A quantitative model of optimal data selection in Wason's selection task.

The optimal data selection model proposed by Oaksford and Chater (1994) successfully formalized Wason's selection task (Wason, 1966). The model, however, involved some questionable assumptions and was also not sufficient as a model of the task because it could not provide quantitative predictions of the card selection frequencies. In this paper, the model was revised to provide quantitative fits to the data. The model can predict the selection frequencies of cards based on a selection tendency function (STF), or conversely, it enables the estimation of subjective probabilities from data. Past experimental data were first re-analysed based on the model. In Experiment 1, the superiority of the revised model was shown. However, when the relationship between antecedent and consequent was forced to deviate from the biconditional form, the model was not supported. In Experiment 2, it was shown that sufficient emphasis on probabilistic information can affect participants' performance. A detailed experimental method to sort participants by probabilistic strategies was introduced. Here, the model was supported by a subgroup of participants who used the probabilistic strategy. Finally, the results were discussed from the viewpoint of adaptive rationality.     

The effects of problem content and negation on Wason's selection task

The present study examined performance on Wason's selection task for two types of thematic content that have been shown to lead reliably to correct responding in this task. The four versions of the implication rule that are possible when negative components (antecedent and consequent) are allowed were used. This permitted a test of the hypothesis that matching bias and verification bias are cognitive short-circuiting strategies which are used when subjects have no prior experience with the problem content. In support of this hypothesis, facilitation was observed for the negated thematic rules when compared to performance on negated abstract rules. In addition, neither matching bias nor verification bias explained very well the data for negated abstract rules which were recodable into non-negative form. For both thematic and abstract problems, a fairly substantial percentage of the selections were unaccounted for with respect to processing strategy.     

Alternative antecedents, probabilities, and the suppression of fallacies in Wason's selection task

Three experiments examined the influence of a second rule on the pattern of card selections on Wason's selection task. In Experiment 1 participants received a version of the task with a single test rule or one of two versions of the task with the same original test rule together with a second rule. The probability of q was manipulated in the two-rules conditions by varying the size of the antecedent set in the second rule. The results showed a significant suppression of q card and not-p card selections in the alternative-rule conditions, but no difference as a function of antecedent set size. In Experiment 2 the size of the antecendent set in the two-rules conditions was manipulated using the context of a computer printing double-sided cards. The results showed a significant reduction of q card selections in the two-rules conditions, but no effect of p set size. In Experiment 3 the scenario accompanying the rule was manipulated, and it specified a single alternative antecedent or a number of alternative antecedents. The q card selection rates were not affected by the scenario manipulation but again were suppressed by the presence of a second rule. Our results suggest that people make inferences about the unseen side of the cards when engaging with the task and that these inferences are systematically influenced by the presence of a second rule, but are not influenced by the probabilistic characteristics of this rule. These findings are discussed in the context of decision theoretic views of selection task performance (Oaksford & Chater, 1994).     

Misinterpretation of instructions in an aftereffect task

Some subjects in studies of kinesthetic aftereffect erroneously believe the task is to show the width of the aftereffect inducing rather than the standard stimulus. Although such subjects may be encountered rarely, the errors they make are very large. Precautionary steps are indicated.     

Learning conditional frequencies in a probability learning task

The study was prompted by a theoretical discussion of probability learning by Estes (1976). In three separate experiments, subjects were presented with frequency information in the form of wins and losses among 3 teams, and later predicted future wins and losses. Frequencies were devised so that conditional win frequencies for a pair of teams were either inconsistent or consistent with marginal win frequencies for each team. In experiment 1, when subjects predicted future events on the basis of known past frequencies, predictions were generally based on conditional frequencies. In experiment 2 six blocks of observations were presented, with predictions following each block. What little learning did occur was in the direction of the conditional frequencies. Subjects in experiment 3 were able to learn conditional frequencies when given explicit instructions to do so. Results were discussed in terms of a two-stage hypothesis generation model that might operate within the framework of an associative theory of probability learning.     

Generation of hypotheses in Wason's 2-4-6 task: an information theory approach.

We explored the "context of discovery" in Wason's 2-4-6 task, focusing on how the first hypothesis is generated. According to Oaksford and Chater (1994a) people generate hypotheses extracting "common features", or regularities, from the available triples, but their model does not explain why some regularities contribute to the hypothesis more than do other regularities. Our conjecture is that some regularities contribute to the hypothesis more than do other regularities because people estimate the amount of information in the perceived regularities and try to preserve as much information as possible in their initial hypotheses. Experiment 1, which used two initial triples, showed that the presence of high-information relational regularities in the initial triples affected the information in the initial hypotheses more than did the presence of low-information object regularities. Experiment 2 extended the results to the classic situation in which only one initial triple is given. It also suggested that amount of information is the only aspect of the structure of the triple that affects hypotheses generation. Experiment 3 confirmed the latter finding: Although relations are commonly distinguished between first-order and higher order relations, the latter being most important for generating hypotheses (Gentner, 1983), higher order relations do have an effect on Wason's 2-4-6 task only if their presence incre ases information. In the conclusion we discuss the statistical soundness of human hypotheses generation processes, and we ask an unanswered question: Amount of information explains why some regularities are preferred to others, but only within a set of "nonarbitrary" regularities; there are object regularities that are rich in information content, but are considered "arbitrary", and are not used in generating hypotheses. Which formal property can distinguish between these two sets of regularities?     

Rational choices in wason's selection task

Sixty-eight subjects were asked to solve a series of six Wason selection problems by physically turning relevant cards over until they could say whether the rule was correct or false. In the first experiment most of the subjects misunderstood the rule they were asked to verify, different subjects misunderstanding in different ways, but commonly reading (a) top/underneath for one side/other side and (b) a dual conditional for if..., then.... However, a majority of subjects thereafter responded in complete logical consistency with the rule as they understood it to be. When the misunderstandings revealed in the first experiment were themselves presented as rules to be verified in a second experiment, performance was much more logical than is usually reported. It is concluded that the illogicality commonly associated with Wason's selection task is only apparent.     

A comparison of disconfirmatory, confirmatory and control strategies on Wason's 2-4-6 task

Attempts to instruct subjects to falsify on inference tasks designed to model scientific problem-solving have indicated that, in most cases, falsification does not lead to improved performance. The only study in which instructions to falsify did improve performance was done with groups, using a novel inference task. The present study is an attempt to replicate the success of falsification in the group study with subjects run individually on an inference task that has been used extensively in the literature: Wason's 2-4-6 problem. Each subject was run in one of three strategy conditions: confirmatory, disconfirmatory or control (no-strategy).

Results indicated that subjects in the disconfirmatory condition solved the 2-4-6 problem significantly more often than subjects in other conditions. The superior performance of disconfirmatory subjects was explained by the fact that they deliberately sought and obtained significantly more falsificatory information than subjects in other conditions.

The critical difference between this study and previous attempts to instruct individual subjects to falsify on the 2-4-6 task is that subjects in the present study were given no feedback as to whether their guesses were right or wrong until the experiment was over. The implications of this result for scientific problem-solving are discussed.     

Matching versus optimal data selection in the Wason selection task

It has been reported as a robust effect that people are likely to select a matching case in the Wason selection task. For example, they usually select the 5 case, in the Wason selection task with the conditional “if an E, then a not-5”. This was explained by the matching bias account that people are likely to regard a matching case as relevant to the truth of the conditional (Evans, 1998). However, because a positive concept usually constructs a smaller set than its negative one does (a rarity assumption), it is more effective to get information on the truth of the conditional in a positive set than in a negative set. Thus the optimal data selection account can also explain the effect. The set size of Q and matching by introducing negation were manipulated independently in four experiments. From the results it was inferred that the so-called matching bias was an amalgam of two different cognitive components—relevance judgement by matching and optimal data selection.     

Effects of response selection on the task repetition benefit in task switching

A task switch typically leads to worse performance than a repetition does. This shift cost can be reduced with sufficient task preparation time, but a residual cost usually remains. We propose that a large part of this residual cost is caused by an activation bias produced by response selection processes in the preceding trial. In our experiments, we manipulated response selection requirements using a go/no-go methodology. The residual shift cost disappeared after no-go trials, suggesting that response selection is crucial to establish an activation bias for the current category-response rules and that this bias persists into the next trial. A comparison with a go-only group confirmed this analysis by revealing no differences in preparatory strategy due to the inclusion of no-go trials. In addition, no-go trials had no significant effects on subsequent trials in a single-task experiment, suggesting that no-go trials are not coded as a task different from go trials and that there is no inhibition of the prepared task in a no-go trial. We thus conclude that a persisting activation bias of response rules plays a major role in task switching.     

A conditional logit model of collegiate major selection

The choice of a major by a college student is viewed as depending upon the quantity of various outputs (such as income and status) each major provides and the taste structure of the student for these outputs. Tradeoffs in outputs occur so that high status may overcome low-income potential in the occupation into which the major provides entry. Different taste structures among students mean tradeoffs occur at different rates, so that taste structues are best associated with student major selection in a probability sense. Changes in the probability of selecting a collegiate major are associated with changes in student taste structures via a conditional logit model. The taste structure of a student is hypothesized to depend upon the environment in which the student was raised and the environment in which the student now lives. The relationship between environment and taste is also best stated in a probability sense and a second logit model is used to describe this relationship. Estimation of the two logit models, using survey data, attempts to quantify the hypothesized route from environment to taste structure to major selection for entry into an occupation. An example of this route is the finding that women students place more importance on obtaining high income than do men students and the greater the importance of high income, the lower the probability of selecting an education major, the greater the probability of selecting a humanities or social science major. Other results of estimation are presented and discussed.     

The role of response selection for inhibition of task sets in task shifting

Response selection in task shifting was explored using a go/no-go methodology. The no-go signal occurred unpredictably with stimulus onset so that all trials required task preparation but only go trials required response selection. Experiment 1 showed that shift costs were absent after no-go trials, indicating that response processes are crucial for shift costs. In Experiment 2, backward inhibition was absent after no-go trials. Experiments 3 and 4 demonstrated that response selection, rather than execution, causes backward inhibition. All 4 experiments showed effects of preparation time in go trials, suggesting that advance preparation must have also occurred in no-go trials. The authors concluded that inhibition of irrelevant task sets arises only at response selection and that residual shift costs reflect such persisting inhibition.     

Permission schemas and the selection task

Cheng and Holyoak's abstract permission schema version of Wason's selection task and the standard abstract version of the task were examined in two experiments, each a factorial design with type of problem (permission vs. standard), presence or absence of a checking context, explicit or implicit negatives on the not-p and not-q cards, and presence or absence of a rule clarification statement as factors. The original permission problem violation-type instruction was employed in Experiment 1, and Margolis's not-p and not-q violation instruction (Griggs & Jackson, 1990) was used in Experiment 2. Subjects were 640 university undergraduates, with each subject solving only one problem. The major findings for permission tasks were: (1) facilitation for the abstract permission version was replicated but found to be dependent upon the presence of explicit negatives on the not-p and not-q cards; and (2) this facilitation was enhanced by the Margolis not-p and not-q instruction. Per Girotto, Mazzocco, and Cherubini (1992), these findings and the observed error patterns are consistent with pragmatic schema theory. The major findings for the standard version of the task were: (1) none of the factors significantly impacted proportion correct [performance was poor, ≦10% correct in 15 of 16 conditions] and (2) the number of not-p & not-q incorrect selections was increased significantly for the not-p and not-q instruction. These results are discussed in terms of Manktelow and Over's argument that the standard abstract task and the permission schema version are actually different problems.     

The effect of emotion on interpretation and logic in a conditional reasoning task

The effect of emotional content on logical reasoning is explored in three experiments. Theparticipants completed a conditional reasoning task (If p, then q) with emotional and neutral contents. In Experiment 1, existing emotional and neutral words were used. The emotional value of initially neutral words was experimentally manipulated in Experiments 1B and 2, using classical conditioning. In all experiments, participants were less likely to provide normatively correct answers when reasoning about emotional stimuli, compared with neutral stimuli. This was true for both negative (Experiments 1B and 2) and positive contents (Experiment 2). The participants' interpretations of the conditional statements were also measured (perceived sufficiency, necessity, causality, and plausibility). The results showed the expected relationship between interpretation and reasoning. However, emotion did not affect interpretation. Emotional and neutral conditional statements were interpreted similarly. The results are discussed in light of current models of emotion and reasoning.     

The online processing of only if and even if conditional statements: Implications for mental models

A sentential connective like only if or even if merges two simple propositions into a complex statement. This study used a visual world paradigm experiment to explore how this merging process proceeds online. We first presented participants with a short animation, illustrating different simple propositions that are possible to be merged by the sentential connectives. We then auditorily played an only if or an even if statement and recorded participants' eye movements on the concurrent test image. We observed that hearing the sentential connective results in more fixations on the tokens of the appropriate propositions that are eligible to be merged by the sentential connective. Each sentential connective elicited anticipatory effect suggests that once they heard the sentential connective, participants knew which propositions could be merged. We then discussed the implications of our results to the mental model theory of conditionals and the experimental studies reported in literature.     

The role of verbal short-term memory in task selection: How articulatory suppression influences task choice in voluntary task switching

The roles of verbal short-term memory (vSTM) in task selection and task performance processes were examined when individuals were asked to voluntarily choose which of two tasks to perform on each trial randomly. Consistent with previous voluntary task-switching (VTS) research, we hypothesized that vSTM would support random task selection by maintaining a sequence of previously executed tasks that would be used by a representativeness heuristic. Furthermore, because using a representativeness heuristic requires sufficient time for updating and comparison processes, we expected that vSTM would have a greater effect on task selection when more time was available. Participants completed VTS under concurrent articulatory suppression and foot tapping at short and long response-to-stimulus intervals (RSIs). Task selection in VTS was more repetitive under suppression than under foot tapping, but this effect did not vary with RSI, suggesting that vSTM does not maintain the sequence of executed tasks to guide task selection. Instead, vSTM is critical for maintaining the intended task and ensuring that it is carried out. In contrast to the finding that a working memory load impairs task performance, we found no difference in reaction times and no switch costs between suppression and foot-tapping conditions, suggesting that vSTM is not critical for task performance.     

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。     

Inspection times, the change task, and the rapid-response selection task

Three experiments are reported, which are based upon the Wason four-card selection task inspection time paradigm, in which subjects solve computer-presented trials while using a mouse to indicate the card currently under consideration. Evans (1996) had shown that selected cards were inspected for longer than non-selected cards, and this was taken as support for the existence of pre-conscious heuristic processes that direct attention towards relevant aspects of a problem. However, Roberts (1998b) suggested that this inspection time effect is artefactual, due to task format induced biases. Experiment 1 utilized a "change" task: Cards were presented either as selected or not selected, and subjects changed these where necessary. This demonstrated an association between card selection and inspection time independently of one between the act of response and inspection time. Experiment 2 utilized a standard selection task, but subjects either responded within 2 s of each card presentation, or made selections with no time pressure. The curtailment of thinking time increased matching behaviour—more cards matching the terms in the rules were selected—and was replicated in Experiment 3 using a within-subjects design. Overall, the data support Evans' heuristic-analytic framework albeit with some caveats.     

Task selection cost asymmetry without task switching

The switch cost asymmetry (i.e., larger costs when switching from a nondominant into a dominant task than vice versa) has been explained in terms of the trial-to-trial carryover of activation levels required for the dominant versus the nondominant task. However, there is an open question about whether an actual switch in task is in fact necessary to obtain a “selection” cost asymmetry. In Experiments 1 and 2, we modified an alternatingruns paradigm to include either long or short response-to-stimulus intervals (RSIs) after each pair of trials (i.e., AA-AA-BB-BB), thereby inducing selection costs not only at the point of a task switch (i.e., AA-BB), but also between same-task pairs (i.e., AA-AA). Using spatially compatible versus incompatible response rules (Experiment 1) and Stroop word versus color naming (Experiment 2), we found asymmetric effects not only at task-change transitions, but also at task-repeat transitions when the RSI was long (presumably inducing frequent losses of set). In Experiments 3A and 3B, a cost asymmetry for long RSIs was obtained even when competing tasks were separated into alternating single task blocks, but not when the tasks were compared in a betweensubjects design. This general pattern cannot be explained by activation carryover models, but is consistent with the idea that the asymmetry arises as a result of interference from long-term memory traces.     

Response selection during a joint action task

It has been suggested that a shared task representation is used to predict a coactors' needs and that these predictions influence each coactor's response selection in a joint action task. The authors tested this idea using a joint action task in which participants passed a jug to a confederate under different conditions. They hypothesized that if participants predicted the needs of their coactor and planned their movement according to these predictions, the jug would be passed with the handle available to the confederate. Consistent with this hypothesis, the jug was passed with the handle available on 86% of the trials. This strategy may be adopted to improve the efficiency of the whole task as opposed to each individual's portion of the task.