Information Seeking in a Non-Hypothesis Testing Task

The information gain model (Oaksford and Chater, Psychological Review 101, 608–631, 1994) advocates that participants attempt to achieve a larger expected information gain when they have to test an if-then rule or hypothesis. However, acquisition of larger expected information gain could also be operational when participants do not have to test a hypothesis. This study devised a new task to investigate whether participants would seek larger expected information gain when they were not required to test a hypothesis. The task required participants to select one out of two balance scales for weighing coins in order to detect an underweight coin. We discovered that participants more frequently selected the balance scale that provided smaller expected information gain. This finding suggests that the preference for larger expected information gain may not apply to non-hypothesis testing settings.     

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.     

Non-monotonicity and Informal Reasoning: Comment on Ferguson (2003)

In this paper, it is argued that Ferguson’s (2003, Argumentation 17, 335–346) recent proposal to reconcile monotonic logic with defeasibility has three counterintuitive consequences. First, the conclusions that can be derived from his new rule of inference are vacuous, a point that as already made against default logics when there are conflicting defaults. Second, his proposal requires a procedural “hack” to the break the symmetry between the disjuncts of the tautological conclusions to which his proposal leads. Third, Ferguson’s proposal amounts to arguing that all everyday inferences are sound by definition. It is concluded that the informal logic response to defeasibility, that an account of the context in which inferences are sound or unsound is required, still stands. It is also observed that another possible response is given by Bayesian probability theory (Oaksford and Chater, in press, Bayesian Rationality: The Probabilistic Approach to Human Reasoning, Oxford University Press, Oxford, UK; Hahn and Oaksford, in press, Synthese).     

Logical reasoning and probabilities: A comprehensive test of Oaksford and Chater (2001)

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.     

Data selection and natural sampling: Probabilities do matter

Probabilistic accounts of Wason's selection task (Oaksford & Chater, 1994, 1996) are controversial, with some researchers failing to replicate the predicted effects of probability manipulations. This paper reports a single experiment in which participants sampled the data naturally-that is, sequentially. The proportions of possible data types (i.e., cards in the selection task) also reflected the probability manipulation. Other than this procedural difference, the materials were the same as those in Oberauer, Wilhelm, and Rosas-Diaz's (1999) Experiment 3, which failed to show probabilistic effects. Significant probabilistic effects were observed. Moreover, in a comparative model-fitting exercise, a revised version of the information gain model (Hattori, 1999, 2002; Oaksford & Chater, in press-b) was shown to provide better fits to these data than did competing explanations.     

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.     

Discussion Task Demands and Revising Probabilities in the Selection Task: A Comment on Green,Over, and Pyne

Green, Over, and Pyne's (1997) paper (hereafter referred to as “GOP”) seems to provide a novel approach to examining probabilistic effects in Wason's selection task. However, in this comment, it is argued that their chosen experimental paradigm confounds most of their results. The task demands of the externalisation procedure (Green, 1995) enforce a correlation between card selections and the probability of finding a counterexample, which was the main finding of GOP's experiments. Consequently GOP cannot argue that their data support Kirby's (1994) proposal that people's normal strategy in the selection task is to seek falsifying evidence. Despite this methodological problem, effects of the probability of the antecedent (p) of a conditional rule, if p then q, predicted by Kirby (1994) and by Oaksford and Chater (1994) were observed, although they were inconsistent between Experiments 1 and 2. Moreover, the probability estimates that GOP collected, which are not vulnerable to that methodological criticism, do support the idea that when P (p)> P (q), participants revise P (p) down as suggested by Oaksford and Chater (1994).     

Deciding between accounts of the selection task: A reply to Oaksford (2002)

In this paper we report on our attempts to fit the optimal data selection (ODS) model (Oaksford & Chater, 1994; Oaksford, Chater, & Larkin, 2000) to the selection task data reported in Feeney and Handley (2000) and Handley, Feeney, and Harper (2002). Although Oaksford (2002b) reports good fits to the data described in Feeney and Handley (2000), the model does not adequately capture the data described in Handley et al. (2002). Furthermore, across all six of the experiments modelled here, the ODS model does not predict participants' behaviour at the level of selection rates for individual cards. Finally, when people's probability estimates are used in the modelling exercise, the model adequately captures only 1 out of 18 conditions described in Handley et al. We discuss the implications of these results for models of the selection task and claim that they support deductive, rather than probabilistic, accounts of the task.     

Optimal data selection: Revision,review, and reevaluation

Since it first appeared, there has been much research and critical discussion on the theory of optimal data selection as an explanation of Wason’s (1966, 1968) selection task (Oaksford & Chater, 1994). In this paper, this literature is reviewed, and the theory of optimal data selection is reevaluated in its light. The information gain model is first located in the current theoretical debate in the psychology of reasoning concerning dual processes in human reasoning. A model comparison exercise is then presented that compares a revised version of the model with its theoretical competitors. Tests of the novel predictions of the model are then reviewed. This section also reviews experiments claimed not to be consistent with optimal data selection. Finally, theoretical criticisms of optimal data selection are discussed. It is argued either that the revised model accounts for them or that they do not stand up under analysis. It is concluded that some version of the optimal data selection model still provides the best account of the selection task. Consequently, the conclusion of Oaksford and Chater’s (1994) original rational analysis (Anderson, 1990), that people’s hypothesis-testing behavior on this task is rational and well adapted to the environment, still stands.     

Contrast class cues and performance facilitation in a hypothesis-testing task: evidence for an iterative counterfactual model

Hypothesis-testing performance on Wason’s (Quarterly Journal of Experimental Psychology 12:129–140, 1960) 2–4–6 task is typically poor, with only around 20% of participants announcing the to-be-discovered “ascending numbers” rule on their first attempt. Enhanced solution rates can, however, readily be observed with dual-goal (DG) task variants requiring the discovery of two complementary rules, one labeled “DAX” (the standard “ascending numbers” rule) and the other labeled “MED” (“any other number triples”). Two DG experiments are reported in which we manipulated the usefulness of a presented MED exemplar, where usefulness denotes cues that can establish a helpful “contrast class” that can stand in opposition to the presented 2–4–6 DAX exemplar. The usefulness of MED exemplars had a striking facilitatory effect on DAX rule discovery, which supports the importance of contrast-class information in hypothesis testing. A third experiment ruled out the possibility that the useful MED triple seeded the correct rule from the outset and obviated any need for hypothesis testing. We propose that an extension of Oaksford and Chater’s (European Journal of Cognitive Psychology 6:149–169, 1994) iterative counterfactual model can neatly capture the mechanisms by which DG facilitation arises.     

WoMMBAT: A user interface for hierarchical Bayesian estimation of working memory capacity

The change detection paradigm has become an important tool for researchers studying working memory. Change detection is especially useful for studying visual working memory, because recall paradigms are difficult to employ in the visual modality. Pashler (Perception & Psychophysics, 44, 369–378, 1988) and Cowan (Behavioral and Brain Sciences, 24, 87–114, 2001) suggested formulas for estimating working memory capacity from change detection data. Although these formulas have become widely used, Morey (Journal of Mathematical Psychology, 55, 8–24, 2011) showed that the formulas suffer from a number of issues, including inefficient use of information, bias, volatility, uninterpretable parameter estimates, and violation of ANOVA assumptions. Morey presented a hierarchical Bayesian extension of Pashler’s and Cowan’s basic models that mitigates these issues. Here, we present WoMMBAT (Working Memory Modeling using Bayesian Analysis Techniques) software for fitting Morey’s model to data. WoMMBAT has a graphical user interface, is freely available, and is cross-platform, running on Windows, Linux, and Mac operating systems.     

An Excel sheet for inferring children’s number-knower levels from give-<Emphasis Type="Italic">N</Emphasis> data

Number-knower levels are a series of stages of number concept development in early childhood. A child’s number-knower level is typically assessed using the give-N task. Although the task procedure has been highly refined, the standard ways of analyzing give-N data remain somewhat crude. Lee and Sarnecka (Cogn Sci 34:51–67, 2010, in press) have developed a Bayesian model of children’s performance on the give-N task that allows knower level to be inferred in a more principled way. However, this model requires considerable expertise and computational effort to implement and apply to data. Here, we present an approximation to the model’s inference that can be computed with Microsoft Excel. We demonstrate the accuracy of the approximation and provide instructions for its use. This makes the powerful inferential capabilities of the Bayesian model accessible to developmental researchers interested in estimating knower levels from give-N data.     

Increasing Active Student Responding in a University Applied Behavior Analysis Course: The Effect of Daily Assessment and Response Cards on End of Week Quiz Scores

The study compared the effects of daily assessment and response cards on average weekly quiz scores in an introduction to applied behavior analysis course. An alternating treatments design (Kazdin 1982, Single-case research designs. New York: Oxford University Press; Cooper et al. 2007, Applied behavior analysis. Upper Saddle River: Merrill/Prentice Hall) was used to analyze the effects of response cards and daily assessment on average weekly quiz scores. Differential treatment effects were found between the daily assessment and response card conditions. When compared to baseline, students’ consistently earned higher quiz scores on end of week quizzes in the daily assessment condition. Response cards produced mixed results. More substantial effects were revealed when analyzing individual student performance. In some cases, twice as many students earned 90% or better when either response cards or daily assessment were used compared to baseline. We discuss the implications of these results for other content areas and student demographics.     

The role of familiarity in binary choice inferences

In research on the recognition heuristic (Goldstein & Gigerenzer, Psychological Review, 109, 75–90, 2002), knowledge of recognized objects has been categorized as “recognized” or “unrecognized” without regard to the degree of familiarity of the recognized object. In the present article, we propose a new inference model—familiarity-based inference. We hypothesize that when subjective knowledge levels (familiarity) of recognized objects differ, the degree of familiarity of recognized objects will influence inferences. Specifically, people are predicted to infer that the more familiar object in a pair of two objects has a higher criterion value on the to-be-judged dimension. In two experiments, using a binary choice task, we examined inferences about populations in a pair of two cities. Results support predictions of familiarity-based inference. Participants inferred that the more familiar city in a pair was more populous. Statistical modeling showed that individual differences in familiarity-based inference lie in the sensitivity to differences in familiarity. In addition, we found that familiarity-based inference can be generally regarded as an ecologically rational inference. Furthermore, when cue knowledge about the inference criterion was available, participants made inferences based on the cue knowledge about population instead of familiarity. Implications of the role of familiarity in psychological processes are discussed.     

Classifying retrieval strategies as a function of working memory

Strategy selection may help explain performance differences between individuals with high working memory capacity (HWMs) and low working memory capacity (LWMs) (Budd, Whitney, & Turley, (Memory & Cognition, 23, 735–748 1995); Cokely, Kelley, & Gilchrist, (Psychonomic Bulletin & Review, 13, 991–997 2006). We compared the independent and spontaneous strategy use of HWMs and LWMs during a category fluency (retrieval) task that required participants to retrieve animal names. HWMs were more successful at the fluency task under normal conditions, but under increased cognitive load, there were no WM-related performance differences. One strategy (i.e., retrieving animals according to their scientific classification) significantly aided performance, irrespective of cognitive load. Under normal conditions, HWMs were more likely to use the effective strategy; however, under load, WM did not predict strategy use. Use of the classification strategy was more strongly related to retrieval performance than was WM. These results suggest that retrieval strategy use is related to WM capacity, and that employing a successful strategy may make up for WM disadvantages during a demanding retrieval task.     

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).     

Probabilities,causation, and logic programming in conditional reasoning: reply to Stenning and Van Lambalgen (2016)

Oaksford and Chater (2014 Oaksford, M., &; Chater, N. (2014). Probabilistic single function dual process theory and logic programming as approaches to non-monotonicity in human vs. artificial reasoning. Thinking and Reasoning, 20, 269–295. doi:10.1080/13546783.2013.877401[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Thinking and Reasoning, 20, 269–295) critiqued the logic programming (LP) approach to nonmonotonicity and proposed that a Bayesian probabilistic approach to conditional reasoning provided a more empirically adequate theory. The current paper is a reply to Stenning and van Lambalgen's rejoinder to this earlier paper entitled ‘Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater’ (2016) in Thinking and Reasoning. It is argued that causation is basic in human cognition and that explaining how abnormality lists are created in LP requires causal models. Each specific rejoinder to the original critique is then addressed. While many areas of agreement are identified, with respect to the key differences, it is concluded the current evidence favours the Bayesian approach, at least for the moment.     

Construct Validity of ADHD-IN,ADHD-HI,ODD toward Adults,Academic and Social Competence Dimensions with Teacher Ratings of Thai Adolescents: Additional Validity for the Child and Adolescent Disruptive Behavior Inventory

Confirmatory factor analysis was used to test the construct validity of an attention-deficit/hyperactivity disorder-inattention, attention-deficit/hyperactivity disorder-hyperactivity/impulsivity, oppositional defiant disorder toward adults, academic and social competence factor model with teacher ratings of Thai adolescents (n = 872) with the Child and Adolescent Disruptive Behavior Inventory. The five-factor model resulted in an adequate fit in an absolute sense (i.e., CFI = .960; TLI = .985; RMSEA = .065; and WRMR = .883). All the items had significant and substantial loadings on their respective factors (i.e., > .78) with the five-factors showing discriminant validity. The five-factor model also resulted in similar results for boys and girls separately as well as younger and older adolescents. The current findings with the teacher version of the measure in conjunction with earlier research with mothers’ and fathers’ ratings of Brazilian, Thai, and American children (Burns et al., Psychological Assessment, 20, 121-130, 2008) and Thai adolescents (Burns et al., Psychological Assessment, 21, 635-641, 2009) provide increasing support for the construct validity of Child and Adolescent Disruptive Behavior Inventory within multiple cultures. Procedures are also outlined to improve the content validity as well as test the construct validity of forthcoming parent and teacher DSM-V ADHD/ODD rating scales.     

Toward a scalable holographic word-form representation

Phenomena in a variety of verbal tasks—for example, masked priming, lexical decision, and word naming—are typically explained in terms of similarity between word-forms. Despite the apparent commonalities between these sets of phenomena, the representations and similarity measures used to account for them are not often related. To show how this gap might be bridged, we build on the work of Hannagan, Dupoux, and Christophe, Cognitive Science 35:79-118, (2011) to explore several methods of representing visual word-forms using holographic reduced representations and to evaluate them on their ability to account for a wide range of effects in masked form priming, as well as data from lexical decision and word naming. A representation that assumes that word-internal letter groups are encoded relative to word-terminal letter groups is found to predict qualitative patterns in masked priming, as well as lexical decision and naming latencies. We then show how this representation can be integrated with the BEAGLE model of lexical semantics (Jones & Mewhort, Psychological Review 114:1–37, 2007) to enable the model to encompass a wider range of verbal tasks.     

More than one kind of happiness: Can we recognize vocal expressions of different positive states?

Several theorists have proposed that distinctions are needed between different positive emotional states, and that these discriminations may be particularly useful in the domain of vocal signals (Ekman, 1992b, Cognition and Emotion, 6, 169–200; Scherer, 1986, Psychological Bulletin, 99, 143–165). We report an investigation into the hypothesis that positive basic emotions have distinct vocal expressions (Ekman, 1992b, Cognition and Emotion, 6, 169–200). Non-verbal vocalisations are used that map onto five putative positive emotions: Achievement/Triumph, Amusement, Contentment, Sensual Pleasure, and Relief. Data from categorisation and rating tasks indicate that each vocal expression is accurately categorised and consistently rated as expressing the intended emotion. This pattern is replicated across two language groups. These data, we conclude, provide evidence for the existence of robustly recognisable expressions of distinct positive emotions.