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51
How to improve Bayesian reasoning without instruction: Frequency formats
 Psychological Review
, 1995
"... 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 s ..."
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Cited by 220 (21 self)
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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. NonBayesian algorithms included simple versions of Fisherian and NeymanPearsonian 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,
Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty
 Cognition
, 1996
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Predictive and diagnostic learning within causal models: Asymmetries in cue competition
 Journal of Experimental Psychology: General
, 1992
"... Several researchers have recently claimed that higher order types of learning, such as categorization and causal induction, can be reduced to lower order associative learning. These claims are based in part on reports of cue competition in higher order learning, apparently analogous to blocking in c ..."
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Cited by 63 (10 self)
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Several researchers have recently claimed that higher order types of learning, such as categorization and causal induction, can be reduced to lower order associative learning. These claims are based in part on reports of cue competition in higher order learning, apparently analogous to blocking in classical conditioning. Three experiments are reported in which subjects had to learn to respond on the basis of cues that were defined either as possible causes of a common effect (predictive learning) or as possible effects of a common cause (diagnostic learning). The results indicate that diagnostic and predictive reasoning, far from being identical as predicted by associationistic models, are not even symmetrical. Although cue competition occurs among multiple possible causes during predictive learning, multiple possible effects need not compete during diagnostic learning. The results favor a causalmodel theory.
Constraints and preferences in inductive learning: An experimental study of human and machine performance
 Cognitive Science
, 1987
"... 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 i ..."
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Cited by 33 (2 self)
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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 cotegory given that it hos some property) to o greater extent than did the Al progroms. 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 inductive 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 systems from developing overgenerolizotions.
Using natural frequencies to improve diagnostic inferences
 Academic Medicine
, 1998
"... 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. Metho ..."
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Cited by 29 (8 self)
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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,
What Educated Citizens Should Know About Statistics and Probability
 The American Statistician
, 2003
"... 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. ..."
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Cited by 16 (1 self)
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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 policymakers, physicians, and others at worst.
AIDS counselling for lowrisk clients
 AIDS Care
, 1998
"... Abstract. Th is study addresses the counselling of heterosexual men with lowrisk 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 t ..."
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Cited by 9 (5 self)
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Abstract. Th is study addresses the counselling of heterosexual men with lowrisk 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 HIVpositive 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).
The Role of Causality in Judgment Under Uncertainty
"... 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 explai ..."
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Cited by 9 (0 self)
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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 realworld judgments, and propose an alternative normative framework based on Bayesian inferences over causal models. Deviations from traditional norms of judgment, such as "baserate 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.
Giving advice: decision theory perspectives on sexual violence . Am Psychol
 47 : 577 – 588 . 484 VOLUME 5 • ISSUE 6 WWW.CTSJOURNAL.COM and Fischhoff � Sexual Risk and Nonconsent
, 1992
"... What entitles us to give general advice? This general question is explored here in the specific context of providing responsible advice to women on how to make decisions about possible ways of reducing their risk of sexual assault. An approach is advanced that is a combination of decision analysis, ..."
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Cited by 7 (6 self)
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What entitles us to give general advice? This general question is explored here in the specific context of providing responsible advice to women on how to make decisions about possible ways of reducing their risk of sexual assault. An approach is advanced that is a combination of decision analysis, used to provide a formal characterization of decision situations, and behavioral decision theory, used to provide a descriptive characterization of how people perceive those situations. The approach is illustrated with a set of studies using three diverse groups of women; a group of men, paralleling one of the groups of women; and a national sample of sexual assault experts. The approach is evaluated in terms of its feasibility, its strengths and weaknesses relative to alternative approaches, and its implicit position on broader political and philosophical issues.
20 STATISTICAL COGNITION: TOWARDS EVIDENCEBASED PRACTICE IN STATISTICS AND STATISTICS EDUCATION 4
"... Practitioners and teachers should be able to justify their chosen techniques by taking into account research results: This is evidencebased practice (EBP). We argue that, specifically, statistical practice and statistics education should be guided by evidence, and we propose statistical cognition ( ..."
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Cited by 6 (3 self)
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Practitioners and teachers should be able to justify their chosen techniques by taking into account research results: This is evidencebased 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.