TY - JOUR
T1 - Second-order probability affects hypothesis confirmation
AU - Tentori, Katya
AU - Crupi, Vincenzo
AU - Osherson, Daniel
N1 - Funding Information:
K.T. and V.C. acknowledge support from the SMC/Fondazione Cassa di Risparmio di Trento e Rovereto for the CIMeC (University of Trento) project “Inductive Reasoning.” D.O. acknowledges support from the Henry Luce Foundation. We thank Eric-Jan Wagenmakers, Branden Fitelson, and an anonymous reviewer for helpful comments on an earlier draft.
PY - 2010/2
Y1 - 2010/2
N2 - Bayesian confirmation measures give numerical expression to the impact of evidence E on a hypothesis H. All measures proposed to date are formal-that is, functions of the probabilities Pr(E∧H), Pr(E∧¬H), Pr(¬E∧H), Pr(¬E∧¬H), and nothing more. Experiments reported in Tentori, Crupi, and Osherson (2007) suggest that human confirmation judgment is not formal, but this earlier work leaves open the possibility that formality holds relative to a given semantic domain. The present study discredits even this weaker version of formality by demonstrating the role in confirmation judgments of a probability distribution defined over the possible values of Pr(E∧H), Pr(E∧¬H), Pr(¬E∧H), and Pr(¬E∧¬H)-that is, a second-order probability. Specifically, when for each of the latter quantities a pointwise value is fixed with a maximal second-order probability, evidence impact is rated in accordance with formal and normatively credible confirmation measures; otherwise evidence impact is systematically judged as more moderate.
AB - Bayesian confirmation measures give numerical expression to the impact of evidence E on a hypothesis H. All measures proposed to date are formal-that is, functions of the probabilities Pr(E∧H), Pr(E∧¬H), Pr(¬E∧H), Pr(¬E∧¬H), and nothing more. Experiments reported in Tentori, Crupi, and Osherson (2007) suggest that human confirmation judgment is not formal, but this earlier work leaves open the possibility that formality holds relative to a given semantic domain. The present study discredits even this weaker version of formality by demonstrating the role in confirmation judgments of a probability distribution defined over the possible values of Pr(E∧H), Pr(E∧¬H), Pr(¬E∧H), and Pr(¬E∧¬H)-that is, a second-order probability. Specifically, when for each of the latter quantities a pointwise value is fixed with a maximal second-order probability, evidence impact is rated in accordance with formal and normatively credible confirmation measures; otherwise evidence impact is systematically judged as more moderate.
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U2 - 10.3758/PBR.17.1.129
DO - 10.3758/PBR.17.1.129
M3 - Article
C2 - 20081173
AN - SCOPUS:74849091999
SN - 1069-9384
VL - 17
SP - 129
EP - 134
JO - Psychonomic Bulletin and Review
JF - Psychonomic Bulletin and Review
IS - 1
ER -