts of judgment under uncertainty evaluate performance within purely statistical frameworks, holding people to the standards of classical Bayesian (Tversky & Kahneman, 1974) or frequentist (Gigerenzer & Hoffrage, 1995) norms. We argue that these frameworks have limited ability to explain the success and flexibility of people's real-world judgments, and propose an alternative normative framework based on Bayesian inferences over causal models. Deviations from traditional norms of judgment, such as "base-rate neglect", may then be explained in terms of a mismatch between the statistics given to people and the causal models they intuitively construct to support probabilistic reasoning. Four experiments show that when a clear mapping can be established from given statistics to the parameters of an intuitive causal model, people are more likely to use the statistics appropriately, and that when the classical and causal Bayesian norms differ in their prescriptions, people's judgments are more consistent with causal Bayesian norms.

How do people make difficult decisions in situations involving substantial risk and uncertainty? In this study, we presented a difficult medical decision to three expert physicians in a combined "thinking aloud" and "cross examination" experiment. Verbatim transcripts were analyzed using script analysis to observe the process of constructing and making the decision, and using referring phrase analysis to determine the representation of knowledge of likelihoods. These analyses are compared with a formal decision analysis of the same problem to highlight similarities and differences. The process of making the decision resembles an incremental, sequential-refinement planning algorithm, where a complex decision is broken into a sequence of choices to be made with a simplified description of the alternatives. This strategy results in certain kinds of relevant information being under-weighted in the final decision. Knowledge of likelihood appears to be represented as symbolic descriptions c...

Numerous studies of how people reason with statistical data suggest that human judgment often fails to approximate rational probabilistic (Bayesian) inference. We argue that a major source of error in these experiments may be misunderstanding causal structure. Most laboratory studies demonstrating probabilistic reasoning deficits fail to explain the causal relationships behind the statistics presented, or they suggest causal mechanisms that are not compatible with people’s prior theories. We propose that human reasoning under uncertainty naturally operates over causal mental models, rather than pure statistical representations, and that statistical data typically support correct Bayesian inference only when they can be incorporated into a causal model consistent with people’s theory of the relevant domain. We show that presenting people with questions that clearly explain an intuitively natural causal structure responsible for a set of statistical data significantly improves their performance. In particular, we describe two modifications to the standard medical diagnosis scenario that each eliminates the phenomenon of base-rate neglect, merely by clarifying the causal structure behind false-positive test results.