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.     

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.     

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.     

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.     

Rephrasing between Disjunctives and Conditionals: Mental Models and the Effects of Thematic Content

Two experiments are reported thatinvestigate whether the logical equivalence of conditionals and disjunctives is paralleled by a psychological equivalence. In these experiments, subjects rephrased from one form into the other. Experiment 1 demonstrated strong effects of familiarity and causality of rule content. Similar findings were found in Experiment 2 with a different conditional rule syntax. An account of the experiments is given in terms of mental models theory: In this account, task performance can be seen to depend upon the extent to which the model sets used by subjects to generate rephrasings are complete, task content being the most important factor affecting model set completion. A 'Minimal Completion' strategy is proposed to operate in the absence of thematic content. The experiments also falsify the long-held assumption that conditionals with negative antecedents are always interpreted as their disjunctive equivalents. This raises doubts about the mental models explanation for matching bias in conditional reasoning.     

Conservation acquisition, maintenance, and generalization by mentally retarded children using equality-rule training.

To teach conservation to mildly retarded, preoperational preadolescents (9 to 12 years old), a number-representational system was used to mediate the invariance of quantity as part of "equality-rule" training. Before viewing a perceptually misleading configuration of either two equal quantities or two unequal quantities entailing the dimensions of number or length, participants learned that equality involved the assignment of two identical numbers and inequality the assignment of two different numbers. These numbers were then applied to the actual quantities and became the basis for rule statements that were rehearsed, memorized, and subject-generated each time the quantities were transformed into a new configuration. Following equality training, correct judgments and verbal justifications of conservation were high (M greater than or equal to 85%) during both immediate and delayed post-tests and for near-generalization (number and length) and far-generalization (weight, liquid substance, and solid substance) tasks. In contrast, the post-test levels of comparable participants given learning-set (LS) training, LS plus verbal-rule training (a combination of statements about identity, negation, and compensation), or no training at all were substantially and significantly lower. Equality training is of theoretical and practical interest because of its potential to teach a symbolic representational rule that directly and meaningfully articulates the quantitative properties of objects and counteracts the overreliance on task-specific and faulty perceptual cues inherent in the conservation task.     

四卡问题解决中的内容与逻辑分析效应

选取条件概率(P(Q|P))由低到高的四个命题作为四卡问题中的检验规则,探讨了大学生被试对四张卡片的逻辑证明作用的推断能力及其对解决四卡问题的影响。结果发现:(1)不同条件概率的命题之间正确选择P-Q的人数百分比不存在显著差异,命题的条件概率因素对四卡问题的正确解决没有影响。(2)逻辑分析过程对四卡问题的正确解决产生了一定的抑制作用,这可能是因为被试不能从整体上思考四张卡片在命题检验中的逻辑作用的缘故。(3)一些被试即使在逻辑分析过程中表现出知道-Q卡片的证伪作用,仍然倾向于选择卡片Q而非-Q,这一现象再次证实了人类思维的非形式逻辑的一面。     

Spatial and Selective Attention in the Cerebral Hemispheres in Depression, Mania, and Schizophrenia

Two tachistoscopic tests examining distinct aspects of attention were administered to normal subjects and patients with depression, mania, and schizophrenia. The first examined spatial attentional bias using happy-sad chimeric faces, known to elicit a perceptual bias to the left side of space in normal right-handers provided the right cerebral hemisphere is intact. The second used a lateralized version of the Stroop task, a traditional test of selective attention. Normals showed the expected leftward perceptual bias but showed equivalent susceptibility to the Stroop effect in both visual fields. As previously demonstrated with chimeric faces viewed in free vision, depression and mania were associated with weak and strong biases respectively with schizophrenics showing no bias to either side of space. The relationship between perceptual bias, as assessed by reaction time and absolute performance and the Stroop effect, showed differences according to diagnosis. This may be interpreted as evidence for the dissociability of attentional processes as well as lateralized differences in the pattern of cerebral activation in affective disorders and schizophrenia. The independence of performance variables on these tests in the schizophrenic group points to severe neuropsychological dysfunction.     

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.     

四卡问题解决中的匹配偏向再探

选取经典的四卡问题作为实验材料,深入探讨了“综合考虑证真证伪作用”的提示以及逻辑分析过程对被试解决四卡问题不能产生促进效应的原因。结果发现:(1)多数被试能对卡片P和-Q进行正确的逻辑推断,但是最后却仍然倾向于选择卡片Q而非-Q,这种错误并非是由于附加的认知任务使得被试的短时记忆容量超载所致。(2)元音偶数组与元音非偶数组的被试对四张卡片作出正确逻辑推断的人数百分比基本一致,但是后者选择P-Q的人数百分比却显著高于前者,这表明多数被试似乎并不依据逻辑分析的结果及其命题检验的规则来作出选择,而是采用匹配策略,错误地选择了Q卡片。     

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.     

Matching and oddity learning in the pigeon: Transfer effects and the absence of relational learning

Three experiments examined the extent to which pigeons trained on a matching or oddity discrimination with one pair of colours showed transfer when tested on a new matching or oddity discrimination with a new pair of colours. Experiment 1 examined the effects of key spacing and a delay procedure and replicated previous reports that in the transfer stage subjects given the same kind of problem (Non-shift condition) in general learn more rapidly than those given the opposite problem (Shift condition). However, this difference appeared only when pigeons given matching in both training and transfer stages were compared to those shifted from oddity to matching; it did not appear in birds transferred to oddity. Transfer was not significantly affected by key spacing or by the delay.

Experiments 2 and 3 examined transfer from a non-relational conditional discrimination based on one set of colours to a subsequent matching or oddity task based on two new colours. Both a comparison between the results of Experiment 1 and 2 and the corresponding within-experiment comparison from Experiment 3 showed that transfer from conditional training to matching was as great as from prior training on matching, while prior training on oddity produced negative transfer on shift to matching. It was suggested that this negative transfer occurs because pigeons trained on oddity have not learned to override an initial bias towards the odd stimulus in an array. Whatever the correct explanation; the present results provide no support for the claim that pigeons solve matching or oddity discriminations relationally.     

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.     

Misinterpretation of conditional statements in Wason's selection task

Errors may be made on Wason's selection task because either (a) the rule to be tested is misunderstood, or (b) reasoning from that rule is inaccurate, or both. We report two experiments using the experimental paradigm introduced by Gebauer and Laming in which subjects are given six problems in succession. We use the subset of cards selected by each subject as (a) an indication of how the rule is understood and, when that selection is consistent throughout all six problems (so that we can infer a consistent understanding of the rule), as (b) a basis for evaluating the accuracy of the subject's reasoning according to three independent criteria. Experiment 1 adds an exactly parallel contextual version of the task to permit comparison between performances (by the same subjects) on the two versions. Experiment 2 repeats Exp. 1, but with negatives inserted in the conditional rule. Most subjects make a consistent selection of cards throughout all six problems, but typically appear to misunderstand the rule. This is so in both abstract and contextual tasks and replicates the finding by Gebauer and Laming. Most misunderstandings consisted of either (a) reading the simple conditional rule as a bi-conditional or (b) substituting “top/underneath” for “one side/other side”. In Exp. 1 subjects seldom misevaluated the rule they appeared to be testing, but such “errors” of evaluation were common in Exp. 2. Negatives confuse the subjects and should not be used in any conditional application that matters. In Exp. 2 (but not 1) there was a significant correlation between interpretations of the two tasks. We provide an explanation of “matching bias” (it results from the confluence of the two common misunderstandings above) and comment on “mental models” which are, at present, unable to accommodate the variety of results we present here. We also relate our experimental paradigm to the conditional inference task and to truth tables. Received: 26 February 1999 / Accepted: 5 November 1999     

Evidence of a transition from perceptual to category induction in 3- to 9-year-old children

We examined whether inductive reasoning development is better characterized by accounts assuming an early category bias versus an early perceptual bias. We trained 264 children aged 3 to 9 years to categorize novel insects using a rule that directly pitted category membership against appearance. This was followed by an induction task with perceptual distractors at different levels of featural similarity. An additional 52 children were given the same training followed by an induction task with alternative stimuli. Categorization performance was consistently high; however, we found a gradual transition from a perceptual bias in our youngest children to a category bias around 6 or 7 years of age. In addition, children of all ages were equally distracted by higher levels of featural similarity. The transition is unlikely to be due to an increased ability to inhibit perceptual distractors. Instead, we argue that the transition is driven by a fundamental change in children's understanding of category membership.     

Are People Successful at Learning Sequences of Actions on a Perceptual Matching Task?

We report the results of an experiment in which human subjects were trained to perform a perceptual matching task. Subjects were asked to manipulate comparison objects until they matched target objects using the fewest manipulations possible. An unusual feature of the experimental task is that efficient performance requires an understanding of the hidden or latent causal structure governing the relationships between actions and perceptual outcomes. We use two benchmarks to evaluate the quality of subjects' learning. One benchmark is based on optimal performance as calculated by a dynamic programming procedure. The other is based on an adaptive computational agent that uses a reinforcement-learning method known as Q-learning to learn to perform the task. Our analyses suggest that subjects were successful learners. In particular, they learned to perform the perceptual matching task in a near-optimal manner (i.e., using a small number of manipulations) at the end of training. Subjects were able to achieve near-optimal performance because they learned, at least partially, the causal structure underlying the task. In addition, subjects' performances were broadly consistent with those of model-based reinforcement-learning agents that built and used internal models of how their actions influenced the external environment. We hypothesize that people will achieve near-optimal performances on tasks requiring sequences of action-especially sensorimotor tasks with underlying latent causal structures-when they can detect the effects of their actions on the environment, and when they can represent and reason about these effects using an internal mental model.     

Improved mental representation of space in beginner orienteers

The purpose of the present study was to monitor any improvement in orienteering skills attributable to acquiring a better mental representation of space. Two groups were examined: the experimental group, who attended 6 mo. of orienteering lessons, versus the control group, who did jogging training instead. Each group, consisting of 20 children, was tested on the Corsi Block-tapping Test, run Forward and Backward, and the Star-Butterfly Test. Pre- and post-tests were administered. In the experimental group, scores increased in mean complexity from pre- to post-test on the Forward and the Backward Corsi tests, while on the Star-Butterfly Test both time and mistakes had decreased after the training. In the control group, mean complexity and Star-Butterfly Test scores were unchanged from pre- to post-test. These results showed that after continual training in orienteering techniques, the orienteering group was able to remember and repeat sequences of events with greater precision than before the training, while these skills were unchanged in the control group after training in jogging.     

The attentional demands of negation in a memory-scanning task

Subjects were run in a Sternberg recognition memory task modified to occasionally require a transformation prior to response. The transformation was similar to logical negation since onplus or nontransformed trials subjects responded "yes" if the probe was from the current memory set and "no" otherwise, while onminus or transformed trials subjects responded "no" to memory set probes and "yes" to nonmemory set probes. Two models proposed to account for the effects of logical negation were compared: The encoding and comparison model predicts that logical negation requires an additional processing stage, while the capacity sharing model argues that negation adds a processing stage and also retards the rate of memory search. The results indicated that minus probes had 50% larger mean reaction time by set size slopes than the corresponding plus probes. This finding offers clear support for the capacity sharing model.     

The role of perceptual laws in the Rorschach test

The purpose of this study is twofold: to ascertain the perceptual deficits in schizophrenic subjects and to test the assumption that the Rorschach is mainly a perceptual task. Forty-eight subjects participated in the study, distributed in six groups of eight subjects each: normals, affective disorders, and four groups of schizophrenics (chronic paranoid, chronic nonparanoid, acute paranoid, and acute nonparanoid). They were given a perceptual test developed by Fernández-Trespalacios, Bermudez, and Luna (1979). Contrary to previous findings, no differences in the perceptual test were found among the groups. In the second part of the study, a group of schizophrenic subjects was given the Rorschach and the perceptual test in a balanced order. Subsequently, subjects in the experimental group were trained in the perceptual laws they had failed. Comparison of the Rorschach protocols obtained before and after this training failed to show any significant differences in the expected direction, thus questioning the perceptual nature of this test. Interestingly, an increase in negative categories of the Rorschach subsequent to the perceptual training was observed.     

Decreasing influence of arbitrarily applicable verbal relations of recreational gamblers: A randomized controlled trial

Twenty‐one recreational gamblers were randomly assigned to two groups; one group was exposed to a conditional discrimination relational training task to bias choice allocation to a black machine presented concurrently with a red machine, and the other group underwent the same relational training task immediately followed by a defusion procedure, designed to expand upon the relations developed in the initial relational task. Both groups completed a simulated slot‐machine task before and after the relational training task, with or without the defusion procedure. Results showed that 9 of 11 participants in the relational training only group showed an increased bias toward the black machine, compared to only 4 of 10 in the relational training plus defusion group; this latter group also showed greater matched responding. Results suggest that expanding verbal–relational networks may reduce the influence of any single verbal relation on gambling choice behavior.