Academic journal article Psychonomic Bulletin & Review

Logical Reasoning and Probabilities: A Comprehensive Test of Oaksford and Chater (2001)

Academic journal article Psychonomic Bulletin & Review

Logical Reasoning and Probabilities: A Comprehensive Test of Oaksford and Chater (2001)

Article excerpt

We report two experiments testing a central prediction of the probabilistic account of reasoning provided by Oaksford and Chater (2001): Acceptance of standard conditional inferences, card choices in the Wason selection task, and quantifiers chosen for conclusions from syllogisms should vary as a function of the frequency of the concepts involved. Frequency was manipulated by a probability-learning phase preceding the reasoning tasks to simulate natural sampling. The effects predicted by Oaksford and Chater (2001) were not obtained with any of the three paradigms.

For several decades, psychological research on deductive reasoning and research on probabilistic reasoning have largely been separate. Recently, there has been increasing awareness that probabilities might matter also in tasks framed as deductive inferences (see, e.g., Evans & Over, 1996a; Kirby, 1994; Nickerson, 1996). One of the most elaborated theories highlighting the role of probabilistic reasoning in deductive tasks has been advanced by Oaksford and Chater ( 1994,2001 ). In this article, we report two experiments testing central predictions of this theory for three paradigms: the Wason selection task, conditional inferences, and syllogisms.

The Wason Selection Task

Wason's (1966) task requires selection of information necessary to test a conditional of the form "if p then q." Four cards are given, each representing a combination of p or not-p with q or not-q. The visible sides of the cards correspond to the four logically possible cases: p, not-p, q, and not-q, respectively. In order to test whether the conditional, interpreted as a material implication, is true for the four cards, one has to turn over the cards displaying ρ and not-q. Few participants, however, choose this combination for task versions with nonthematic materials (see Evans, Newstead, & Byrne, 1993).

Oaksford and Chater (1994) developed a theory of people's choices in the selection task based on the expected information gain (EIG) associated with turning each card. Their optimal data selection (ODS) theory interprets the selection task as an inductive, not a deductive, task: Participants understand that they should test a universal law, not a statement about the four cards shown; their task, therefore, consists of selecting those cards that promise to be most informative with regard to evaluating the universal hypothesis.

The result of Oaksford and Chater's (1994) analysis is that the relative EIG of the cards depends on the assumptions about the proportions of p to not-p cases and of q to not-q cases in the population. The default assumption of the cognitive system, they argue, is rarity: Both p and q are less frequent than their negations. Under the assumption of rarity, the p card would be most informative, and the q card would come next. Thus, the modal pattern of selections, p and g, would be rational.

The most important prediction of ODS is that the probability of selecting individual cards should vary as a function of the relative frequencies of p and q. The main predicted effects of ODS in its revised version (Oaksford & Chater, 2001) are that the selection probability of p decreases and that of not-p increases as the frequency of p increases. Likewise, the selection probability of q decreases and of not-q increases as the frequency of q increases (see Table 1). In other words, ODS predicts that people tend to select cards from the rare categories.

Empirical tests of this prediction are sparse and inconclusive. Oaksford, Chater, Grainger, and Larkin (1997) gained support for predictions from ODS with the reducedarray selection task (RAST). The RAST is a simplified version of Wason's original task, and it is not clear whether the results can be generalized to the original task (cf. Oberauer, Wilhelm, & Rosas Diaz, 1999). Oaksford, Chater, and Grainger (1999) varied the probabilities of p and of q in the Wason selection task. …

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