Linda is not a bearded lady: Configural weighting and adding as the cause of extension errors.

Nilsson, Håkan; Winman, Anders; Juslin, Peter; Hansson, Göran

doi:10.1037/a0017351

Cited by 67 publications

(178 citation statements)

References 91 publications

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“…One relevant example is human estimation of the joint probability of two independent events. The normative rule is to multiply the probabilities of the independent events together, but some researchers have instead proposed that people respond with the weighted average of the probabilities of the two independent events (Fantino, Kulik, StolarzFantino, & Wright, 1997;Nilsson, Winman, Juslin, & Hansson, 2009). The normative rule and the weighted average rule are the usual hypotheses that are compared in these experiments.…”

Section: When the Truth Is A Combination Of The Hypothesesmentioning

confidence: 99%

The frequentist implications of optional stopping on Bayesian hypothesis tests

Sanborn

Hills

2013

Psychon Bull Rev

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Null hypothesis significance testing (NHST) is the most commonly used statistical methodology in psychology. The probability of achieving a value as extreme or more extreme than the statistic obtained from the data is evaluated, and if it is low enough then the null hypothesis is rejected. However, because common experimental practice often clashes with the assumptions underlying NHST, these calculated probabilities are often incorrect. Most commonly, experimenters use tests that assume sample sizes are fixed in advance of data collection, but then use the data to determine when to stop; in the limit, experimenters can use data monitoring to guarantee the null hypothesis will be rejected. Bayesian hypothesis testing (BHT) provides a solution to these ills, because the stopping rule used is irrelevant to the calculation of a Bayes factor. In addition, there are strong mathematical guarantees on the frequentist properties of BHT that are comforting for researchers concerned that stopping rules could influence the Bayes factors produced. Here we show that these guaranteed bounds have limited scope and often do not apply in psychological research. Specifically, we quantitatively demonstrate the impact of optional stopping on the resulting Bayes factors in two common situations: 1) when the truth is a combination of the hypotheses, such as in a heterogeneous population, and 2) when a hypothesis is composite-taking multiple parameter values-such as the alternative hypothesis in a t-test. We found that for these situations that while the Bayesian interpretation remains correct regardless of the stopping rule used, the choice of stopping rule can, in some situations, greatly increase the chance of an experimenter finding evidence in the direction they desire. We suggest ways to control these frequentist implications of stopping rules on BHT.The standard statistical methods of psychological research, such as the ANOVA and the t-test, are examples of null hypothesis significance testing (NHST). These familiar frequentist methods compare a statistic calculated from the data, such as an F-test statistic or a t-test statistic, to a sampling distribution associated with the null hypothesis. If the probability of achieving a result

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Section: When the Truth Is A Combination Of The Hypothesesmentioning

confidence: 99%

The frequentist implications of optional stopping on Bayesian hypothesis tests

Sanborn

Hills

2013

Psychon Bull Rev

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“…Several accounts have been argued for, but no one has reached an uncontroversial status today (as noted by Fisk 2004;Nilsson et al 2009;Jarvstad and Hahn 2011;. First, Tversky and Kahneman originally suggested that a representativeness heuristic (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…But it has been argued that the representativeness concept involved is informal and ill-specified (Gigerenzer 1996;Birnbaum et al 1990), and suggestions to specify it in the technical sense of a likelihood value (Shafir et al 1990;Massaro 1994) account for limited cases only ). According to another suggestion, agents actually evaluate the probability of the conjunction from some combination of the probabilities of the components, like averaging or adding (Fantino et al 1997;Nilsson et al 2009). However, such explanations do not resist empirical tests, as have argued.…”

Section: Introductionmentioning

confidence: 99%

Quantum-like models cannot account for the conjunction fallacy

2016

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Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities-this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed.

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“…Tversky et Kahneman ont initialement proposé une heuristique de représentativité mais il á eté objecté que ce concept est mal défini (Gigerenzer 1996, Birnbaum et al 1990, et des suggestions pour le préciser formellement (Shafir et al 1990, Massaro 1994) ne s'appliquent qu'à certains cas seulement (Crupi et al 2008). Gavanski et al (1991) ou Nilsson et al (2009) ont considéré que la probabilité d'une conjonctionétaitéva-luéeà partir d'une combinaison des probabilités respectives de chaqueévénement qui la compose, mais cette explication ne résiste pas aux tests expérimentaux . Ces derniers ont proposé une explication reposant sur la notion de la confirmation inductive, dans un cadre bayésien, et il s'agit d'une explication prometteuse.…”

Section: Introductionunclassified

Une nouvelle approche expérimentale pour tester les modèles quantiques de l’erreur de conjonction

Duchêne

Boyer-Kassem²,

Guerci

2017

Revue Économique

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a paraître dans la Revueéconomique Résumé La théorie classique des probabilités requiert que la probabilité de la conjonction de deuxévénements soit inférieureà la probabilité d'un desévénements seul. Or les sujets ne jugent empiriquement pas toujours ainsi : c'est la traditionnelle erreur de conjonction. L'une des explications actuellement prometteuses de ce paradoxe repose sur des modèles dits « quantiques », développésà partir des outils mathématiques de la mécanique quantique. Mais ces modèles sont-ils empiriquement adéquats ? Quelles versions de ces modèles peuventêtre employées ? En particulier, les versions les plus simples, dites non-dégénérées, peuvent-ellesêtre suffisantes ? Nous proposons ici un protocole expérimental original pour tester en laboratoire les modèles quantiques de l'erreur de conjonction. Les résultats obtenus suggèrent que les modèles non-dégénérés ne sont pas empiriquement adéquats, et que la recherche future concernant les modèles quantiques devrait s'orienter vers les modèles dégénérés.

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Linda is not a bearded lady: Configural weighting and adding as the cause of extension errors.

Cited by 67 publications

References 91 publications

The frequentist implications of optional stopping on Bayesian hypothesis tests

The frequentist implications of optional stopping on Bayesian hypothesis tests

Quantum-like models cannot account for the conjunction fallacy

Une nouvelle approche expérimentale pour tester les modèles quantiques de l’erreur de conjonction

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