Interactive effects of the probability of the cue and the probability of the outcome on the overestimation of null contingency

A large-scale study and six-month follow-up of an intervention to reduce causal illusions in high school students

Causal illusions consist of believing that there is a causal relationship between events that are actually unrelated. This bias is associated with pseudoscience, stereotypes and other unjustified beliefs. Thus, it seems important to develop educational interventions to reduce them. To our knowledge, the only debiasing intervention designed to be used at schools was developed by Barberia et al. (Barberia et al. 2013 PLoS One 8, e71303 (doi:10.1371/journal.pone.0071303)), focusing on base rates, control conditions and confounding variables. Their assessment used an active causal illusion task where participants could manipulate the candidate cause. The intervention reduced causal illusions in adolescents but was only tested in a small experimental project. The present research evaluated it in a large-scale project through a collaboration with the Spanish Foundation for Science and Technology (FECYT), and was conducted in schools to make it ecologically valid. It included a pilot study (n = 287), a large-scale implementation (n = 1668; 40 schools) and a six-month follow-up (n = 353). Results showed medium-to-large and long-lasting effects on the reduction of causal illusions. To our knowledge, this is the first research showing the efficacy and long-term effects of a debiasing intervention against causal illusions that can be used on a large scale through the educational system.

Does perceptual disfluency affect the illusion of causality?

When a subjective experience of difficulty is associated with a mental task, people tend to engage in systematic and deliberative reasoning, which can reduce the usage of intuitive and effortless thinking that gives rise to cognitive biases. One such bias is the illusion of causality, where people perceive a causal link between two unrelated events. In 2019, Díaz-Lago and Matute found that a superficial perceptual feature of the task could modulate the magnitude of the illusion (i.e., a hard-to-read font led to a decrease in the magnitude of the illusion). The present study explored the generalisability of the idea that perceptual disfluency can lead to a decrease in the magnitude of the illusion. In the first experiment, we tested whether a physical-perceptual manipulation of the stimuli, specifically the contrast between the written text and the background, could modulate the illusion in a contingency learning task. The results of the online experiment (N = 200) showed no effect of contrast on the magnitude of the illusion, despite our manipulation having successfully induced task fluency or disfluency. Building upon this null result, our second experiment (N = 100) focused on manipulating the font type, in an attempt to replicate the results obtained by Díaz-Lago and Matute. In contrast to their findings, we found no discernible effect of font type on the magnitude of the illusion, even though this manipulation also effectively induced variations in task fluency or disfluency. These results underscore the notion that not all categories of (dis)fluency in cognitive processing wield a modulatory influence on cognitive biases, and they call for a re-evaluation and a more precise delineation of the (dis)fluency construct.

Instruction on the Scientific Method Provides (Some) Protection Against Illusions of Causality

People tend to overestimate the efficacy of an ineffective treatment when they experience the treatment and its supposed outcome co-occurring frequently. This is referred to as the outcome density effect. Here, we attempted to improve the accuracy of participants' assessments of an ineffective treatment by instructing them about the scientific practice of comparing treatment effects against a relevant base-rate, i.e., when no treatment is delivered. The effect of these instructions was assessed in both a trial-by-trial contingency learning task, where cue administration was either decided by the participant (Experiments 1 & 2) or pre-determined by the experimenter (Experiment 3), as well as in summary format where all information was presented on a single screen (Experiment 4). Overall, we found two means by which base-rate instructions influence efficacy ratings for the ineffective treatment: 1) When information was presented sequentially, the benefit of base-rate instructions on illusory belief was mediated by reduced sampling of cue-present trials, and 2) When information was presented in summary format, we found a direct effect of base-rate instruction on reducing causal illusion. Together, these findings suggest that simple instructions on the scientific method were able to decrease participants' (over-)weighting of cue-outcome coincidences when making causal judgements, as well as decrease their tendency to over-sample cue-present events. However, the effect of base-rate instructions on correcting illusory beliefs was incomplete, and participants still showed illusory causal judgements when the probability of the outcome occurring was high. Thus, simple textual information about assessing causal relationships is partially effective in influencing people's judgements of treatment efficacy, suggesting an important role of scientific instruction in debiasing cognitive errors.

Unidirectional rating scales overestimate the illusory causation phenomenon

Illusory causation is a phenomenon in which people mistakenly perceive a causal relationship between a cue and outcome even though the contingency between them is actually zero. Illusory causation studies typically use a unidirectional causal rating scale, where one endpoint refers to no relationship and the other to a strongly positive causal relationship. This procedure may bias mean causal ratings in a positive direction, either by censoring negative ratings or by discouraging participants from giving the normative rating of zero which is at the bottom extreme of the scale. To test this possibility, we ran two experiments that directly compared the magnitude of causal illusions when assessed with a unidirectional (zero-positive) versus a bidirectional (negative-zero-positive) rating scale. Experiment 1 used high cue and outcome densities (both 75%), whereas Experiment 2 used neutral cue and outcome densities (both 50%). Across both experiments, we observed a larger illusory causation effect in the unidirectional group compared with the bidirectional group, despite both groups experiencing the same training trials. The causal illusions in Experiment 2 were observed despite participants accurately learning the conditional probabilities of the outcome occurring in both the presence and absence of the cue, suggesting that the illusion is driven by the inability to accurately integrate conditional probabilities to infer causal relationships. Our results indicate that although illusory causation is a genuine phenomenon that is observable with either a undirectional or a bidirectional rating scale, its magnitude may be overestimated when unidirectional rating scales are used.

Grounding Intuitive Physics in Perceptual Experience

This review article explores the foundation of laypeople's understanding of the physical world rooted in perceptual experience. Beginning with a concise historical overview of the study of intuitive physics, the article presents the hypothesis that laypeople possess accurate internalized representations of physical laws. A key aspect of this hypothesis is the contention that correct representations of physical laws emerge in ecological experimental conditions, where the scenario being examined resembles everyday life experiences. The article critically examines empirical evidence both supporting and challenging this claim, revealing that despite everyday-life-like conditions, fundamental misconceptions often persist. Many of these misconceptions can be attributed to a domain-general heuristic that arises from the overgeneralization of perceptual-motor experiences with physical objects. To conclude, the article delves into ongoing controversies and highlights promising future avenues in the field of intuitive physics, including action-judgment dissociations, insights from developmental psychology, and computational models integrating artificial intelligence.

Scarcity affects cognitive biases: The case of the illusion of causality

Previous research indicates that economic scarcity affects people's judgments, decisions, and cognition in a variety of contexts, and with various consequences. We hypothesized that scarcity could sometimes reduce cognitive biases. Specifically, it could reduce the causal illusion, a cognitive bias that is at the heart of superstitions and irrational thoughts, and consists of believing that two events are causally connected when they are not. In three experiments, participants played the role of doctors deciding whether to administer a drug to a series of patients. The drug was ineffective, because the percentage of patients recovering was identical regardless of whether they took the drug. We manipulated the budget available to buy the drugs, tough all participants had enough for all their patients. Even so, participants in the scarce group reduced the use of the drug and showed a lower causal illusion than participants in the wealthy group. Experiments 2 and 3 added a phase in which the budget changed. Participants who transitioned from scarcity to wealth exhibited a reduced use of resources and a lower causal illusion, whereas participants transitioning from wealth to scarcity were unaffected by their previous history.

A debiasing intervention to reduce the causality bias in undergraduates: the role of a bias induction phase

The causality bias, or causal illusion, occurs when people believe that there is a causal relationship between events that are actually uncorrelated. This bias is associated with many problems in everyday life, including pseudoscience, stereotypes, prejudices, and ideological extremism. Some evidence-based educational interventions have been developed to reduce causal illusions. To the best of our knowledge, these interventions have included a bias induction phase prior to the training phase, but the role of this bias induction phase has not yet been investigated. The aim of the present research was to examine it. Participants were randomly assigned to one of three groups (induction + training, training, and control, as a function of the phases they received before assessment). We evaluated their causal illusion using a standard contingency judgment task. In a null contingency scenario, the causal illusion was reduced in the training and induction-training groups as compared to the control group, suggesting that the intervention was effective regardless of whether or not the induction phase was included. In addition, in a positive contingency scenario, the induction + training group generated lower causal judgments than the control group, indicating that sometimes the induction phase may produce an increase in general skepticism. The raw data of this experiment are available at the Open Science Framework at https://osf.io/k9nes/

Dispersion vs Disparity: Hiding Variability Can Encourage Stereotyping When Visualizing Social Outcomes

Visualization research often focuses on perceptual accuracy or helping readers interpret key messages. However, we know very little about how chart designs might influence readers' perceptions of the people behind the data. Specifically, could designs interact with readers' social cognitive biases in ways that perpetuate harmful stereotypes? For example, when analyzing social inequality, bar charts are a popular choice to present outcome disparities between race, gender, or other groups. But bar charts may encourage deficit thinking, the perception that outcome disparities are caused by groups' personal strengths or deficiencies, rather than external factors. These faulty personal attributions can then reinforce stereotypes about the groups being visualized. We conducted four experiments examining design choices that influence attribution biases (and therefore deficit thinking). Crowdworkers viewed visualizations depicting social outcomes that either mask variability in data, such as bar charts or dot plots, or emphasize variability in data, such as jitter plots or prediction intervals. They reported their agreement with both personal and external explanations for the visualized disparities. Overall, when participants saw visualizations that hide within-group variability, they agreed more with personal explanations. When they saw visualizations that emphasize within-group variability, they agreed less with personal explanations. These results demonstrate that data visualizations about social inequity can be misinterpreted in harmful ways and lead to stereotyping. Design choices can influence these biases: Hiding variability tends to increase stereotyping while emphasizing variability reduces it.

Causal illusion in the core of pseudoscientific beliefs: The role of information interpretation and search strategies

The prevalence of pseudoscientific beliefs in our societies negatively influences relevant areas such as health or education. Causal illusions have been proposed as a possible cognitive basis for the development of such beliefs. The aim of our study was to further investigate the specific nature of the association between causal illusion and endorsement of pseudoscientific beliefs through an active contingency detection task. In this task, volunteers are given the opportunity to manipulate the presence or absence of a potential cause in order to explore its possible influence over the outcome. Responses provided are assumed to reflect both the participants’ information interpretation strategies as well as their information search strategies. Following a previous study investigating the association between causal illusion and the presence of paranormal beliefs, we expected that the association between causal illusion and pseudoscientific beliefs would disappear when controlling for the information search strategy (i.e., the proportion of trials in which the participants decided to present the potential cause). Volunteers with higher pseudoscientific beliefs also developed stronger causal illusions in active contingency detection tasks. This association appeared irrespective of the participants with more pseudoscientific beliefs showing (Experiment 2) or not (Experiment 1) differential search strategies. Our results suggest that both information interpretation and search strategies could be significantly associated to the development of pseudoscientific (and paranormal) beliefs.

Superstitious learning of abstract order from random reinforcement

Humans and other animals often infer spurious associations among unrelated events. However, such superstitious learning is usually accounted for by conditioned associations, raising the question of whether an animal could develop more complex cognitive structures independent of reinforcement. Here, we tasked monkeys with discovering the serial order of two pictorial sets: a "learnable" set in which the stimuli were implicitly ordered and monkeys were rewarded for choosing the higher-rank stimulus and an "unlearnable" set in which stimuli were unordered and feedback was random regardless of the choice. We replicated prior results that monkeys reliably learned the implicit order of the learnable set. Surprisingly, the monkeys behaved as though some ordering also existed in the unlearnable set, showing consistent choice preference that transferred to novel untrained pairs in this set, even under a preference-discouraging reward schedule that gave rewards more frequently to the stimulus that was selected less often. In simulations, a model-free reinforcement learning algorithm (Q-learning) displayed a degree of consistent ordering among the unlearnable set but, unlike the monkeys, failed to do so under the preference-discouraging reward schedule. Our results suggest that monkeys infer abstract structures from objectively random events using heuristics that extend beyond stimulus-outcome conditional learning to more cognitive model-based learning mechanisms.

Pseudocontingencies: Flexible contingency inferences from base rates

Humans are evidently able to learn contingencies from the co-occurrence of cues and outcomes. But how do humans judge contingencies when observations of cue and outcome are learned on different occasions? The pseudocontingency framework proposes that humans rely on base-rate correlations across contexts, that is, whether outcome base rates increase or decrease with cue base rates. Here, we elaborate on an alternative mechanism for pseudocontingencies that exploits base rate information within contexts. In two experiments, cue and outcome base rates varied across four contexts, but the correlation by base rates was kept constant at zero. In some contexts, cue and outcome base rates were aligned (e.g., cue and outcome base rates were both high). In other contexts, cue and outcome base rates were misaligned (e.g., cue base rate was high, but outcome base rate was low). Judged contingencies were more positive for contexts in which cue and outcome base rates were aligned than in contexts in which cue and outcome base rates were misaligned. Our findings indicate that people use the alignment of base rates to infer contingencies conditional on the context. As such, they lend support to the pseudocontingency framework, which predicts that decision makers rely on base rates to approximate contingencies. However, they challenge previous conceptions of pseudocontingencies as a uniform inference from correlated base rates. Instead, they suggest that people possess a repertoire of multiple contingency inferences that differ with regard to informational requirements and areas of applicability.

Pseudoscientific Health Beliefs and the Perceived Frequency of Causal Relationships

Beliefs about cause and effect, including health beliefs, are thought to be related to the frequency of the target outcome (e.g., health recovery) occurring when the putative cause is present and when it is absent (treatment administered vs. no treatment); this is known as contingency learning. However, it is unclear whether unvalidated health beliefs, where there is no evidence of cause–effect contingency, are also influenced by the subjective perception of a meaningful contingency between events. In a survey, respondents were asked to judge a range of health beliefs and estimate the probability of the target outcome occurring with and without the putative cause present. Overall, we found evidence that causal beliefs are related to perceived cause–effect contingency. Interestingly, beliefs that were not predicted by perceived contingency were meaningfully related to scores on the paranormal belief scale. These findings suggest heterogeneity in pseudoscientific health beliefs and the need to tailor intervention strategies according to underlying causes.

The Accuracy of Causal Learning Over Long Timeframes: An Ecological Momentary Experiment Approach

The ability to learn cause-effect relations from experience is critical for humans to behave adaptively - to choose causes that bring about desired effects. However, traditional experiments on experience-based learning involve events that are artificially compressed in time so that all learning occurs over the course of minutes. These paradigms therefore exclusively rely upon working memory. In contrast, in real-world situations we need to be able to learn cause-effect relations over days and weeks, which necessitates long-term memory. 413 participants completed a smartphone study, which compared learning a cause-effect relation one trial per day for 24 days versus the traditional paradigm of 24 trials back- to- back. Surprisingly, we found few differences between the short versus long timeframes. Subjects were able to accurately detect generative and preventive causal relations, and they exhibited illusory correlations in both the short and long timeframe tasks. These results provide initial evidence that experience-based learning over long timeframes exhibits similar strengths and weaknesses as in short timeframes. However, learning over long timeframes may become more impaired with more complex tasks.

Illusion of control affects ERP amplitude reductions for auditory outcomes of self-generated actions

The reduction of neural responses to self-generated stimuli compared to external stimuli is thought to result from the matching of motor-based sensory predictions and sensory reafferences and to serve the identification of changes in the environment as caused by oneself. The amplitude of the auditory event-related potential (ERP) component N1 seems to closely reflect this matching process, while the later positive component (P2/ P3a) has been associated with judgments of agency, which are also sensitive to contextual top-down information. In this study, we examined the effect of perceived control over sound production on the processing of self-generated and external stimuli, as reflected in these components. We used a new version of a classic two-button choice task to induce different degrees of the illusion of control (IoC) and recorded ERPs for the processing of self-generated and external sounds in a subsequent task. N1 amplitudes were reduced for self-generated compared to external sounds, but not significantly affected by IoC. P2/3a amplitudes were affected by IoC: We found reduced P2/3a amplitudes after a high compared to a low IoC induction training, but only for self-generated, not for external sounds. These findings suggest that prior contextual belief information induced by an IoC affects later processing as reflected in the P2/P3a, possibly for the formation of agency judgments, while early processing reflecting motor-based predictions is not affected.

The tendency to stop collecting information is linked to illusions of causality

Previous research proposed that cognitive biases contribute to produce and maintain the symptoms exhibited by deluded patients. Specifically, the tendency to jump to conclusions (i.e., to stop collecting evidence soon before making a decision) has been claimed to contribute to delusion formation. Additionally, deluded patients show an abnormal understanding of cause-effect relationships, often leading to causal illusions (i.e., the belief that two events are causally connected, when they are not). Both types of bias appear in psychotic disorders, but also in healthy individuals. In two studies, we test the hypothesis that the two biases (jumping to conclusions and causal illusions) appear in the general population and correlate with each other. The rationale is based on current theories of associative learning that explain causal illusions as the result of a learning bias that tends to wear off as additional information is incorporated. We propose that participants with higher tendency to jump to conclusions will stop collecting information sooner in a causal learning study than those participants with lower tendency to jump to conclusions, which means that the former will not reach the learning asymptote, leading to biased judgments. The studies provide evidence in favour that the two biases are correlated but suggest that the proposed mechanism is not responsible for this association.

Hearing hooves, thinking zebras: A review of the inverse base-rate effect

People often fail to use base-rate information appropriately in decision-making. This is evident in the inverse base-rate effect, a phenomenon in which people tend to predict a rare outcome for a new and ambiguous combination of cues. While the effect was first reported in 1988, it has recently seen a renewed interest from researchers concerned with learning, attention and decision-making. However, some researchers have raised concerns that the effect arises in specific circumstances and is unlikely to provide insight into general learning and decision-making processes. In this review, we critically evaluate the evidence for and against the main explanations that have been proposed to explain the effect, and identify where this evidence is currently weak. We argue that concerns about the effect are not well supported by the data. Instead, the evidence supports the conclusion that the effect is a result of general mechanisms that provides a useful opportunity to understand the processes involved in learning and decision making. We discuss gaps in our knowledge and some promising avenues for future research, including the relevance of the effect to models of attentional change in learning, an area where the phenomenon promises to contribute new insights.

Causal illusions in the classroom: how the distribution of student outcomes can promote false instructional beliefs

Teachers sometimes believe in the efficacy of instructional practices that have little empirical support. These beliefs have proven difficult to efface despite strong challenges to their evidentiary basis. Teachers typically develop causal beliefs about the efficacy of instructional practices by inferring their effect on students’ academic performance. Here, we evaluate whether causal inferences about instructional practices are susceptible to an outcome density effect using a contingency learning task. In a series of six experiments, participants were ostensibly presented with students’ assessment outcomes, some of whom had supposedly received teaching via a novel technique and some of whom supposedly received ordinary instruction. The distributions of the assessment outcomes was manipulated to either have frequent positive outcomes (high outcome density condition) or infrequent positive outcomes (low outcome density condition). For both continuous and categorical assessment outcomes, participants in the high outcome density condition rated the novel instructional technique as effective, despite the fact that it either had no effect or had a negative effect on outcomes, while the participants in the low outcome density condition did not. These results suggest that when base rates of performance are high, participants may be particularly susceptible to drawing inaccurate inferences about the efficacy of instructional practices.

The more, the merrier: Treatment frequency influences effectiveness perception and further treatment choice

Causal illusions have been postulated as cognitive mediators of pseudoscientific beliefs, which, in turn, might lead to the use of pseudomedicines. However, while the laboratory tasks aimed to explore causal illusions typically present participants with information regarding the consequences of administering a fictitious treatment versus not administering any treatment, real-life decisions frequently involve choosing between several alternative treatments. In order to mimic these realistic conditions, participants in two experiments received information regarding the rate of recovery when each of two different fictitious remedies were administered. The fictitious remedy that was more frequently administered was given higher effectiveness ratings than the low-frequency one, independent of the absence or presence of information about the spontaneous recovery rate. Crucially, we also introduced a novel dependent variable that involved imagining new occasions in which the ailment was present and asking participants to decide which treatment they would opt for. The inclusion of information about the base rate of recovery significantly influenced participants' choices. These results imply that the mere prevalence of popular treatments might make them seem particularly effective. It also suggests that effectiveness ratings should be interpreted with caution as they might not accurately reflect real treatment choices. Materials and datasets are available at the Open Science Framework [https://osf.io/fctjs/].

Biased Sampling and Causal Estimation of Health-Related Information: Laboratory-Based Experimental Research

Background

The internet is a relevant source of health-related information. The huge amount of information available on the internet forces users to engage in an active process of information selection. Previous research conducted in the field of experimental psychology showed that information selection itself may promote the development of erroneous beliefs, even if the information collected does not.

Objective

The aim of this study was to assess the relationship between information searching strategy (ie, which cues are used to guide information retrieval) and causal inferences about health while controlling for the effect of additional information features.

Methods

We adapted a standard laboratory task that has previously been used in research on contingency learning to mimic an information searching situation. Participants (N=193) were asked to gather information to determine whether a fictitious drug caused an allergic reaction. They collected individual pieces of evidence in order to support or reject the causal relationship between the two events by inspecting individual cases in which the drug was or was not used or in which the allergic reaction appeared or not. Thus, one group (cause group, n=105) was allowed to sample information based on the potential cause, whereas a second group (effect group, n=88) was allowed to sample information based on the effect. Although participants could select which medical records they wanted to check—cases in which the medicine was used or not (in the cause group) or cases in which the effect appeared or not (in the effect group)—they all received similar evidence that indicated the absence of a causal link between the drug and the reaction. After observing 40 cases, they estimated the drug–allergic reaction causal relationship.

Results

Participants used different strategies for collecting information. In some cases, participants displayed a biased sampling strategy compatible with positive testing, that is, they required a high proportion of evidence in which the drug was administered (in the cause group) or in which the allergic reaction appeared (in the effect group). Biased strategies produced an overrepresentation of certain pieces of evidence at the detriment of the representation of others, which was associated with the accuracy of causal inferences. Thus, how the information was collected (sampling strategy) demonstrated a significant effect on causal inferences (F_1,185=32.53, P<.001, η^2p=0.15) suggesting that inferences of the causal relationship between events are related to how the information is gathered.

Conclusions

Mistaken beliefs about health may arise from accurate pieces of information partially because of the way in which information is collected. Patient or person autonomy in gathering health information through the internet, for instance, may contribute to the development of false beliefs from accurate pieces of information because search strategies can be biased.

Causal illusion as a cognitive basis of pseudoscientific beliefs

Causal illusion has been proposed as a cognitive mediator of pseudoscientific beliefs. However, previous studies have only tested the association between this cognitive bias and a closely related but different type of unwarranted beliefs, those related to superstition and paranormal phenomena. Participants (n = 225) responded to a novel questionnaire of pseudoscientific beliefs designed for this study. They also completed a contingency learning task in which a possible cause, infusion intake, and a desired effect, headache remission, were actually non-contingent. Volunteers with higher scores on the questionnaire also presented stronger causal illusion effects. These results support the hypothesis that causal illusions might play a fundamental role in the endorsement of pseudoscientific beliefs.

Base-rate expectations modulate the causal illusion

Previous research revealed that people's judgments of causality between a target cause and an outcome in null contingency settings can be biased by various factors, leading to causal illusions (i.e., incorrectly reporting a causal relationship where there is none). In two experiments, we examined whether this causal illusion is sensitive to prior expectations about base-rates. Thus, we pretrained participants to expect either a high outcome base-rate (Experiment 1) or a low outcome base-rate (Experiment 2). This pretraining was followed by a standard contingency task in which the target cause and the outcome were not contingent with each other (i.e., there was no causal relation between them). Subsequent causal judgments were affected by the pretraining: When the outcome base-rate was expected to be high, the causal illusion was reduced, and the opposite was observed when the outcome base-rate was expected to be low. The results are discussed in the light of several explanatory accounts (associative and computational). A rational account of contingency learning based on the evidential value of information can predict our findings.

Persistence of Causal Illusions After Extensive Training

We carried out an experiment using a conventional causal learning task but extending the number of learning trials participants were exposed to. Participants in the standard training group were exposed to 48 learning trials before being asked about the potential causal relationship under examination, whereas for participants in the long training group the length of training was extended to 288 trials. In both groups, the event acting as the potential cause had zero correlation with the occurrence of the outcome, but both the outcome density and the cause density were high, therefore providing a breeding ground for the emergence of a causal illusion. In contradiction to the predictions of associative models such the Rescorla-Wagner model, we found moderate evidence against the hypothesis that extending the learning phase alters the causal illusion. However, assessing causal impressions recurrently did weaken participants’ causal illusions.

Bridging the divide between causal illusions in the laboratory and the real world: the effects of outcome density with a variable continuous outcome

Illusory causation refers to a consistent error in human learning in which the learner develops a false belief that two unrelated events are causally associated. Laboratory studies usually demonstrate illusory causation by presenting two events-a cue (e.g., drug treatment) and a discrete outcome (e.g., patient has recovered from illness)-probabilistically across many trials such that the presence of the cue does not alter the probability of the outcome. Illusory causation in these studies is further augmented when the base rate of the outcome is high, a characteristic known as the outcome density effect. Illusory causation and the outcome density effect provide laboratory models of false beliefs that emerge in everyday life. However, unlike laboratory research, the real-world beliefs to which illusory causation is most applicable (e.g., ineffective health therapies) often involve consequences that are not readily classified in a discrete or binary manner. This study used a causal learning task framed as a medical trial to investigate whether similar outcome density effects emerged when using continuous outcomes. Across two experiments, participants observed outcomes that were either likely to be relatively low (low outcome density) or likely to be relatively high (high outcome density) along a numerical scale from 0 (no health improvement) to 100 (full recovery). In Experiment 1, a bimodal distribution of outcome magnitudes, incorporating variance around a high and low modal value, produced illusory causation and outcome density effects equivalent to a condition with two fixed outcome values. In Experiment 2, the outcome density effect was evident when using unimodal skewed distributions of outcomes that contained more ambiguous values around the midpoint of the scale. Together, these findings provide empirical support for the relevance of the outcome density bias to real-world situations in which outcomes are not binary but occur to differing degrees. This has implications for the way in which we apply our understanding of causal illusions in the laboratory to the development of false beliefs in everyday life.

Behavior and illusions: a model to study superstition in a participant replacement experiment

The notion of superstitious behavior can provide a basic background for understanding such notions as illusions and beliefs. The present study investigated the social mechanism of the transmission of superstitious behavior in an experiment that utilized participant replacement. The sample was composed of a total of 38 participants. Participants performed a task on a computer: they could click a colored rectangle using the mouse. When the rectangle was in a particular color, the participants received points independently of their behavior (variable time schedule). When the color of the rectangle was changed, no points were presented (extinction). Under an Individual Exposure condition, ten participants worked alone on the task. Other participants were exposed to the same experimental task under a Social Exposure condition, in which each participant first learned by observation and then worked on the task in a participant replacement (chain) procedure. The first participant in each chain in the Social Exposure condition was a confederate who worked on the task "superstitiously," clicking the rectangle when points were presented. Superstitious responding was transmitted because of the behavior of the confederate. This also influenced estimates of personal control. These findings suggest that social learning can facilitate the acquisition and maintenance of superstitious behavior and the illusion of control. Our data also suggest that superstitious behavior and the illusion of control may involve similar learning principles.

A comparator-hypothesis account of biased contingency detection

Our ability to detect statistical dependencies between different events in the environment is strongly biased by the number of coincidences between them. Even when there is no true covariation between a cue and an outcome, if the marginal probability of either of them is high, people tend to perceive some degree of statistical contingency between both events. The present paper explores the ability of the Comparator Hypothesis to explain the general pattern of results observed in this literature. Our simulations show that this model can account for the biasing effects of the marginal probabilities of cues and outcomes. Furthermore, the overall fit of the Comparator Hypothesis to a sample of experimental conditions from previous studies is comparable to that of the popular Rescorla-Wagner model. These results should encourage researchers to further explore and put to the test the predictions of the Comparator Hypothesis in the domain of biased contingency detection.

Thinking in a Foreign language reduces the causality bias

The purpose of this research is to investigate the impact of a foreign language on the causality bias (i.e., the illusion that two events are causally related when they are not). We predict that using a foreign language could reduce the illusions of causality. A total of 36 native English speakers participated in Experiment 1, 80 native Spanish speakers in Experiment 2. They performed a standard contingency learning task, which can be used to detect causal illusions. Participants who performed the task in their native tongue replicated the illusion of causality effect, whereas those performing the task in their foreign language were more accurate in detecting that the two events were causally unrelated. Our results suggest that presenting the information in a foreign language could be used as a strategy to debias individuals against causal illusions, thereby facilitating more accurate judgements and decisions in non-contingent situations. They also contribute to the debate on the nature and underlying mechanisms of the foreign language effect, given that the illusion of causality is rooted in basic associative processes.

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.

Causal illusions in children when the outcome is frequent

Causal illusions occur when people perceive a causal relation between two events that are actually unrelated. One factor that has been shown to promote these mistaken beliefs is the outcome probability. Thus, people tend to overestimate the strength of a causal relation when the potential consequence (i.e. the outcome) occurs with a high probability (outcome-density bias). Given that children and adults differ in several important features involved in causal judgment, including prior knowledge and basic cognitive skills, developmental studies can be considered an outstanding approach to detect and further explore the psychological processes and mechanisms underlying this bias. However, the outcome density bias has been mainly explored in adulthood, and no previous evidence for this bias has been reported in children. Thus, the purpose of this study was to extend outcome-density bias research to childhood. In two experiments, children between 6 and 8 years old were exposed to two similar setups, both showing a non-contingent relation between the potential cause and the outcome. These two scenarios differed only in the probability of the outcome, which could either be high or low. Children judged the relation between the two events to be stronger in the high probability of the outcome setting, revealing that, like adults, they develop causal illusions when the outcome is frequent.

Statistical numeracy as a moderator of (pseudo)contingency effects on decision behavior

Pseudocontingencies denote contingency estimates inferred from base rates rather than from cell frequencies. We examined the role of statistical numeracy for effects of such fallible but adaptive inferences on choice behavior. In Experiment 1, we provided information on single observations as well as on base rates and tracked participants' eye movements. In Experiment 2, we manipulated the availability of information on cell frequencies and base rates between conditions. Our results demonstrate that a focus on base rates rather than cell frequencies benefits pseudocontingency effects. Learners who are more proficient in (conditional) probability calculation prefer to rely on cell frequencies in order to judge contingencies, though, as was evident from their gaze behavior. If cell frequencies are available in summarized format, they may infer the true contingency between options and outcomes. Otherwise, however, even highly numerate learners are susceptible to pseudocontingency effects.

Causal judgments about empirical information in an interrupted time series design

Empirical information available for causal judgment in everyday life tends to take the form of quasi-experimental designs, lacking control groups, more than the form of contingency information that is usually presented in experiments. Stimuli were presented in which values of an outcome variable for a single individual were recorded over six time periods, and an intervention was introduced between the fifth and sixth time periods. Participants judged whether and how much the intervention affected the outcome. With numerical stimulus information, judgments were higher for a pre-intervention profile in which all values were the same than for pre-intervention profiles with any other kind of trend. With graphical stimulus information, judgments were more sensitive to trends, tending to be higher when an increase after the intervention was preceded by a decreasing series than when it was preceded by an increasing series ending on the same value at the fifth time period. It is suggested that a feature-analytic model, in which the salience of different features of information varies between presentation formats, may provide the best prospect of explaining the results.

Single- and Dual-Process Models of Biased Contingency Detection

Decades of research in causal and contingency learning show that people's estimations of the degree of contingency between two events are easily biased by the relative probabilities of those two events. If two events co-occur frequently, then people tend to overestimate the strength of the contingency between them. Traditionally, these biases have been explained in terms of relatively simple single-process models of learning and reasoning. However, more recently some authors have found that these biases do not appear in all dependent variables and have proposed dual-process models to explain these dissociations between variables. In the present paper we review the evidence for dissociations supporting dual-process models and we point out important shortcomings of this literature. Some dissociations seem to be difficult to replicate or poorly generalizable and others can be attributed to methodological artifacts. Overall, we conclude that support for dual-process models of biased contingency detection is scarce and inconclusive.

Individuals Who Believe in the Paranormal Expose Themselves to Biased Information and Develop More Causal Illusions than Nonbelievers in the Laboratory

In the reasoning literature, paranormal beliefs have been proposed to be linked to two related phenomena: a biased perception of causality and a biased information-sampling strategy (believers tend to test fewer hypotheses and prefer confirmatory information). In parallel, recent contingency learning studies showed that, when two unrelated events coincide frequently, individuals interpret this ambiguous pattern as evidence of a causal relationship. Moreover, the latter studies indicate that sampling more cause-present cases than cause-absent cases strengthens the illusion. If paranormal believers actually exhibit a biased exposure to the available information, they should also show this bias in the contingency learning task: they would in fact expose themselves to more cause-present cases than cause-absent trials. Thus, by combining the two traditions, we predicted that believers in the paranormal would be more vulnerable to developing causal illusions in the laboratory than nonbelievers because there is a bias in the information they experience. In this study, we found that paranormal beliefs (measured using a questionnaire) correlated with causal illusions (assessed by using contingency judgments). As expected, this correlation was mediated entirely by the believers' tendency to expose themselves to more cause-present cases. The association between paranormal beliefs, biased exposure to information, and causal illusions was only observed for ambiguous materials (i.e., the noncontingent condition). In contrast, the participants' ability to detect causal relationships which did exist (i.e., the contingent condition) was unaffected by their susceptibility to believe in paranormal phenomena.

Illusions of causality: how they bias our everyday thinking and how they could be reduced

Illusions of causality occur when people develop the belief that there is a causal connection between two events that are actually unrelated. Such illusions have been proposed to underlie pseudoscience and superstitious thinking, sometimes leading to disastrous consequences in relation to critical life areas, such as health, finances, and wellbeing. Like optical illusions, they can occur for anyone under well-known conditions. Scientific thinking is the best possible safeguard against them, but it does not come intuitively and needs to be taught. Teaching how to think scientifically should benefit from better understanding of the illusion of causality. In this article, we review experiments that our group has conducted on the illusion of causality during the last 20 years. We discuss how research on the illusion of causality can contribute to the teaching of scientific thinking and how scientific thinking can reduce illusion.

Exploring the factors that encourage the illusions of control: the case of preventive illusions

Most previous research on illusions of control focused on generative scenarios, in which participants’ actions aim to produce a desired outcome. By contrast, the illusions that may appear in preventive scenarios, in which actions aim to prevent an undesired outcome before it occurs, are less known. In this experiment, we studied two variables that modulate generative illusions of control, the probability with which the action takes place, P(A), and the probability of the outcome, P(O), in two different scenarios: generative and preventive. We found that P(O) affects the illusion in symmetrical, opposite directions in each scenario, while P(A) is positively related to the magnitude of the illusion. Our conclusion is that, in what concerns the illusions of control, the occurrence of a desired outcome is equivalent to the nonoccurrence of an undesired outcome, which explains why the P(O) effect is reversed depending on the scenario.

Reducing the illusion of control when an action is followed by an undesired outcome

The illusion of control is the belief that our behavior produces an effect that is actually independent from it. This illusion is often at the core of superstitious and pseudoscientific thinking. Although recent research has proposed several evidence-based strategies that can be used to reduce the illusion, the majority of these experiments have involved positive illusions-that is, those in which the potential outcomes are desired (e.g., recovery from illness or earning points). By contrast, many real-life superstitions and pseudosciences are tied to negative illusions-that is, those in which the potential consequences are undesired. Examples are walking under a ladder, breaking a mirror, or sitting in row 13, all of which are supposed to generate bad luck. Thus, the question is whether the available evidence on how to reduce positive illusions would also apply to situations in which the outcomes are undesired. We conducted an experiment in which participants were exposed to undesired outcomes that occurred independently of their behavior. One strategy that has been shown to reduce positive illusions consists of warning people that the outcomes might have alternative causes, other than the participants' actions, and telling them that the best they can do to find out whether an alternative cause is at work is to act on only about 50% of the trials. When we gave our participants this information in an experiment in which the outcomes were undesired, their illusion was enhanced rather than reduced, contrary to what happens when the outcome is desired. This suggests that the strategies that reduce positive illusions may work in just the opposite way when the outcome is undesired.

Previous knowledge can induce an illusion of causality through actively biasing behavior

It is generally assumed that the way people assess the relationship between a cause and an outcome is closely related to the actual evidence existing about the co-occurrence of these events. However, people's estimations are often biased, and this usually translates into illusions of causality. Some have suggested that such illusions could be the result of previous knowledge-based expectations. In the present research we explored the role that previous knowledge has in the development of illusions of causality. We propose that previous knowledge influences the assessment of causality by influencing the decisions about responding or not (i.e., presence or absence of the potential cause), which biases the information people are exposed to, and this in turn produces illusions congruent with such biased information. In a non-contingent situation in which participants decided whether the potential cause was present or absent (Experiment 1), the influence of expectations on participants' judgments was mediated by the probability of occurrence of the potential cause (determined by participants' responses). However, in an identical situation, except that the participants were not allowed to decide the occurrence of the potential cause (Experiment 2), only the probability of the cause was significant, not the expectations or the interaction. Together, these results support our hypothesis that knowledge-based expectations affect the development of causal illusions by the mediation of behavior, which biases the information received.

The dark side of cognitive illusions: when an illusory belief interferes with the acquisition of evidence-based knowledge

Cognitive illusions are often associated with mental health and well‐being. However, they are not without risk. This research shows they can interfere with the acquisition of evidence‐based knowledge. During the first phase of the experiment, one group of participants was induced to develop a strong illusion that a placebo medicine was effective to treat a fictitious disease, whereas another group was induced to develop a weak illusion. Then, in Phase 2, both groups observed fictitious patients who always took the bogus treatment simultaneously with a second treatment which was effective. Our results showed that the group who developed the strong illusion about the effectiveness of the bogus treatment during Phase 1 had more difficulties in learning during Phase 2 that the added treatment was effective.

Outcome probability modulates anticipatory behavior to signals that are equally reliable

A stimulus is a reliable signal of an outcome when the probability that the outcome occurs in its presence is different from in its absence. Reliable signals of important outcomes are responsible for triggering critical anticipatory or preparatory behavior, which is any form of behavior that prepares the organism to receive a biologically significant event. Previous research has shown that humans and other animals prepare more for outcomes that occur in the presence of highly reliable (i.e., highly contingent) signals, that is, those for which that difference is larger. However, it seems reasonable to expect that, all other things being equal, the probability with which the outcome follows the signal should also affect preparatory behavior. In the present experiment with humans, we used two signals. They were differentially followed by the outcome, but they were equally (and relatively weakly) reliable. The dependent variable was preparatory behavior in a Martians video game. Participants prepared more for the outcome (a Martians' invasion) when the outcome was most probable. These results indicate that the probability of the outcome can bias preparatory behavior to occur with different intensities despite identical outcome signaling.

Illusion of control: the role of personal involvement

The illusion of control consists of overestimating the influence that our behavior exerts over uncontrollable outcomes. Available evidence suggests that an important factor in development of this illusion is the personal involvement of participants who are trying to obtain the outcome. The dominant view assumes that this is due to social motivations and self-esteem protection. We propose that this may be due to a bias in contingency detection which occurs when the probability of the action (i.e., of the potential cause) is high. Indeed, personal involvement might have been often confounded with the probability of acting, as participants who are more involved tend to act more frequently than those for whom the outcome is irrelevant and therefore become mere observers. We tested these two variables separately. In two experiments, the outcome was always uncontrollable and we used a yoked design in which the participants of one condition were actively involved in obtaining it and the participants in the other condition observed the adventitious cause-effect pairs. The results support the latter approach: Those acting more often to obtain the outcome developed stronger illusions, and so did their yoked counterparts.

The lack of side effects of an ineffective treatment facilitates the development of a belief in its effectiveness

Some alternative medicines enjoy widespread use, and in certain situations are preferred over conventional, validated treatments in spite of the fact that they fail to prove effective when tested scientifically. We propose that the causal illusion, a basic cognitive bias, underlies the belief in the effectiveness of bogus treatments. Therefore, the variables that modulate the former might affect the latter. For example, it is well known that the illusion is boosted when a potential cause occurs with high probability. In this study, we examined the effect of this variable in a fictitious medical scenario. First, we showed that people used a fictitious medicine (i.e., a potential cause of remission) more often when they thought it caused no side effects. Second, the more often they used the medicine, the more likely they were to develop an illusory belief in its effectiveness, despite the fact that it was actually useless. This behavior may be parallel to actual pseudomedicine usage; that because a treatment is thought to be harmless, it is used with high frequency, hence the overestimation of its effectiveness in treating diseases with a high rate of spontaneous relief. This study helps shed light on the motivations spurring the widespread preference of pseudomedicines over scientific medicines. This is a valuable first step toward the development of scientifically validated strategies to counteract the impact of pseudomedicine on society.

Pathological gamblers are more vulnerable to the illusion of control in a standard associative learning task

An illusion of control is said to occur when a person believes that he or she controls an outcome that is uncontrollable. Pathological gambling has often been related to an illusion of control, but the assessment of the illusion has generally used introspective methods in domain-specific (i.e., gambling) situations. The illusion of control of pathological gamblers, however, could be a more general problem, affecting other aspects of their daily life. Thus, we tested them using a standard associative learning task which is known to produce illusions of control in most people under certain conditions. The results showed that the illusion was significantly stronger in pathological gamblers than in a control undiagnosed sample. This suggests (1) that the experimental tasks used in basic associative learning research could be used to detect illusions of control in gamblers in a more indirect way, as compared to introspective and domain-specific questionnaires; and (2), that in addition to gambling-specific problems, pathological gamblers may have a higher-than-normal illusion of control in their daily life.