The impact of problem domain on Bayesian inferences: A systematic investigation.

Sparse (and occasionally contradictory) evidence exists regarding the impact of domain on probabilistic updating, some of which suggests that Bayesian word problems with medical content may be especially challenging. The present research aims to address this gap in knowledge through three pre-registered online studies, which involved a total of 2,238 participants. Bayesian word problems were related to one of three domains: medical, daily-life, and abstract. In the first two cases, problems presented realistic content and plausible numerical information, while in the latter, problems contained explicitly imaginary elements. Problems across domains were matched in terms of all relevant statistical values and, as much as possible, wording. Studies 1 and 2 utilized the same set of problems, but different response elicitation methods (i.e., an open-ended and a multiple-choice question, respectively). Study 3 involved a larger number of participants per condition and a smaller set of problems to more thoroughly investigate the magnitude of differences between the domains. There was a generally low rate of correct responses (17.2%, 17.4%, and 14.3% in Studies 1, 2, and 3, respectively), consistent with accuracy levels commonly observed in the literature for this specific task with online samples. Nonetheless, a small but significant difference between domains was observed: participants' accuracy did not differ between medical and daily-life problems, while it was significantly higher in corresponding abstract problems. These results suggest that medical problems are not inherently more difficult to solve, but rather that performance is improved with abstract problems for which participants cannot draw from their background knowledge.

Decision making under stress: mild hypoxia leads to increased risk-taking.

People tend to take more risks under stressful conditions. In the present study, we examined the effect of mild hypoxia, an unconscious and ongoing stressor, on decisions under uncertainty where probabilities are unknown. Participants completed the Balloon Analogue Risk Taking task (BART) in both a normoxic (20.9% oxygen concentration) and a mildly hypoxic (14.1% oxygen concentration) environment. The results indicate that people take more risks in a mildly hypoxic than in a normoxic environment. Despite inducing significant changes in physiological parameters, the oxygen manipulation remained undetected by participants allowing us to rule out a cognitive appraisal account for the effect. Moreover, the stressor was ongoing allowing us to discount possible post-stress reaction explanations. The current findings extend previous ones about the effect of stress on risk-taking and demonstrate that undetected stressors can increase risk-taking in decision making under ambiguity.

Fostering the Understanding of Positive Test Results.

Background: The majority of health-service users seem unable to properly compute the positive predictive value of medical tests. The research reported in the present study sought to investigate whether, and to what extent, probabilistic inferences about a positive test result can be improved by changing the traditional way in which probability judgments are elicited and medical information is presented. Methods: Online survey respondents were presented with a positive test result regarding a pregnant woman, and had to estimate the chances that her unborn baby had an anomaly (standard judgment), to apportion the numbers of chances for and against this hypothesis (distributive judgment), and to indicate whether the hypothesis that the baby had an anomaly was more or less likely than its alternative (relative judgment). Test sensitivity and information framing were also manipulated. Results: Irrespective of education and to some extent of numeracy, the majority of respondents produced correct distributive assessments of chances, which were in line with relative judgments and more accurate than standard ones. When information displayed exclusively positive test results, inferences resulted further improved and unaffected by test sensitivity. Conclusions: Simple communication strategies that prompt extensional reasoning on the relevant set of number of chances can help individuals to overcome probabilistic inference errors.

Communicating Down syndrome risk according to maternal age: "1-in-X" effect on perceived risk.

OBJECTIVE: The appropriateness of the 1-in-X numerical format to convey quantitative medical probabilities is currently under discussion because of its distortive effect on subjective probability assessment. Previous research, however, always asked participants to imagine a hypothetical scenario. The aim of the present research is to support the existence of the 1-in-X effect in a real setting: when pregnant women have to evaluate their personal risk of Down syndrome according to their maternal age. METHOD: During the first prenatal visit, pregnant women were asked to evaluate their own risk of having a child with Down syndrome according to their age, when such risk was presented either in the 1-in-X or in the N-in-NX format. Then, they were asked to assess their risk of having a child with Down syndrome. RESULTS: Results showed a systematic higher risk assessment when pregnant women were presented with the 1-in-X format (mean = 3.57, standard deviation = 1.4) than with the N-in-NX format (mean = 3.03, standard deviation = 1.4), P = 0.007. Whereas the effect was shown to be not moderated by a differential comprehension of the two numerical formats, women with a low educational level and those who were at their first pregnancy were shown to be significantly more vulnerable. CONCLUSION: The present findings corroborate the existence of the 1-in-X effect in a real-world setting, showing that, in pregnant women, the 1-in-X format actually elicits a higher perceived risk of Down syndrome, compared with the N-in-NX format.

Loss aversion and hypoxia: less loss aversion in oxygen-depleted environment.

Hypoxia, the deprivation of adequate oxygen supply, constitutes a direct threat to survival by disrupting cardiovascular or respiratory homeostasis and eliciting a respiratory distress. Although hypoxia has been shown to increase brain vulnerability and impair basic cognitive functions, only one study has examined its effect on decision-making. The present study examined the effect of mild hypoxia on individual's loss aversion, that is, the tendency to be more affected by losses than equal sized gains. A sample of 26 participants were asked to either accept or reject a series of mixed gambles once in an oxygen-depleted environment (14.1% oxygen concentration) and once in a normoxic environment (20.9% oxygen concentration). Each gamble involved a 50-50 chance of winning or losing specified amounts of money. Mild hypoxia decreased loss aversion: on average in the normoxic condition participants accepted gambles if the gain was at least 2.4 times as large as the loss, whereas in the oxygen-depleted condition participants accepted gambles if the gain was at least 1.7 times as large as the loss. Mild hypoxia may push individuals to be less cautious in daily decisions that involve a trade-off between a gain and a loss.

Sensory and multisensory reasoning: Is Bayesian updating modality-dependent?

Bayesianism assumes that probabilistic updating does not depend on the sensory modality by which information is processed. In this study, we investigate whether probability judgments based on visual and auditory information conform to this assumption. In a series of five experiments, we found that this is indeed the case when information is acquired through a single modality (i.e., only auditory or only visual) but not necessarily so when it comes from multiple modalities (i.e., audio-visual). In the latter case, judgments prove more accurate when both visual and auditory information individually support (i.e., increase the probability of) the hypothesis they also jointly support (synergy condition) than when either visual or auditory information support one hypothesis that is not the one they jointly support (contrast condition). In the extreme case in which both visual and auditory information individually support an alternative hypothesis to the one they jointly support (i.e., double-contrast condition), participants' accuracy is not only lower than in the synergy condition but near chance. This synergy-contrast effect represents a violation of the assumption that information modality is irrelevant for Bayesian updating and indicates an important limitation of multisensory integration, one which has not been previously documented.

Nudging COVID-19 Vaccine Uptake by Changing the Default: A Randomized Controlled Trial.

BACKGROUND: Although vaccination against SARS-CoV-2 is considered the central strategy against the pandemic, uptake lags behind target rates. METHOD: To explore whether this rate could be enhanced by a nudging strategy that exploits the status quo bias, we conducted a randomized controlled trial in northern Italy comparing vaccination acceptance among 2000 adults, ages 50 to 59 years, who were either invited to set an appointment (opt-in group) or assigned an individual appointment (opt-out group). RESULTS: Results indicate a difference of 3.2 percentage points, which represents a 32% relative increase in the vaccination rate for the opt-out group compared with the opt-in group. CONCLUSIONS: A significant portion of those who remain unvaccinated may not hold strong beliefs against vaccination but rather tend to inaction and may therefore be nudged toward vaccination with a reduction of action required. HIGHLIGHTS: Reluctant adults (50-59 years), who had not yet received vaccines against COVID-19, were sent letters announcing appointment availabilityIn an RCT, the status quo option in the notices influenced the rate of vaccine acceptanceNudging via pre-scheduled appointments encouraged vaccine uptake more than invitations to schedule didSwitching the default option yielded a 32% relative increase (13.1% vs. 9.9%) in vaccination.

Hypoxia and risk preferences: Mild hypoxia impacts choices for low-probability high-payoff bets.

Mild degrees of hypoxia are known to exert a detrimental effect on cognitive functions. In a lab study, we assessed the effect of mild hypoxia on risk-taking behavior. Participants (N = 25) were presented with pairs of bets of equal expected monetary value, one having a higher probability of winning/losing a lower payoff (safer bet) and one having a lower probability of winning/losing a higher payoff (riskier bet). We systematically varied the ratio of the probabilities (and corresponding payoffs) of the two bets and examined how this affected participants' choice between them. Following a familiarization session, participants performed the task twice: once in a normoxic environment (20.9% oxygen concentration) and once in a mildly hypoxic environment (14.1% oxygen concentration). Participants were not told and could not guess which environment they were in. We found a higher preference for the riskier bet in the mild hypoxic than normoxic environment but only in the loss domain. Furthermore, as the probability ratio increased, mild hypoxia increased the preference for the riskier bet in the domain of losses but decreased it for gains. The present findings support that mild hypoxia promotes riskier choices in the loss domain and provide new insights into the impact of mild hypoxia in moderating the effect of probability ratio on risky choices.

Overcoming number numbness in prenatal risk communication.

OBJECTIVE: Efficient prenatal risk communication hinges upon parents' grasp of statistical information. When forming their subjective representation of a probability, pregnant women may focus on inappropriate factors and ignore the appropriate factors. METHOD: The present research investigates the subjective probability that pregnant women derive from statements of the form 'There is a 1 in X chance that the baby will have condition Y,' where the number X and the severity of the condition Y were orthogonally manipulated. RESULTS: Study 1 showed that when judging how big is a 1 in X chance that a child will be affected by condition Y, pregnant women (n = 336) were sensitive to the severity of Y, but selectively numb to the objective number X. Study 2 (n = 461) replicated this pattern, but also showed that numerical numbness could be overcome by a simple intervention, namely, a quick comment that 1 in X was 'above average.' CONCLUSION: Practitioners must be aware that when forming a subjective probability assessment, pregnant women might be inappropriately sensitive to the severity of Y, and inappropriately numb to the number X, and that a simple communicative intervention can help in overcoming this selective number numbness.

Public's understanding of swab test results for SARS-CoV-2: an online behavioural experiment during the April 2020 lockdown.

OBJECTIVE: Although widespread testing for SARS-CoV-2 is in place, little is known about how well the public understands these results. We aimed to provide a comprehensive overview of the general public's grasp of the accuracy and significance of the results of the swab test. DESIGN: Web-based behavioural experiment. SETTING: Italy during the April 2020 lockdown. PARTICIPANTS: 566 Italian residents. MAIN OUTCOME MEASURES: Participants' estimates of the SARS-CoV-2 prevalence; the predictive and diagnostic accuracy of the test; the behavioural impact of (positive vs negative) test results; the perceived usefulness of a short-term repetition of the test following positive or negative results; and rankings of causes for false positives and false negatives. RESULTS: Most participants considered the swab test useful (89.6%) and provided predictive values consistent with their estimates of test diagnostic accuracy and infection prevalence (67.0%). Participants acknowledged the effects of symptomatic status and geographical location on prevalence (all p<0.001) but failed to take this information into account when estimating the positive or negative predictive value. Overall, test specificity was underestimated (91.5%, 95% CI 90.2% to 92.8%); test sensitivity was overestimated (89.7%, 95% CI 88.3% to 91.0%). Positive results were evaluated as more informative than negative ones (91.6, 95% CI 90.2 to 93.1 and 41.0, 95% CI 37.9 to 44.0, respectively, p<0.001); a short-term repetition of the test was considered more useful after a positive than a negative result (62.7, 95% CI 59.6 to 65.7 and 47.2, 95% CI 44.4 to 50.0, respectively, p=0.013). Human error and technical characteristics were assessed as more likely to be the causes of false positives (p<0.001); the level of the viral load as the cause of false negatives (p<0.001). CONCLUSIONS: While some aspects of the swab for SARS-CoV-2 are well grasped, others are not and may have a strong bearing on the general public's health and well-being. The obtained findings provide policymakers with a detailed picture that can guide the design and implementation of interventions for improving efficient communication with the general public as well as adherence to precautionary behaviour.

The challenge of mental simulation in preference-sensitive treatment decisions.

This commentary discusses the importance for preference-sensitive treatment decisions of episodic future thinking, which is the capacity to mentally simulate and pre-experience what might occur in one's personal future. Our aim is to call attention to this important topic since patients confronted with preference-sensitive treatment decisions could benefit from professional support that promotes the construction of comprehensive and detailed mental simulations of what might affect their future well-being and satisfaction.

The Effect of Evidential Impact on Perceptual Probabilistic Judgments.

In a series of three behavioral experiments, we found a systematic distortion of probability judgments concerning elementary visual stimuli. Participants were briefly shown a set of figures that had two features (e.g., a geometric shape and a color) with two possible values each (e.g., triangle or circle and black or white). A figure was then drawn, and participants were informed about the value of one of its features (e.g., that the figure was a "circle") and had to predict the value of the other feature (e.g., whether the figure was "black" or "white"). We repeated this procedure for various sets of figures and, by varying the statistical association between features in the sets, we manipulated the probability of a feature given the evidence of another (e.g., the posterior probability of hypothesis "black" given the evidence "circle") as well as the support provided by a feature to another (e.g., the impact, or confirmation, of evidence "circle" on the hypothesis "black"). Results indicated that participants' judgments were deeply affected by impact, although they only should have depended on the probability distributions over the features, and that the dissociation between evidential impact and posterior probability increased the number of errors. The implications of these findings for lower and higher level cognitive models are discussed.

Interpolating causal mechanisms: The paradox of knowing more.

Causal knowledge is not static; it is constantly modified based on new evidence. The present set of seven experiments explores 1 important case of causal belief revision that has been neglected in research so far: causal interpolations. A simple prototypic case of an interpolation is a situation in which we initially have knowledge about a causal relation or a positive covariation between 2 variables but later become interested in the mechanism linking these 2 variables. Our key finding is that the interpolation of mechanism variables tends to be misrepresented, which leads to the paradox of knowing more: The more people know about a mechanism, the weaker they tend to find the probabilistic relation between the 2 variables (i.e., weakening effect). Indeed, in all our experiments we found that, despite identical learning data about 2 variables, the probability linking the 2 variables was judged higher when follow-up research showed that the 2 variables were assumed to be directly causally linked (i.e., C→E) than when participants were instructed that the causal relation is in fact mediated by a variable representing a component of the mechanism (M; i.e., C→M→E). Our explanation of the weakening effect is that people often confuse discoveries of preexisting but unknown mechanisms with situations in which new variables are being added to a previously simpler causal model, thus violating causal stability assumptions in natural kind domains. The experiments test several implications of this hypothesis. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Mind the gap: Physicians' assessment of patients' importance weights in localized prostate cancer.

BACKGROUND: The management of localized prostate cancer is challenging because of the many therapeutic options available, none of which is generally acknowledged as superior to the others in every respect. The selection of the most appropriate treatment should therefore reflect patients' preferences. OBJECTIVE: The purpose of the following study was to pilot a new approach for investigating whether urologists who had previously provided patients with therapeutic advice actually knew their patients' importance weights concerning the relevant aspects of the treatments at issue. METHOD: Participants were patients recently diagnosed with localized prostate cancer (n = 20), urologists (n = 10), and non-medical professionals (architects, n = 10). These last served as a control group for the urologists and were matched to them for age and gender. Patients' importance weights were elicited by two standard methods (Direct Rating and Value Hierarchy). Each urologist was asked to estimate (with Direct Rating) his/her patient's importance weights. The same task was performed by a corresponding architect, who never met the patient and knew only the patient's age. Univariate and bivariate statistical analyses were performed to investigate the association between importance weights as elicited from patients and as estimated by urologists and architects, as well as to assess whether such agreement was attribute-dependent. RESULTS: Participants found both elicitation methods easy to use. The correlation between patients' actual importance weights and urologists' estimates was poor and comparable to that obtained between patients and architects. This result did not depend on the attribute considered, with the sole exception of the attribute "Effectiveness in curing the cancer", which was evaluated as the most important attribute by the majority of participants. CONCLUSION: These findings demonstrate the feasibility of the employed methodology and highlight the need to support preference-sensitive decisions in clinical practice by facilitating the elicitation of patients' importance weights, as well as their communication to physicians.

Another chance for good reasoning.

Disagreement on the "probability status" of chances casts doubt on Girotto and Gonzalez's (2001) conclusion that the human mind can make sound Bayesian inferences involving single-event probabilities. The main objection raised has been that chances are de facto natural frequencies disguised as probabilities. In the present study, we empirically demonstrated that numbers of chances are perceived as being distinct from natural frequencies and that they have a facilitatory effect on Bayesian inference tasks that is completely independent from their (minor) frequentist readings. Overall, therefore, our results strongly disconfirm the hypothesis that natural frequencies are a privileged cognitive representational format for Bayesian inferences and suggest that a significant portion of laypeople adequately handle genuine single-event probability problems once these are rendered computationally more accessible by using numbers of chances.

Children's quantitative Bayesian inferences from natural frequencies and number of chances.

Zhu and Gigerenzer (2006) showed that an appreciable number of Chinese children aged between 9 and 12years old made correct quantitative Bayesian inferences requiring the integration of priors and likelihoods as long as they were presented with numerical information phrased in terms of natural frequencies. In this study, we sought to replicate this finding and extend the investigation of children's Bayesian reasoning to a different numerical format (chances) and other probability questions (distributive and relative). In Experiment 1, a sample of Italian children was presented with the natural frequency version of five Bayesian inference problems employed by Zhu and Gigerenzer (2006), but only a tiny minority of them were able to produce correct responses. In Experiment 2, we found that the children's accuracy, as well as the coherence between their probability judgments, depended on the type of question but not on the format (natural frequency vs. chance) in which information was presented. We conclude that children's competence in drawing quantitative Bayesian inferences is lower than suggested by Zhu and Gigerenzer (2006) and, similarly to what happens with adults, it relies more on a problem representation that fosters an extensional evaluation of possibilities than on a specific numerical format.

Natural Frequencies Do Not Foster Public Understanding of Medical Test Results.

Major organizations recommend presenting medical test results in terms of natural frequencies, rather than single-event probabilities. The evidence, however, is that natural frequency presentations benefit at most one-fifth of samples of health service users and patients. Only one study reported a substantial benefit of these presentations. Here, we replicate that study, testing online survey respondents. Study 1 attributed the previously reported benefit of natural frequencies to a scoring artifact. Study 2 showed that natural frequencies may elicit evaluations that conflict with the normatively correct one, potentially hindering informed decision making. Ironically, these evaluations occurred less often when respondents reasoned about single-event probabilities. These results suggest caution in promoting natural frequencies as the best way to communicate medical test data to health service users and patients.

Improving public interpretation of probabilistic test results: distributive evaluations.

Health service users err in posttest probability evaluations. Here we document for the first time that users succeed when they reason about numbers of cases and make distributive evaluations. A sample of women interested in prenatal testing incorrectly evaluated the posttest probability that a given fetus had an anomaly, but regardless of their numeracy level, they correctly apportioned the cases for and against that hypothesis. This finding shows that health service users are not doomed to fail in dealing with single-case probabilities and suggests that probabilistic data can be used effectively for communicating test results.

Using comparison scenarios to improve prenatal risk communication.

UNLABELLED: The present research provides empirical evidence of whether communicating the prenatal risk of chromosomal anomalies using comparison scenarios influences women's ability to distinguish between different risk levels. In 2 experiments, participants read a description of a hypothetical woman who was learning of the risk of chromosomal anomaly as a result of a prenatal screening test. Both experiments used a 3 (risk level) × 3 (scenario) full between-subjects design. In accordance with the experimental condition, participants were presented with a low (e.g., 1 in 5390), a medium (e.g., 1 in 770), or a high risk value (e.g., 1 in 110). Such risk values were presented either on their own or along with additional information illustrating a comparison scenario that provided 2 numerical comparison points. Participants were asked to evaluate the risk of chromosomal anomaly. In Experiment 2, participants' numeracy skills were also assessed. RESULTS: showed that the use of comparison scenarios results in significant differences in perceived risk across risk levels whereas such differences are not significant without the comparison scenario, but such a technique has differential effects according to participants' capacity to deal with numbers. Although the technique is beneficial for high-numerate participants, it has no effect on low-numerate participants.