A visualization technique for Bayesian reasoning

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed problems with no instruction or external support, participants watched a video describing a visualization technique that used the length of bars to represent the probabilities provided in the problem. Participants then completed more problems with a chance to implement the technique by clicking interactive bars on the computer screen. Performance improved dramatically from the pretraining phase to the interactive‐bar phase. Participants maintained improved performance in transfer phases in which they were required to implement the visualization technique with either pencil‐and‐paper or no external medium. Accuracy levels for participants using the visualization technique were very similar to participants trained to solve the Bayes theorem equation. The results showed no evidence of learning across problems in the pretraining phase or for control participants who did not receive training, so the improved performance of participants using the visualization method could be uniquely attributed to the method itself. A classroom sample demonstrated that these benefits extend to instructional settings. The results show that people can quickly learn to perform Bayesian reasoning without using mathematical equations. We discuss ways that a spatial solution method can enhance classroom instruction on Bayesian inference and help students apply Bayesian reasoning in everyday settings.     

Within-subject consistency and between-subject variability in Bayesian reasoning strategies

It is well known that people tend to perform poorly when asked to determine a posterior probability on the basis of a base rate, true positive rate, and false positive rate. The present experiments assessed the extent to which individual participants nevertheless adopt consistent strategies in these Bayesian reasoning problems, and investigated the nature of these strategies. In two experiments, one laboratory-based and one internet-based, each participant completed 36 problems with factorially manipulated probabilities. Many participants applied consistent strategies involving use of only one of the three probabilities provided in the problem, or additive combination of two of the probabilities. There was, however, substantial variability across participants in which probabilities were taken into account. In the laboratory experiment, participants’ eye movements were tracked as they read the problems. There was evidence of a relationship between information use and attention to a source of information. Participants’ self-assessments of their performance, however, revealed little confidence that the strategies they applied were actually correct. These results suggest that the hypothesis of base rate neglect actually underestimates people’s difficulty with Bayesian reasoning, but also suggest that participants are aware of their ignorance.     

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.     

Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning

The idea that naturally sampled frequencies facilitate performance in statistical reasoning tasks because they are a cognitively privileged representational format has been challenged by findings that similarly structured numbers presented as chances similarly facilitate performance, on the basis of the claim that these are technically single-event probabilities. A crucial opinion, however, is that of the research participants, who possibly interpret chances as de facto frequencies. A series of experiments here indicate that not only is performance improved by clearly presented natural frequencies, rather than chances phrasing, but also that participants who interpreted chances as frequencies, rather than as probabilities, were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.     

Teaching moral reasoning through gesture

Stem‐cell research. Euthanasia. Personhood. Marriage equality. School shootings. Gun control. Death penalty. Ethical dilemmas regularly spark fierce debate about the underlying moral fabric of societies. How do we prepare today's children to be fully informed and thoughtful citizens, capable of moral and ethical decisions? Current approaches to moral education are controversial, requiring adults to serve as either direct (‘top‐down’) or indirect (‘bottom‐up’) conduits of information about morality. A common thread weaving throughout these two educational initiatives is the ability to take multiple perspectives – increases in perspective taking ability have been found to precede advances in moral reasoning. We propose gesture as a behavior uniquely situated to augment perspective taking ability. Requiring gesture during spatial tasks has been shown to catalyze the production of more sophisticated problem‐solving strategies, allowing children to profit from instruction. Our data demonstrate that requiring gesture during moral reasoning tasks has similar effects, resulting in increased perspective taking ability subsequent to instruction. A video abstract of this article can be viewed at http://www.youtube.com/watch?v/gAcRIClU_GY     

Older adults prefer less choice than young adults

Previous research has demonstrated that older adults prefer less autonomy and seek less information when making decisions on their own relative to young adults (for a review, see M. Mather, 2006). Would older adults also prefer fewer options from which to choose? The authors tested this hypothesis in the context of different decision domains. Participants completed a choice preferences survey in which they indicated their desired number of choices across 6 domains of health care and everyday decisions. The hypothesis was confirmed across all decision domains. The authors discuss implications from these results as they relate to theories of aging and health care policy.     

When less is not always more: stereotype knowledge and reasoning development

Developmental studies on heuristics and biases have reported controversial findings suggesting that children sometimes reason more logically than do adults. We addressed the controversy by testing the impact of children's knowledge of the heuristic stereotypes that are typically cued in these studies. Five-year-old preschoolers and 8-year-old children were tested with a card game version of the classic base-rate task. Problems were based on stereotypes that were familiar or unfamiliar for preschoolers. We also manipulated whether the cued stereotypical response was consistent (no-conflict problems) or inconsistent (conflict problems) with the correct analytic response that was cued in the problem. Results showed that an age-related performance decrease on the conflict problems was accompanied by an age-related performance increase on the no-conflict problems. These age effects were most pronounced for problems that adopted stereotypes that were unfamiliar for the 5-year-old preschoolers. When preschoolers were familiar with the stereotypes, their performance also started being affected. Findings support the claim that previously reported age-related performance decreases on classic reasoning tasks need to be attributed to the increased need to deal with tempting heuristics and not to a decrease in analytic thinking skills per se.     

Classifying color materials: children are less holistic than adults

Much recent research indicates that children respond to materials which are separable for adults as though those materials were integral. The present studies examined differences between 5-year-olds and adults in the processing of integral materials. In Study 1, both children and adults made a majority of similarity classifications for those materials. However, the children were found to make fewer of those integral similarity classifications and more dimensional classifications than adults for materials varying in the integral dimensions of chroma and value. In Study 2, children's similarity judgments were also indicative of greater separability of those dimensions. For both children and adults, similarity ratings given in Study 2 were predictive of classification behavior in Study 1. Age differences in similarity ratings were also predictive of age differences in classification. The overall pattern of results is consistent with the idea that children's perception is neither more nor less holistic than that of adults. Whether children or adults are found to be more holistic depends on the nature of the material presented. With integral materials, young children respond in a manner which appears less holistic than that of adults.     

The whole moves less than the spin of its parts

When individually moving elements in the visual scene are perceptually grouped together into a coherently moving object, they can appear to slow down. In the present article, we show that the perceived speed of a particular global-motion percept is not dictated completely by the speed of the local moving elements. We investigated a stimulus that leads to bistable percepts, in which local and global motion may be perceived in an alternating fashion. Four rotating dot pairs, when arranged into a square-like configuration, may be perceived either locally, as independently rotating dot pairs, or globally, as two large squares translating along overlapping circular trajectories. Using a modified version of this stimulus, we found that the perceptually grouped squares appeared to move more slowly than the locally perceived rotating dot pairs, suggesting that perceived motion magnitude is computed following a global analysis of form. Supplemental demos related to this article can be downloaded from app.psychonomic-journals.org/content/supplemental.     

Characterizing belief bias in syllogistic reasoning: A hierarchical Bayesian meta-analysis of ROC data

The belief-bias effect is one of the most-studied biases in reasoning. A recent study of the phenomenon using the signal detection theory (SDT) model called into question all theoretical accounts of belief bias by demonstrating that belief-based differences in the ability to discriminate between valid and invalid syllogisms may be an artifact stemming from the use of inappropriate linear measurement models such as analysis of variance (Dube et al., Psychological Review, 117(3), 831–863, 2010). The discrepancy between Dube et al.’s, Psychological Review, 117(3), 831–863 (2010) results and the previous three decades of work, together with former’s methodological criticisms suggests the need to revisit earlier results, this time collecting confidence-rating responses. Using a hierarchical Bayesian meta-analysis, we reanalyzed a corpus of 22 confidence-rating studies (N =?993). The results indicated that extensive replications using confidence-rating data are unnecessary as the observed receiver operating characteristic functions are not systematically asymmetric. These results were subsequently corroborated by a novel experimental design based on SDT’s generalized area theorem. Although the meta-analysis confirms that believability does not influence discriminability unconditionally, it also confirmed previous results that factors such as individual differences mediate the effect. The main point is that data from previous and future studies can be safely analyzed using appropriate hierarchical methods that do not require confidence ratings. More generally, our results set a new standard for analyzing data and evaluating theories in reasoning. Important methodological and theoretical considerations for future work on belief bias and related domains are discussed.     

The rationality of informal argumentation: a Bayesian approach to reasoning fallacies

Classical informal reasoning "fallacies," for example, begging the question or arguing from ignorance, while ubiquitous in everyday argumentation, have been subject to little systematic investigation in cognitive psychology. In this article it is argued that these "fallacies" provide a rich taxonomy of argument forms that can be differentially strong, dependent on their content. A Bayesian theory of content-dependent argument strength is presented. Possible psychological mechanisms are identified. Experiments are presented investigating whether people's judgments of the strength of 3 fallacies--the argumentum ad ignorantiam, the circular argument or petitio principii, and the slippery slope argument--are affected by the factors a Bayesian account predicts. This research suggests that Bayesian accounts of reasoning can be extended to the more general human activity of argumentation.     

An overview of Bayesian reasoning in the analysis of delay‐discounting data

Statistical inference (including interval estimation and model selection) is increasingly used in the analysis of behavioral data. As with many other fields, statistical approaches for these analyses traditionally use classical (i.e., frequentist) methods. Interpreting classical intervals and p‐values correctly can be burdensome and counterintuitive. By contrast, Bayesian methods treat data, parameters, and hypotheses as random quantities and use rules of conditional probability to produce direct probabilistic statements about models and parameters given observed study data. In this work, we reanalyze two data sets using Bayesian procedures. We precede the analyses with an overview of the Bayesian paradigm. The first study reanalyzes data from a recent study of controls, heavy smokers, and individuals with alcohol and/or cocaine substance use disorder, and focuses on Bayesian hypothesis testing for covariates and interval estimation for discounting rates among various substance use disorder profiles. The second example analyzes hypothetical environmental delay‐discounting data. This example focuses on using historical data to establish prior distributions for parameters while allowing subjective expert opinion to govern the prior distribution on model preference. We review the subjective nature of specifying Bayesian prior distributions but also review established methods to standardize the generation of priors and remove subjective influence while still taking advantage of the interpretive advantages of Bayesian analyses. We present the Bayesian approach as an alternative paradigm for statistical inference and discuss its strengths and weaknesses.     

Better safe than sorry: Precautionary reasoning and implied dominance in risky decisions

In four studies, student and nonstudent participants evaluated the possible outcomes of binary decisions involving health, safety, and environmental risks (e.g., whether to issue a dam‐failure evacuation order). Many participants indicated that false positives (e.g., evacuation, but no dam failure) were better than true negatives (e.g., no evacuation and no dam failure), thereby implying that the more protective action dominated the less protective action. A common rationale for this response pattern was the precautionary maxim “better safe than sorry.” Participants apparently evaluated outcomes partly on the basis of the decisions that might lead to them, in conflict with consequentialist decision models. Consistent with this explanation, the prevalence of implied dominance decreased substantially when the emphasis on decisions was reduced. These results demonstrate that an initial preference for a decision alternative can alter the evaluation of possible consequences of both the preferred alternative and a competing alternative, suggesting positive feedback loops that reinforce the initial preference. The rationality of considering the decision itself as an attribute of possible outcomes is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

In two minds: dual-process accounts of reasoning

Researchers in thinking and reasoning have proposed recently that there are two distinct cognitive systems underlying reasoning. System 1 is old in evolutionary terms and shared with other animals: it comprises a set of autonomous subsystems that include both innate input modules and domain-specific knowledge acquired by a domain-general learning mechanism. System 2 is evolutionarily recent and distinctively human: it permits abstract reasoning and hypothetical thinking, but is constrained by working memory capacity and correlated with measures of general intelligence. These theories essentially posit two minds in one brain with a range of experimental psychological evidence showing that the two systems compete for control of our inferences and actions.     

Sociomoral reasoning in children and adolescents from two collectivistic cultures

This study compared the sociomoral reasoning of 7-, 9-, 12-, and 15-year-old children and adolescents of two collectivistic cultures in the 1990s: Spain (horizontal collectivism; N = 208) and Russia (vertical collectivism; N = 247). Participants reasoned about choices and moral justifications of a protagonist in a sociomoral dilemma where participants can focus on different moral and non-moral concerns (e.g., going with their best friend, going with a new classmate or trying to do something with both). Results support previous research in western societies: participants tend to choose the option “visiting the best friend”, and self-interest tends to decrease with age whereas altruism tends to increase. Moreover, Spanish participants tended to consider all parties involved in the dilemma (i.e., old friend and new classmate), whereas Russian participants did not. These results are discussed in light of their differences as horizontal and vertical collectivistic societies. Overall, the results open an avenue for new studies when comparing the effects of culture on children's and adolescents' development.     

Dual processing in reasoning: two systems but one reasoner

Human reasoning has been characterized as an interplay between an automatic belief-based system and a demanding logic-based reasoning system. The present study tested a fundamental claim about the nature of individual differences in reasoning and the processing demands of both systems. Participants varying in working memory capacity performed a reasoning task while their executive resources were burdened with a secondary task. Results were consistent with the dual-process claim: The executive burden hampered correct reasoning when the believability of a conclusion conflicted with its logical validity, but not when beliefs cued the correct response. However, although participants with high working memory spans performed better than those with lower spans in cases of a conflict, all reasoners showed similar effects of load. The findings support the idea that there are two reasoning systems with differential processing demands, but constitute evidence against qualitative individual differences in the human reasoning machinery.     

Hearing cheats touch, but less in congenitally blind than in sighted individuals

Abstract— The principles of cross-modal integration were investigated with an auditory-tactile illusion in sighted and congenitally blind adults. Participants had to judge the number of rapidly presented tactile stimuli, which were presented together with task-irrelevant sounds. When one tactile stimulus was accompanied by more than one tone, participants reported perceiving more than a single touch. This illusion was more pronounced in sighted than congenitally blind participants. Given that the congenitally blind were more precise in judging the number of tactile stimuli in a control condition without tones, the present data are in accordance with a modality-appropriateness account suggesting that interference by a task-irrelevant modality is reduced if processing accuracy of the task-relevant modality is high.