Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty (original) (raw)
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Psychonomic Bulletin & Review, 2008
The idea that naturally sampled frequencies facilitate performance in statistical reasoning tasks because they are a cognitively privileged representational format has been challenged by findings that similarly structured numbers presented as “chances” similarly facilitate performance, based on the claim that these are technically single-event probabilities. A crucial opinion, however, is that of the research participants, who possibly interpret chances as de facto frequencies. A series of experiments here indicate that not only is performance improved by clearly presented natural frequencies rather than chances phrasing, but also that participants who interpreted chances as frequencies rather than probabilities were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.
Probabilistic Biases Meet the Bayesian Brain
Current Directions in Psychological Science
In Bayesian cognitive science, the mind is seen as a spectacular probabilistic-inference machine. But judgment and decision-making (JDM) researchers have spent half a century uncovering how dramatically and systematically people depart from rational norms. In this article, we outline recent research that opens up the possibility of an unexpected reconciliation. The key hypothesis is that the brain neither represents nor calculates with probabilities but approximates probabilistic calculations by drawing samples from memory or mental simulation. Sampling models diverge from perfect probabilistic calculations in ways that capture many classic JDM findings, which offers the hope of an integrated explanation of classic heuristics and biases, including availability, representativeness, and anchoring and adjustment.
2021
Bayesian statistics offers a normative description for how a person should combine their original beliefs (i.e., their priors) in light of new evidence (i.e., the likelihood). Previous research suggests that people tend to under-weight both their prior (base rate neglect) and the likelihood (conservatism), although this varies by individual and situation. Yet this work generally elicits people's knowledge as single point estimates (e.g., x has 5% probability of occurring) rather than as a full distribution. Here we demonstrate the utility of eliciting and fitting full distributions when studying these questions. Across three experiments, we found substantial variation in the extent to which people showed base rate neglect and conservatism, which our method allowed us to measure for the first time simultaneously at the level of the individual. We found that while most people tended to disregard the base rate, they did so less when the prior was made explicit. Although many indivi...
Cognitive factors affecting subjective probability assessment
1994
Prior probabilities are central to Bayesian statistics. The Bayesian paradigm assumes that people can express uncertainty in terms of subjective probability distributions. This article will consider Hogarth's 1975 assessment that \man is a selective, sequential information processing system with limited capacity,. .. ill-suited for assessing probability distributions." Particular attention will be paid to when people make normatively \good" or \poor" probability assessments, what techniques are e ective in eliciting \good," coherent probability assessments, and on how these ideas are relevant to the practicing Bayesian statistician. While there are situations where experts can make well-calibrated judgments, it will be argued that more research needs to be done into the e ects of expertise, training, and feedback.
心理学报, 2007
What happens when format manipulations improve Bayesian reasoning? One view is that naturally sampled frequencies help induce a privileged representational system that is relatively specific in its operation. A contrasting view is that naturally sampled frequencies are but one way to induce a more general process of appreciating nested set relationships. This later view implies that fairly brief and immediate interventions (e.g., simple directives) should produce improvement, whereas the former view implies that more extensive interventions and/or more insightful understanding are necessary for improvement. The present research indicates that neither brief and immediate interventions nor pre-existing representational biases or representational flexibility facilitate performance. Some evidence emerged, on the other hand, that frequentist problem interpretation can improve statistical reasoning performance and increase confidence in responses at times. These results support the privileged representational system view.
Journal of Behavioral …, 1997
demonstrated that over-and undercon®dence can be observed simultaneously in judgment studies, as a function of the method used to analyze the data. They proposed a general model to account for this apparent paradox, which assumes that overt responses represent true judgments perturbed by random error. To illustrate that the model reproduces the pattern of results, they assumed perfectly calibrated true opinions and a particular form (log-odds plus normally distributed error) of the model to simulate data from the full-range paradigm. In this paper we generalize these results by showing that they can be obtained with other instantiations of the same general model (using the binomial error distribution), and that they apply to the half-range paradigm as well. These results illustrate the robustness and generality of the model. They emphasize the need for new methodological approaches to determine whether observed patterns of over-or undercon®dence represent real eects or are primarily statistical artifacts.
Frequency, Probability, and Prediction: Easy Solutions to Cognitive Illusions?
Cognitive Psychology, 1999
Many errors in probabilistic judgment have been attributed to people's inability to think in statistical terms when faced with information about a single case. Prior theoretical analyses and empirical results imply that the errors associated with casespecific reasoning may be reduced when people make frequentistic predictions about a set of cases. In studies of three previously identified cognitive biases, we find that frequency-based predictions are different from-but no better than-case-specific judgments of probability. First, in studies of the ''planning fallacy,'' we compare the accuracy of aggregate frequency and case-specific probability judgments in predictions of students' real-life projects. When aggregate and single-case predictions are collected from different respondents, there is little difference between the two: Both are overly optimistic and show little predictive validity. However, in withinsubject comparisons, the aggregate judgments are significantly more conservative than the single-case predictions, though still optimistically biased. Results from studies of overconfidence in general knowledge and base rate neglect in categorical prediction underline a general conclusion. Frequentistic predictions made for sets of events are no more statistically sophisticated, nor more accurate, than predictions made for individual events using subjective probability.
Cognition, 2002
Do individuals unfamiliar with probability and statistics need a specific type of data in order to draw correct inferences about uncertain events? Girotto and Gonzalez (Cognition 78 (2001) 247) showed that naive individuals solve frequency as well as probability problems, when they reason extensionally, in particular when probabilities are represented by numbers of chances. Hoffrage, Gigerenzer, Krauss, and Martignon (Cognition 84 (2002) 343) argued that numbers of chances are natural frequencies disguised as probabilities, though lacking the properties of true probabilities. They concluded that we failed to demonstrate that naive individuals can deal with true probabilities as opposed to natural frequencies. In this paper, we demonstrate that numbers of chances do represent probabilities, and that naive individuals do not confuse numbers of chances with frequencies. We conclude that there is no evidence for the claim that natural frequencies have a special cognitive status, and the evolutionary argument that the human mind is unable to deal with probabilities.
Representativeness and fallacies of probability judgment
Acta Psychologica, 1984
Representativeness is the name given to the heuristic people often employ when they judge the probability of a sample by how well it represents certain salient features of the population from which it was drawn. The representativeness heuristic has also been used to account for how people judge the probability that a given population is the source of some sample. The latter probability, however, depends on other factors (e.g., the population's prior probability) as well as on the sample characteristics. A review of existing evidence suggests that the ignoring of such factors, a central finding of the heuristics approach to judgment under uncertainty, is a phenomenon which is conceptually distinct from the representativeness heuristic. These factors (base rates, sample size, and predictability) do not always exert the proper influence on people's first-order probability judgments, but they are not ignored when people make second-order (i.e., confidence)judgments. Other fallacies and biases in subjective evaluations of probability are, however, direct causal results of the employment of representativeness. For example, representativeness may be applied to the wrong features. Most devastating, perhaps, is that subjective probability judgments obey a logic of representativeness judgments, even though probability ought to obey an altogether different logic. Yet although the role of representativeness judgments in probability estimation leaves a lot to be desired, it is hard to envision prediction and inference completely unaided by representativeness. In a landmark paper, Kahneman and Tversky (1972) presented their representativeness thesis, according to which
Probability biases as Bayesian inference
Judgment and Decision Making, 2006
In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the laboratory conditions in which they are demonstrated, they can be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions.