The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditiona... more 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: Emotionalbased 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.
High numerate individuals tend to be more successful probabilistic problem solvers than those low... more High numerate individuals tend to be more successful probabilistic problem solvers than those lower in numeracy. These individual differences, however, can be modulated through the presentation format of external information, although discrepancies have been reported. The present investigation addressed these discrepancies by using formally equivalent Bayesian reasoning problems differing in numerical format and problem complexity. As previously observed, with a complex problem all participants were at floor level with probabilistic information, while individual differences emerged with natural frequency data. In sharp contrast, with a simple problem, differences between numeracy levels were diminished with natural frequencies, with group differences emerging only with probabilistic formats. Accordingly, the impact of numeracy in Bayesian reasoning depends both on numerical format and verbal complexity, and further suggests that lower numerate individuals are not inherently unable to reason in a Bayesian-like manner.
The authors argue that human sequential learning is often but not always characterized by a shift... more 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 frequencyinduced 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.
It has been shown that Bayesian reasoning is affected by the believability of the data, but it is... more 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.
This article analyzes the leading theoretical approaches to Bayesian reasoning in the literature,... more This article analyzes the leading theoretical approaches to Bayesian reasoning in the literature, and its main sources of empirical support. Many errors in probability estimates are attributed to people's inability to think in statistical tems when faced with information about a single event. Specifically, in situations where the normative model is Bayes's theorem, the well-known base rate neglect is analyzed both from rhe heuristic and biases approach, of Tversky and Kahneman, and from the frequentist hypothesis defended by Gigerenzer, Cosmides et al. The discrepancy between intuitions and formal mathenlatical reasoning is also analyzed through the studies with the three prisoners problem. Finally, we present the mental rnodel theoly of extensional probabilistic reasoning (Johnsorl-Laid et al., 1999) which explains how naive individuals can infer posterior probabilities without relying on Bayes 's theorern
Humans are traditionally depicted as suboptimal decision-makers, since they often fail to maximiz... more Humans are traditionally depicted as suboptimal decision-makers, since they often fail to maximize expected utility. However, recent studies claim people choose optimally in tasks called motor lotteries, where participants reach to different targets within a maximum time window in order to get a reward. A difference is that, while in classical tasks probability information is explicitly given, in motor tasks it is implicit in each participant's motor variability. Once this variability is known, a target can be designed to match a specific probability of being hit. This manipulation is normally implemented through size, but little has been done to explore other ways to represent probability in a motor task: for instance, through distance. Our experiment studied differences in expected utility maximization between these two ways of representing probabilities. In each of our two different conditions, trials consisted in the presentation of two targets, one with a lower probability to be hit but higher gain (risky) and another with higher probability and lower gain (safe). Participants decided to reach for one or another. In the size condition, both targets appeared at the same distance, but the risky was smaller. In the distance condition, both targets had equal size, but the risky was further away. Probabilities were manipulated to sample various expected gain differences between both targets. Results showed clear differences. Risk aversion was more present in the distance condition: participants tended to reach for the safe target even if the optimal choice was the risky target. In the size condition, participants were more sensitive to expected value differences: the more this difference favored the risky target, the more it was chosen. These differences may be interpreted as participants considering additional cost functions (e.g. biomechanical) in the distance condition not captured by the mere probability of hitting. Meeting abstract presented at VSS 2015.
La distinción entre dos tipos de procesamiento cognitivo: implícito o no consciente y explícito o... more La distinción entre dos tipos de procesamiento cognitivo: implícito o no consciente y explícito o consciente es frecuente, dentro de áreas tales como percepción, memoria y aprendizaje. El objetivo de esta comunicación es analizar hasta qué punto esta distinción puede ser útil para la comprensión de un proceso tan complejo, como es el pensamiento humano. Uno de los actuales debates, dentro de este enfoque, es si la distinción implícito versus explícito está relacionada con diferentes estados de conciencia o bien se trata de distintos niveles de abstracción del conocimiento. Desde esta perspectiva, a lo largo de este trabajo se analizarán tareas de pensamiento como son la inducción de categorías y la resolución de problemas. Se trata de considerar hasta qué punto algunos de los resultados observados pueden comprenderse mejor aplicando una herramienta de análisis común a otras áreas de la cognición humana.
Ideally, decisions regarding one's health should be made after assessing the objective probabilit... more 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 richsodium 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.
En este articulo se analizan 10s enfoques teóricos más relevantes sobre razonamiento bayesiano, u... more En este articulo se analizan 10s enfoques teóricos más relevantes sobre razonamiento bayesiano, usí como sus principales apoyos empíricos. Muchos errores en estimaciones de probabilidad se atribuyen a la incapacidad de las personas para pensar en términos estadísticos cunndo se enfrentan con información sobre un suceso único. Especljcicamente, en situaciones en las que el modelo norrnativo es el teorema de Bayes, se analiza el sesgo conocido como ccinsensibilidad a las probabilidades previasu, tanto desde el enfoque de heurísticos y sesgos, de Tversky y Kahneman, como desde la hipótesis frecuentista de Gigerenzer, Cosmides et al. También se aborda la discrepancia entre intuiciones y razonamiento matemático formal a través de 10s estudios sobre el problema de 10s tres prisioneros. Finalmente se presenta la teoria de Johnson-Laird et al. sobre modelos mentales en razonamiento probabilístico extensional, que explica cómo personas no expertas pueden inferir probabilidades a posteriori sin utilizar el teorema de Bayes. Palabras clave: heurísticos y sesgos, razonamiento probabilístico, teorema de Bayes, probabilidades a priori, modelos mentales, razonamiento bayesiano, hipótesis frecuentista. This article analyzes the leading theoretical approaches to Bayesian reasoning in the literature, and its mairz sources of empirical support. Muny errors in probability estimates are attributed to people's inability to think in statistical t e m s when faced with irlformation about a single event. Specijically, in situations where the normative model is Bayes's theorem, the well-known base rate neglect is analyzed both from rhe heuristic and biases approach, of Tversky and Kahneman, and from thefrequentist hypothesis defended by Gigerenzer, Cosmides et al. The discre
El presente trabajo pretendió investigar cómo las similitudes superfkiales afectan al tiempo que ... more El presente trabajo pretendió investigar cómo las similitudes superfkiales afectan al tiempo que tardan los sujetos en recuperar un análogo presentado previamente cuando intentan resolver un problema. Como se habia predicho, a partir de dos modelos sobre el proceso de recuperación de análogos (el de Holland et al., 1986 y el de Keane, 1988), no se encontraron diferencias en cuanto al tiempo de recuperación entre análogos que comparten con el problema exclusivamente la estructura y análogos que además de la estructura contienen similitudes sŭ p erficiales: Una-véz recuperado el análogo, las similitudes superfkiales aceleran el proceso de establecimiento de correspondencias. También se produjo un efecto de «transferencia negativa» generado exclusivamente por similitudes superficiales. Este efecto se explica mejor en el modelo de «suma de activación» de Holland et al., (1986). Finalmente, se propuso una explicación integradora que refiere los dos modelos a momentos distririos del proceso de aprendizaje.
Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nev... more 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.
Cognitive biases such as causal illusions have been related to paranormal and pseudoscientific be... more 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 evidencebased educational interventions like the one presented here could be used to significantly improve critical thinking skills in our students.
Humans have long been characterized as poor probabilistic reasoners when presented with explicit ... more 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.
The popular bat-and-ball problem is a relatively simple math riddle on which people are easily bi... more The popular bat-and-ball problem is a relatively simple math riddle on which people are easily biased by intuitive or heuristic thinking. In two studies we tested the impact of a simple but somewhat neglected manipulation-the impact of minimal accuracy feedback-on bat-and-ball performance. Participants solved a total of 15 standard and 15 control versions of the bat-and-ball problem in three consecutive blocks. Half of the participants received accuracy feedback in the intermediate block. Results of both studies indicated that the feedback had, on average, no significant effect on bat-and-ball accuracy over and above mere repeated presentation. We did observe a consistent improvement for a small number of individual participants. Explorative analyses indicated that this improved group showed a more pronounced conflict detection effect (i.e., latency increase) at the pretest and took more deliberation time after receiving the negative feedback compared to the unimproved group. Most reasoners intuitively conclude that the ball must cost 10 cents
Many tasks require synchronizing our actions with particular moments along the path of moving tar... more 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.
The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditiona... more 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: Emotionalbased 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.
High numerate individuals tend to be more successful probabilistic problem solvers than those low... more High numerate individuals tend to be more successful probabilistic problem solvers than those lower in numeracy. These individual differences, however, can be modulated through the presentation format of external information, although discrepancies have been reported. The present investigation addressed these discrepancies by using formally equivalent Bayesian reasoning problems differing in numerical format and problem complexity. As previously observed, with a complex problem all participants were at floor level with probabilistic information, while individual differences emerged with natural frequency data. In sharp contrast, with a simple problem, differences between numeracy levels were diminished with natural frequencies, with group differences emerging only with probabilistic formats. Accordingly, the impact of numeracy in Bayesian reasoning depends both on numerical format and verbal complexity, and further suggests that lower numerate individuals are not inherently unable to reason in a Bayesian-like manner.
The authors argue that human sequential learning is often but not always characterized by a shift... more 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 frequencyinduced 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.
It has been shown that Bayesian reasoning is affected by the believability of the data, but it is... more 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.
This article analyzes the leading theoretical approaches to Bayesian reasoning in the literature,... more This article analyzes the leading theoretical approaches to Bayesian reasoning in the literature, and its main sources of empirical support. Many errors in probability estimates are attributed to people's inability to think in statistical tems when faced with information about a single event. Specifically, in situations where the normative model is Bayes's theorem, the well-known base rate neglect is analyzed both from rhe heuristic and biases approach, of Tversky and Kahneman, and from the frequentist hypothesis defended by Gigerenzer, Cosmides et al. The discrepancy between intuitions and formal mathenlatical reasoning is also analyzed through the studies with the three prisoners problem. Finally, we present the mental rnodel theoly of extensional probabilistic reasoning (Johnsorl-Laid et al., 1999) which explains how naive individuals can infer posterior probabilities without relying on Bayes 's theorern
Humans are traditionally depicted as suboptimal decision-makers, since they often fail to maximiz... more Humans are traditionally depicted as suboptimal decision-makers, since they often fail to maximize expected utility. However, recent studies claim people choose optimally in tasks called motor lotteries, where participants reach to different targets within a maximum time window in order to get a reward. A difference is that, while in classical tasks probability information is explicitly given, in motor tasks it is implicit in each participant's motor variability. Once this variability is known, a target can be designed to match a specific probability of being hit. This manipulation is normally implemented through size, but little has been done to explore other ways to represent probability in a motor task: for instance, through distance. Our experiment studied differences in expected utility maximization between these two ways of representing probabilities. In each of our two different conditions, trials consisted in the presentation of two targets, one with a lower probability to be hit but higher gain (risky) and another with higher probability and lower gain (safe). Participants decided to reach for one or another. In the size condition, both targets appeared at the same distance, but the risky was smaller. In the distance condition, both targets had equal size, but the risky was further away. Probabilities were manipulated to sample various expected gain differences between both targets. Results showed clear differences. Risk aversion was more present in the distance condition: participants tended to reach for the safe target even if the optimal choice was the risky target. In the size condition, participants were more sensitive to expected value differences: the more this difference favored the risky target, the more it was chosen. These differences may be interpreted as participants considering additional cost functions (e.g. biomechanical) in the distance condition not captured by the mere probability of hitting. Meeting abstract presented at VSS 2015.
La distinción entre dos tipos de procesamiento cognitivo: implícito o no consciente y explícito o... more La distinción entre dos tipos de procesamiento cognitivo: implícito o no consciente y explícito o consciente es frecuente, dentro de áreas tales como percepción, memoria y aprendizaje. El objetivo de esta comunicación es analizar hasta qué punto esta distinción puede ser útil para la comprensión de un proceso tan complejo, como es el pensamiento humano. Uno de los actuales debates, dentro de este enfoque, es si la distinción implícito versus explícito está relacionada con diferentes estados de conciencia o bien se trata de distintos niveles de abstracción del conocimiento. Desde esta perspectiva, a lo largo de este trabajo se analizarán tareas de pensamiento como son la inducción de categorías y la resolución de problemas. Se trata de considerar hasta qué punto algunos de los resultados observados pueden comprenderse mejor aplicando una herramienta de análisis común a otras áreas de la cognición humana.
Ideally, decisions regarding one's health should be made after assessing the objective probabilit... more 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 richsodium 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.
En este articulo se analizan 10s enfoques teóricos más relevantes sobre razonamiento bayesiano, u... more En este articulo se analizan 10s enfoques teóricos más relevantes sobre razonamiento bayesiano, usí como sus principales apoyos empíricos. Muchos errores en estimaciones de probabilidad se atribuyen a la incapacidad de las personas para pensar en términos estadísticos cunndo se enfrentan con información sobre un suceso único. Especljcicamente, en situaciones en las que el modelo norrnativo es el teorema de Bayes, se analiza el sesgo conocido como ccinsensibilidad a las probabilidades previasu, tanto desde el enfoque de heurísticos y sesgos, de Tversky y Kahneman, como desde la hipótesis frecuentista de Gigerenzer, Cosmides et al. También se aborda la discrepancia entre intuiciones y razonamiento matemático formal a través de 10s estudios sobre el problema de 10s tres prisioneros. Finalmente se presenta la teoria de Johnson-Laird et al. sobre modelos mentales en razonamiento probabilístico extensional, que explica cómo personas no expertas pueden inferir probabilidades a posteriori sin utilizar el teorema de Bayes. Palabras clave: heurísticos y sesgos, razonamiento probabilístico, teorema de Bayes, probabilidades a priori, modelos mentales, razonamiento bayesiano, hipótesis frecuentista. This article analyzes the leading theoretical approaches to Bayesian reasoning in the literature, and its mairz sources of empirical support. Muny errors in probability estimates are attributed to people's inability to think in statistical t e m s when faced with irlformation about a single event. Specijically, in situations where the normative model is Bayes's theorem, the well-known base rate neglect is analyzed both from rhe heuristic and biases approach, of Tversky and Kahneman, and from thefrequentist hypothesis defended by Gigerenzer, Cosmides et al. The discre
El presente trabajo pretendió investigar cómo las similitudes superfkiales afectan al tiempo que ... more El presente trabajo pretendió investigar cómo las similitudes superfkiales afectan al tiempo que tardan los sujetos en recuperar un análogo presentado previamente cuando intentan resolver un problema. Como se habia predicho, a partir de dos modelos sobre el proceso de recuperación de análogos (el de Holland et al., 1986 y el de Keane, 1988), no se encontraron diferencias en cuanto al tiempo de recuperación entre análogos que comparten con el problema exclusivamente la estructura y análogos que además de la estructura contienen similitudes sŭ p erficiales: Una-véz recuperado el análogo, las similitudes superfkiales aceleran el proceso de establecimiento de correspondencias. También se produjo un efecto de «transferencia negativa» generado exclusivamente por similitudes superficiales. Este efecto se explica mejor en el modelo de «suma de activación» de Holland et al., (1986). Finalmente, se propuso una explicación integradora que refiere los dos modelos a momentos distririos del proceso de aprendizaje.
Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nev... more 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.
Cognitive biases such as causal illusions have been related to paranormal and pseudoscientific be... more 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 evidencebased educational interventions like the one presented here could be used to significantly improve critical thinking skills in our students.
Humans have long been characterized as poor probabilistic reasoners when presented with explicit ... more 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.
The popular bat-and-ball problem is a relatively simple math riddle on which people are easily bi... more The popular bat-and-ball problem is a relatively simple math riddle on which people are easily biased by intuitive or heuristic thinking. In two studies we tested the impact of a simple but somewhat neglected manipulation-the impact of minimal accuracy feedback-on bat-and-ball performance. Participants solved a total of 15 standard and 15 control versions of the bat-and-ball problem in three consecutive blocks. Half of the participants received accuracy feedback in the intermediate block. Results of both studies indicated that the feedback had, on average, no significant effect on bat-and-ball accuracy over and above mere repeated presentation. We did observe a consistent improvement for a small number of individual participants. Explorative analyses indicated that this improved group showed a more pronounced conflict detection effect (i.e., latency increase) at the pretest and took more deliberation time after receiving the negative feedback compared to the unimproved group. Most reasoners intuitively conclude that the ball must cost 10 cents
Many tasks require synchronizing our actions with particular moments along the path of moving tar... more 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.
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Papers by Elisabet Tubau