Rapid-response versus free-time selection tasks using different logical connectives

When reasoning with conditional statements (i.e., if [not] p then [not] q), people tend to display matching bias: Options that match the entities named in the rule are selected even when logically inappropriate. Three different Wason selection tasks were administered under free-time and rapid-response formats. For the latter, individual cards were presented for one second, and required a response within a further one second. Previous research using these formats (Roberts & Newton, 2001) has shown that this increases matching bias, in line with the action of preconscious heuristic processes which direct attention towards relevant aspects of a problem, but whose action can be overturned if there is sufficient time to apply analytic reasoning processes. The selection tasks administered included a standard abstract conditional task, a disjunctive version (i.e., either [not] p or [not] q), and a conditional task in which the cards showed explicitly negated values. Both conditional tasks demonstrated matching bias, but under rapid-response presentation, matching bias only increased for the standard conditional and disjunctive tasks. Overall, the data support Evans’ (e.g., 2006) heuristic-analytic framework albeit with some caveats, and it is suggested that the broad question, of whether individual selection task formats show or do not show matching bias, requires more detailed investigation.     

The Influence of Linguistic Form on Reasoning: The Case of Matching Bias

A well-established phenomenon in reasoning research is matching bias : a tendency to select information that matches the lexical content of propositional statements, regardless of the logically critical presence of negations. Previous research suggested, however, that the effect might be restricted to reasoning with conditional statements. This paper reports two experiments in which participants were required to construct or identify true and false cases of propositional rules of several kinds, including universal statements, disjunctions, and negated conjunctions. Matching bias was observed across all rule types but largely restricted to problems where participants were required to falsify rather than to verify the rules. A third experiment showed a similar generalization across linguistic forms in the Wason selection task with only if conditionals substituted for universals. The results are discussed with reference to contemporary theories of propositional reasoning.     

MATCHING BIAS IN THE SELECTION TASK

A previous study (Evans, 1972) found that subjects tend to match rather than alter named values when constructing verifying and falsifying cases of conditional rules. It was suggested that this tendency (‘matching bias’) might account for the responses normally observed in Wason's (1968, 1969) ‘selection task’. This suggestion was tested by giving subjects the selection task with conditional rules in which the presence and absence of negative components was systematically varied, to see whether subjects consistently attempted to verify the rules (Wason's theory) or whether they continued to choose the matching values despite the presence of negatives, which would reverse the logical meaning of such selections. Significant matching tendencies were observed on four independent measures, and the overall pattern, with matching bias cancelled out, gave no evidence for a verification bias, indicating instead that the logically correct values were most frequently chosen.     

The elusive matching bias effect in the disjunctive selection task

When reasoning with conditional statements (i.e., if [not] p then [not] q), for example when solving Wason's selection task, subjects tend to display matching bias: Options which match the entities named in the rule tend to be selected irrespective of whether this is logically appropriate. Recently, there have been suggestions that the underlying causes of matching bias reflect a general phenomenon that applies to many types of logical rule, not just conditionals. A study is reported in which performance is investigated for selection tasks with categorical or disjunctive rules. Although matching bias was clearly present for categorical rules, inverted matching bias was identified for disjunctive rules, calling into question the generality of the phenomenon and its explanations. In addition, performance at one task was not correlated with performance at the other, calling into question recent cognitive capacity accounts of selection task performance.     

Efficiency in data gathering: Set size effects in the selection task

Two experiments were conducted with variants of Wason's (1966 Wason, P. C. 1966. “Reasoning”. In New horizons in psychology, Edited by: Foss, B. M. Harmondsworth, , UK: Penguin.  [Google Scholar]) selection task. The common focus was the effect of differences in the sizes of the sets represented by P and not-Q in assertions of the form If P then Q (conditional) or All P are Q (categorical). Results support the conclusion that such set size differences affect the strategies people adopt when asked to determine, efficiently, the truth or falsity of such assertions, but they do not entirely negate the tendency to select the term represented by P (the antecedent of the conditional or the subject of the categorical) in preference to the term represented by not-Q (the complement of the consequent of the conditional or the complement of the predicate of the categorical). Several possible explanations of this perseverance are considered. Results also support the conclusion that people find it easier to assess categorical assertions than logically equivalent conditional assertions.     

Contrast classes and matching bias as explanations of the effects of negation on conditional reasoning

In this paper the arguments for optimal data selection and the contrast class account of negations in the selection task and the conditional inference task are summarised, and contrasted with the matching bias approach. It is argued that the probabilistic contrast class account provides a unified, rational explanation for effects across these tasks. Moreover, there are results that are only explained by the contrast class account that are also discussed. The only major anomaly is the explicit negations effect in the selection task (Evans, Clibbens, & Rood, 1996), which it is argued may not be the result of normal interpretative processes. It is concluded that the effects of negation on human reasoning provide good evidence for the view that human reasoning processes may be rational according to a probabilistic standard.     

条件推理和选择任务的关系：选择任务中的条件推理逻辑

要求大学生被试在相同的情境和规则下先后完成选择任务和条件推理任务,从而系统考察两项条件命题任务之间的关系。结果表明,当规则的语义表征意义为条件命题和反条件命题时,两项任务的反应模式具有一致性;当为双向条件和非条件命题时,两项任务的反应模式出现了分歧,而且四种推理形式和四张卡片之间不存在直接的对应关系。两项条件命题任务之间的关系表现在,它们可能享有共同的语义关系表征空间,但推理过程和策略有所不同。     

Bayesian inference for the information gain model

One of the most popular paradigms to use for studying human reasoning involves the Wason card selection task. In this task, the participant is presented with four cards and a conditional rule (e.g., “If there is an A on one side of the card, there is always a 2 on the other side”). Participants are asked which cards should be turned to verify whether or not the rule holds. In this simple task, participants consistently provide answers that are incorrect according to formal logic. To account for these errors, several models have been proposed, one of the most prominent being the information gain model (Oaksford & Chater, Psychological Review, 101, 608–631, 1994). This model is based on the assumption that people independently select cards based on the expected information gain of turning a particular card. In this article, we present two estimation methods to fit the information gain model: a maximum likelihood procedure (programmed in R) and a Bayesian procedure (programmed in WinBUGS). We compare the two procedures and illustrate the flexibility of the Bayesian hierarchical procedure by applying it to data from a meta-analysis of the Wason task (Oaksford & Chater, Psychological Review, 101, 608–631, 1994). We also show that the goodness of fit of the information gain model can be assessed by inspecting the posterior predictives of the model. These Bayesian procedures make it easy to apply the information gain model to empirical data. Supplemental materials may be downloaded along with this article from .     

Two meanings of “if”? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.     

The Role of Negation in Conditional Inference

This paper addresses the issue of how negative components affect people's ability to draw conditional inferences. The study was motivated by an attempt to resolve a difficulty for the mental models theory of Johnson-Laird and Byrne, whose account of matching bias in the selection task is apparently inconsistent with Johnson-Laird's explanation of the double negation effects in conditional inference reported by Evans, Clibbens, and Rood (1995). Two experiments are reported, which investigate frequencies of conditional inferences with task presentation similar to that of the selection task in two respects: the presence of a picture of four cards and the use of implicit negations in the premises. The latter variable was shown to be critical and demonstrated a new phenomenon: Conditional inferences of all kinds are substantially suppressed when based on implicitly negative premises. This phenomenon was shown to operate independently of and in addition to the double negation effect. A third experiment showed that the implicit negation effect could be extended to the paradigm in which people are asked to produce their own conclusions. It is argued that these two effects can be explained within either the mental models theory or the inference rule theory, of propositional reasoning, but that each will require some revision in order to offer a convincing account.     

Deductive reasoning and matching-bias inhibition training: Evidence from a debiasing paradigm

Using the matching bias example, the aim of the present studies was to show that adults' reasoning biases are due to faulty executive inhibition programming. In the first study, the subjects were trained on Wason's classical card selection task; half were given training in how to inhibit the perceptual matching bias (experimental group) and half in logic without the inhibition component (control group). On the pre- and post-tests, their performance was assessed on the Evans conditional rule falsification task (with a negation in the antecedent of the rule), a task that also involves matching bias. In addition, subjects were tested for perceptual field dependence/independence using the Embedded Figures Test. The results brought out a specific inhibition training effect, as well as a clear-cut relationship in the experimental group between receptiveness to training and perceptual field independence. In the second study, the training paradigm was the same except that on the pre- and post-tests, the negation was in the consequent of the conditional rule (in this case, the perceptual matching response corresponds to the logical response). The subjects succeeded on the pre-test, and the matching-bias inhibition training had a negative effect on post-test performance. This specific negative priming effect confirms the inhibitory impact of our experimental training and outlines the dissociation of inhibition and logical components.     

Matching bias and set sizes: A discussion of Yama (2001)

Yama (2001) has presented an ingenious series of experiments in which he attempts to separate two accounts in the literature of the cause of “matching bias” in conditional reasoning. One account is that the bias arises from the way in which people process negations and the other is that it is due to the larger set sizes associated with negative propositions, rather than negation per se. Yama's experiments show influences of both negation and set size, from which he concludes that both factors contribute to the matching bias that is normally observed. In this note, it is argued that this conclusion is at odds with other findings in the literature, particularly those investigating implicit negation as the cause of the bias. Introducing explicit negations has been shown to remove matching bias completely and not partially, as Yama's account must predict. A possible reconciliation is proposed in terms of subtle contextual differences introduced by Yama's experiments.     

Two meanings of "if"? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.     

Separating value from selection frequency in rapid reaching biases to visual targets

Stimuli associated with positive rewards in one task often receive preferential processing in a subsequent task, even when those associations are no longer relevant. Here we use a rapid reaching task to investigate these biases. In Experiment 1 we first replicated the learning procedure of Raymond and O'Brien (2009), for a set of arbitrary shapes that varied in value (positive, negative) and probability (20%, 80%). In a subsequent task, participants rapidly reached toward one of two shapes, except now the previously learned associations were irrelevant. As in the previous studies, we found significant reach biases toward shapes previously associated with a high probable, positive outcome. Unexpectedly, we also found a bias toward shapes previously associated with a low probable, negative outcome. Closer inspection of the learning task revealed a potential second factor that might account for these results; since a low probable negative shape was always paired with a high probable negative shape, it was selected with disproportionate frequency. To assess how selection frequency and reward value might both contribute to reaching biases we performed a second experiment. The results of this experiment at a group level replicated the reach-bias toward positively rewarding stimuli, but also revealed a separate bias toward stimuli that had been more frequently selected. At the level of individual participants, we observed a variety of preference profiles, with some participants biased primarily by reward value, others by frequency, and a few actually biased away from both highly rewarding and high frequency targets. These findings highlight that: (1) rapid reaching provides a sensitive readout of preferential processing; (2) target reward value and target selection frequency are separate sources of bias; and (3) group-level analyses in complex decision-making tasks can obscure important and varied individual differences in preference profiles.     

Temporal distinctiveness and repetition benefits in task switching: Disentangling stimulus-related and response-related contributions

Despite the popularity of the Wason selection task in the psychology of reasoning, doubt remains as to whether card choices actually reflect a process of reasoning. One view is that while participants reason about the cards and their hidden sides—as indicated by protocol analysis—this reasoning merely confabulates explanations for cards that were preconsciously cued. This hypothesis has apparently been supported by studies that show that participants predominantly inspect cards which they end up selecting. In this paper, we reanalyse the data of one such study, which used eye-movement tracking to record card inspection times (Ball, Lucas, Miles, & Gale, 2003). We show that while cards favoured by matching bias are inspected for roughly equal lengths of times, their selection rates are strongly affected by their logical status. These findings strongly support a two-stage account in which attention is necessary but not sufficient for card selections. Hence, reasoning does indeed affect participants' choices on this task.     

Think-aloud protocols and the selection task: Evidence for relevance effects and rationalisation processes

Two experiments are reported that employed think-aloud methods to test predictions concerning relevance effects and rationalisation processes derivable from Evans' (1996) heuristic-analytic theory of the selection task. Evans' account proposes that card selections are triggered by relevance-determining heuristics, with analytic processing serving merely to rationalise heuristically cued decisions. As such, selected cards should be associated with more references to both their facing and their hidden sides than rejected cards, which are not subjected to analytic rationalisation. Experiment 1 used a standard selection-task paradigm, with negative components permuted through abstract conditional rules. Support was found for all heuristic-analytic predictions. This evidence was shown to be robust in Experiment 2, where “select - don't select” decisions were enforced for all cards. Both experiments also clarify the role played by secondary heuristics in cueing the consideration of hidden card values during rationalisation. We suggest that whilst Evans' heuristic-analytic model and Oaksford and Chater's (e.g., 2003) optimal data selection model can provide compelling accounts of our protocol findings, the mental models theory fares less well as an explanation of our full dataset.     

Speak your mind and I will make it right: the case of “selection task”

ABSTRACT

The “Wason selection task” is still one of the most studied tasks in cognitive psychology. We argue that the low performance originally obtained seems to be caused by how the information of the task is presented. By systematically manipulating the task instructions, making explicit the information that participants are required to infer in accordance with the logical interpretation of the material implication “if, then”, we found an improvement in performance. In Experiment 1, the conditional rule has been formulated within a relevant context and in accordance with the conversational rules of communication, hence transmitting the actual meaning of the material implication. In Experiment 2, a similar improvement has been obtained even without the realistic scenario, only by making explicit the unidirectionality of the material implication. We conclude that task instructions are often formulate neglecting the conversational rules of communication, and this greatly reduces the possibility to succeed in the task.     

Bayesian Rationality for the Wason Selection Task? A Test of Optimal Data Selection Theory

Oaksford and Chater (1994) proposed to analyse the Wason selection task as an inductive instead of a deductive task. Applying Bayesian statistics, they concluded that the cards that participants tend to select are those with the highest expected information gain. Therefore, their choices seem rational from the perspective of optimal data selection. We tested a central prediction from the theory in three experiments: card selection frequencies should be sensitive to the subjective probability of occurrence for individual cards. In Experiment 1, expected frequencies of the p- and the q-card were manipulated independently by concepts referring to large vs. small sets. Although the manipulation had an effect on card selection frequencies, there was only a weak correlation between the predicted and the observed patterns. In the second experiment, relative frequencies of individual cards were manipulated more directly by explicit frequency information. In addition, participants estimated probabilities for the four logical cases and of the conditional statement itself. The experimental manipulations strongly affected the probability estimates, but were completely unrelated to card selections. This result was replicated in a third experiment. We conclude that our data provide little support for optimal data selection theory.     

Against global method safety

The global method safety account of knowledge states that an agent’s true belief that p is safe and qualifies as knowledge if and only if it is formed by method M, such that her beliefs in p and her beliefs in relevantly similar propositions formed by M in all nearby worlds are true. This paper argues that global method safety is too restrictive. First, the agent may not know relevantly similar propositions via M because the belief that p is the only possible outcome of M. Second, there are cases where there is a fine-grained belief that is unsafe and a relevantly similar coarse-grained belief (with looser truth conditions) that is safe and where both beliefs are based on the same method M. Third, the reliability of conditional reasoning, a basic belief-forming method, seems to be sensitive to fine-grained contents, as suggested by the wide variation in success rates for thematic versions of the Wason selection task.

     

The Wished‐For Always Wins Until the Winner Was Inevitable All Along: Motivated Reasoning and Belief Bias Regulate Emotion During Elections

How do biases affect political information processing? A variant of the Wason selection task, which tests for confirmation bias, was used to characterize how the dynamics of the recent U.S. presidential election affected how people reasoned about political information. Participants were asked to evaluate pundit‐style conditional claims like “The incumbent always wins in a year when unemployment drops” either immediately before or immediately after the 2012 presidential election. A three‐way interaction between ideology, predicted winner (whether the proposition predicted that Obama or Romney would win), and the time of test indicated complex effects of bias on reasoning. Before the election, there was partial evidence of motivated reasoning—liberals performed especially well at looking for falsifying information when the pundit's claim predicted Romney would win. After the election, once the outcome was known, there was evidence of a belief bias—people sought to falsify claims that were inconsistent with the real‐world outcome rather than their ideology. These results suggest that people seek to implicitly regulate emotion when reasoning about political predictions. Before elections, people like to think their preferred candidate will win. After elections, people like to think the winner was inevitable all along.