Previous beliefs affect Bayesian reasoning in conditions fostering gist comprehension.

It has been shown that Bayesian reasoning is affected by the believability of the data, but it is unknown which conditions could potentiate or reduce such belief effect. Here, we tested the hypothesis that the belief effect would mainly be observed in conditions fostering a gist comprehension of the data. Accordingly, we expected to observe a significant belief effect in iconic rather than in textual presentations and, in general, when nonnumerical estimates were requested. The results of three studies showed more accurate Bayesian estimates, either expressed numerically or nonnumerically, for icons than for text descriptions of natural frequencies. Moreover, in line with our expectations, nonnumerical estimates were, in general, more accurate for believable rather than for unbelievable scenarios. In contrast, the belief effect on the accuracy of the numerical estimates depended on the format and on the complexity of the calculation. The present findings also showed that single-event posterior probability estimates based on described frequencies were more accurate when expressed nonnumerically rather than numerically, opening new avenues for the development of interventions to improve Bayesian reasoning.

From reading numbers to seeing ratios: a benefit of icons for risk comprehension.

Promoting a better understanding of statistical data is becoming increasingly important for improving risk comprehension and decision-making. In this regard, previous studies on Bayesian problem solving have shown that iconic representations help infer frequencies in sets and subsets. Nevertheless, the mechanisms by which icons enhance performance remain unclear. Here, we tested the hypothesis that the benefit offered by icon arrays lies in a better alignment between presented and requested relationships, which should facilitate the comprehension of the requested ratio beyond the represented quantities. To this end, we analyzed individual risk estimates based on data presented either in standard verbal presentations (percentages and natural frequency formats) or as icon arrays. Compared to the other formats, icons led to estimates that were more accurate, and importantly, promoted the use of equivalent expressions for the requested probability. Furthermore, whereas the accuracy of the estimates based on verbal formats depended on their alignment with the text, all the estimates based on icons were equally accurate. Therefore, these results support the proposal that icons enhance the comprehension of the ratio and its mapping onto the requested probability and point to relational misalignment as potential interference for text-based Bayesian reasoning. The present findings also argue against an intrinsic difficulty with understanding single-event probabilities.

An object-tracking model that combines position and speed explains spatial and temporal responses in a timing task.

Many tasks require synchronizing our actions with particular moments along the path of moving targets. However, it is controversial whether we base these actions on spatial or temporal information, and whether using either can enhance our performance. We addressed these questions with a coincidence timing task. A target varying in speed and motion duration approached a goal. Participants stopped the target and were rewarded according to its proximity to the goal. Results showed larger reward for responses temporally (rather than spatially) equidistant to the goal across speeds, and this pattern was promoted by longer motion durations. We used a Kalman filter to simulate time and space-based responses, where modeled speed uncertainty depended on motion duration and positional uncertainty on target speed. The comparison between simulated and observed responses revealed that a single position-tracking mechanism could account for both spatial and temporal patterns, providing a unified computational explanation.

Too Worried to Judge: On the Role of Perceived Severity in Medical Decision-Making.

Ideally, decisions regarding one's health should be made after assessing the objective probabilities of relevant outcomes. Nevertheless, previous beliefs and emotional reactions also have a role in decision-making. Furthermore, the comprehension of probabilities is commonly affected by the presentation format, and by numeracy. This study aimed to assess the extent to which the influence of these factors might vary between different medical conditions. A sample of university students were presented with two health scenarios containing statistical information on the prevalence of breast cancer and hypertension either through icon arrays (N = 71) or natural frequencies (N = 72). They also received information regarding a preventive measure (mammogram/low-sodium diet) and the likelihood of a positive mammogram or a rich-sodium diet either when suffering or not suffering from the disease. Before seeing the data, participants rated the severity of the disease and the inconvenience of the preventive measure. After reading the health scenario, participants had to rate its difficulty, and how worrisome it was. They had also to rate the prior probability of suffering from this medical condition, and the posterior probability of it, provided a positive mammogram or a rich-sodium diet. Finally, they rated the extent to which they would recommend the preventive measures. All the rates used the same 1 (little)-8 (a great deal) scale. Participants' numeracy was also assessed. The scenarios differed significantly in perceived severity and worry, with the cancer scenario obtaining higher scores. Importantly, regression analyses showed that the recommendations in the two health scenarios depended on different variables. A model taking into consideration severity and worry rates best explained decisions in the cancer scenario; in contrast, in the hypertension scenario the model that best explained the recommendations comprised both the posterior probability estimate and the severity rate. Neither numeracy nor presentation format affected recommendation but both affected difficulty, worrying and probability rates. We conclude that previous perceptions of the severity of a health condition modulate the use of probabilistic information for decision-making. The roles of presentation format and numeracy in enabling patients to understand statistical information are also discussed.

A short educational intervention diminishes causal illusions and specific paranormal beliefs in undergraduates.

Cognitive biases such as causal illusions have been related to paranormal and pseudoscientific beliefs and, thus, pose a real threat to the development of adequate critical thinking abilities. We aimed to reduce causal illusions in undergraduates by means of an educational intervention combining training-in-bias and training-in-rules techniques. First, participants directly experienced situations that tend to induce the Barnum effect and the confirmation bias. Thereafter, these effects were explained and examples of their influence over everyday life were provided. Compared to a control group, participants who received the intervention showed diminished causal illusions in a contingency learning task and a decrease in the precognition dimension of a paranormal belief scale. Overall, results suggest that evidence-based educational interventions like the one presented here could be used to significantly improve critical thinking skills in our students.

Post-error response inhibition in high math-anxious individuals: Evidence from a multi-digit addition task.

The aim of the study was to investigate how high math-anxious (HMA) individuals react to errors in an arithmetic task. Twenty HMA and 19 low math-anxious (LMA) individuals were presented with a multi-digit addition verification task and were given response feedback. Post-error adjustment measures (response time and accuracy) were analyzed in order to study differences between groups when faced with errors in an arithmetical task. Results showed that both HMA and LMA individuals were slower to respond following an error than following a correct answer. However, post-error accuracy effects emerged only for the HMA group, showing that they were also less accurate after having committed an error than after giving the right answer. Importantly, these differences were observed only when individuals needed to repeat the same response given in the previous trial. These results suggest that, for HMA individuals, errors caused reactive inhibition of the erroneous response, facilitating performance if the next problem required the alternative response but hampering it if the response was the same. This stronger reaction to errors could be a factor contributing to the difficulties that HMA individuals experience in learning math and doing math tasks.

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

The Doubting System 1: Evidence for automatic substitution sensitivity.

A long prevailing view of human reasoning suggests severe limits on our ability to adhere to simple logical or mathematical prescriptions. A key position assumes these failures arise from insufficient monitoring of rapidly produced intuitions. These faulty intuitions are thought to arise from a proposed substitution process, by which reasoners unknowingly interpret more difficult questions as easier ones. Recent work, however, suggests that reasoners are not blind to this substitution process, but in fact detect that their erroneous responses are not warranted. Using the popular bat-and-ball problem, we investigated whether this substitution sensitivity arises out of an automatic System 1 process or whether it depends on the operation of an executive resource demanding System 2 process. Results showed that accuracy on the bat-and-ball problem clearly declined under cognitive load. However, both reduced response confidence and increased response latencies indicated that biased reasoners remained sensitive to their faulty responses under load. Results suggest that a crucial substitution monitoring process is not only successfully engaged, but that it automatically operates as an autonomous System 1 process. By signaling its doubt along with a biased intuition, it appears System 1 is "smarter" than traditionally assumed.

Comprehension and computation in Bayesian problem solving.

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on "transparent" Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point.

Efficiency of Arithmetic Procedures Modulates the Problem-Size Effect in Subtraction.

The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies.

Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning.

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning.

Efficiency of arithmetic procedures modulates the problem-size effect in subtraction

The aim of this study was to examine whether differences in strategy selection and/or strategy efficiency can explain the modulation of the problem-size effect by arithmetic skill. More specifically, we wondered whether arithmetic skill increases the use of retrieval strategy in large problems, and/or enhances the efficiency of either retrieval or procedural strategies. The performance of highly-skilled (HS) and less highly-skilled (LS) individuals on a subtraction verification task was analyzed according to problem size and to the strategy reported on a trial-by-trial basis after each problem. The problem size effect was larger for LS individuals than for their HS peers, both in response time and in hit rate. Nevertheless, groups did not differ regarding the strategy reported for each subtraction size. As expected, problems in which retrieval strategy was reported were solved more quickly and more accurately than problems solved by procedural strategies. Responses using retrieval strategy were equally fast in the two groups, but HS individuals performed better than LS when using procedural strategies. The results therefore suggest that the differences in behavioral measures between groups might specifically be due to differences in the efficiency of procedural strategies (AU)

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Individual differences in arithmetic skill reflected in event-related brain potentials.

We used event-related brain potentials (ERP) to study the problem-size effect in individuals with high and low arithmetic skill. Participants were presented with a classic equality verification task, and problem size was manipulated by using small (e.g., 3+4), medium (e.g., 7+8) and large problems (e.g., 16+29). ERP analyses were time-locked to the onset of the second operand in order to address brain potentials during the production phase. High-skill individuals showed a positive slow wave when solving large problems and no differences in the ERP pattern when solving small and medium problems. In contrast, low-skill individuals showed a positive slow wave when solving medium and large problems. Given that differences between high and low skill individuals have been related to differences in calculation strategies, these results provide further support to the utility of using ERP as a signature of arithmetic strategy.

Knowing what to respond in the future does not cancel the influence of past events.

Everyday tasks seldom involve isolate actions but sequences of them. We can see whether previous actions influence the current one by exploring the response time to controlled sequences of stimuli. Specifically, depending on the response-stimulus temporal interval (RSI), different mechanisms have been proposed to explain sequential effects in two-choice serial response tasks. Whereas an automatic facilitation mechanism is thought to produce a benefit for response repetitions at short RSIs, subjective expectancies are considered to replace the automatic facilitation at longer RSIs, producing a cost-benefit pattern: repetitions are faster after other repetitions but they are slower after alternations. However, there is not direct evidence showing the impact of subjective expectancies on sequential effects. By using a fixed sequence, the results of the reported experiment showed that the repetition effect was enhanced in participants who acquired complete knowledge of the order. Nevertheless, a similar cost-benefit pattern was observed in all participants and in all learning blocks. Therefore, results of the experiment suggest that sequential effects, including the cost-benefit pattern, are the consequence of automatic mechanisms which operate independently of (and simultaneously with) explicit knowledge of the sequence or other subjective expectancies.

Utilidad de distintas ayudas en la resolución de un problema de insight y su relación con las estrategias metacognitivas / Usefulness of different hints in solving an insight problem: relation-ship with metacognitive strategies

En este trabajo se analiza la relación entre las estrategias metacognitivas (EM) y la eficacia de distintas ayudas en la resolución de un problema de insight. Los participantes intentaron resolver el problema de las tres bombillas sin ninguna ayuda o después de recibir distintas pistas que diferían en el nivel de abstracción, y respondieron al cuestionario de autoinforme de O’Neil & Abedi (1996) sobre el uso de EM. Sorprendentemente, las distintas ayudas fueron igual de ineficaces, no diferenciándose de la condición «sin ayuda». Sin embargo, análisis adicionales mostraron una interacción entre el tipo de ayuda recibida y el nivel de uso habitual de las EM. El porcentaje de soluciones correctas al problema fue bajo (menos del 30%) cuando la ayuda era muy abstracta o inexistente, independientemente del nivel de uso de las EM. Sin embargo, los participantes con mayor nivel de metacognición mostraron un mejor rendimiento cuando las ayudas eran más directas (referentes a un concepto clave). Estos resultados sugieren que las estrategias metacognitivas juegan un papel importante en el reconocimiento de la información relevante para la resolución de problema

In this work it is studied the relationship between metacognition and the efficacy of different hints while solving an insight problem. Participants attempted to solve the three bulbs problem either without any hint or after receiving hints with different levels of abstraction, and answered the O’Neil & Abedi’s (1996) self-report inventory about metacognitive strategies. Surprisingly, the different hints did not improve performance, compared to the no-hint condition. Nevertheless, a significant interaction between type of hint and level in metacognition was revealed by additional analyses. Only a few participants (less than 30%) solved the problem when the hint was very abstract or no hint was presented, regard-less of their metacognitive level. However, the participants who scored higher on metacognition performed better when more direct hints, referring to a key concept to solve the problem, were presented. Hence, these results suggest that metacognitive strategies play a significant role on recognizing the relevance of specific information to problem solving

Individual differences in sequence learning and auditory pattern sensitivity as revealed with evoked potentials.

Research on motor sequence acquisition has shown significant differences between learners. Learners who develop explicit knowledge respond faster than non-explicit ones and they show larger amplitude in event-related brain potentials to sequence deviants. There is evidence that memory span correlates with the amount of sequence learned, but the specific mechanisms subserving such differences are still unknown. Recently, it has been observed that performance of explicit learners, but not of non-explicit ones, improves when presented with auditory action effects. Accordingly, differences between learners might be related to differences in auditory rhythm perception. To test this hypothesis, the mismatch negativity (MMN)-evoked potential elicited to stimuli violating stimulus alternation (i.e. low pitch, high pitch) was recorded in explicit and non-explicit sequence learners. Results confirmed our prediction: explicit learners showed larger amplitude of the MMN to the violation of the auditory rhythm, suggesting new theoretical implications to account for individual differences in sequential action control.

Modes of executive control in sequence learning: from stimulus-based to plan-based control.

The authors argue that human sequential learning is often but not always characterized by a shift from stimulus- to plan-based action control. To diagnose this shift, they manipulated the frequency of 1st-order transitions in a repeated manual left-right sequence, assuming that performance is sensitive to frequency-induced biases under stimulus- but not plan-based control. Indeed, frequency biases tended to disappear with practice, but only for explicit learners. This tendency was facilitated by visual-verbal target stimuli, response-contingent sounds, and intentional instructions and hampered by auditory (but not visual) noise. Findings are interpreted within an event-coding model of action control, which holds that plans for sequences of discrete actions are coded phonetically, integrating order and relative timing. The model distinguishes between plan acquisition, linked to explicit knowledge, and plan execution, linked to the action control mode.

Spatial interference and response control in sequence learning: the role of explicit knowledge.

In several sequence learning studies it has been suggested that response control shifts from the stimuli to some internal representation (i.e., motor program) through the learning process. The main questions addressed in this paper are whether this control shift is related to explicit knowledge and whether the formation of these internal representations depends on the stimulus attributes. In one experiment we compared the learning of a response sequence triggered by either spatial location or location symbol (left-right) by using a serial response task (SRT). Symbols were presented at either a centered or random location. The results showed that in the symbolic conditions the shift of response control correlated with the emergence of explicit knowledge. Only participants with complete explicit knowledge seemed to learn the sequence structure beyond probabilistic information (response time "RT" did not depend on the frequency of the response). Moreover, these participants were able to overcome, when needed, spatial interference (RT was the same for both spatially corresponding and non-corresponding trials). However, when spatial location was relevant, RT was always faster, especially for more frequent responses. These results suggest that the relevant stimulus dimension (location or symbol) seems to engage different sequence learning mechanisms.

Overcoming illusory inferences in a probabilistic counterintuitive problem: the role of explicit representations.

In the context of conditional probabilities, a good example of the marked discrepancy between intuition and formal reasoning is the Monty Hall dilemma (MHD). We used the MHD to study the effects of practicing the game, making explicit the underlying structure, or enhancing the representation of the different possibilities, on reaching and stating the correct answer. The results of the experiments showed that accumulated experience with the MHD increased the proportion of switching responses but did not change erroneous intuitions (Experiment 1). However, when the dilemma was presented in the form of an adversary game that made the underlying structure more explicit, more participants formed complete mental representations that enabled them to reason correctly (Experiment 2). This result was observed even without any practice with the game if the participants were encouraged to represent possibilities (Experiment 3). Therefore, in this context, correct reasoning seems to depend more on the ability to consider different possibilities than on extensive practice with the game.