Strategy Selection in Risky Choice: The Impact of Numeracy,Affect, and Cross‐Cultural Differences

Real‐world decisions often involve options with outcomes that are uncertain and trigger strong affect (e.g., side effects of a drug). Previous work suggests that when choosing among affect‐rich risky prospects, people are rather insensitive to probability information, potentially compromising decision quality. We modeled the strategies of less and more numerate participants in the United States and in Germany when choosing between affect‐rich prospects and between monetarily equivalent affect‐poor prospects. Using large probabilistic national samples (n = 1047 from the United States and Germany), Study 1 showed that compared with more numerate participants, less numerate participants chose the normatively better option (i.e., the one with the higher expected value) less often, guessed more often, and relied more on a simple risk‐minimizing strategy. U.S. participants—although less numerate—selected the normatively better option more frequently and were more consistent across affect‐rich and affect‐poor problems than the German participants. Using a targeted quota sample (n = 118 from Germany), Study 2 indicated that although both more and less numerate participants paid less attention to probability information in affect‐rich than in affect‐poor problems, the two numeracy groups relied on different outcome‐based heuristics: More numerate participants often followed the minimax heuristic, and less numerate participants the affect heuristic. The observed strategy differences suggest that attempts to improve decision‐making need to take into account individual differences in numeracy as well as cultural‐specific experiences in making trade‐offs. Copyright © 2012 John Wiley & Sons, Ltd.     

Are highly numerate individuals invulnerable to attribute framing bias? Comparing numerically and graphically represented attribute framing

Judgments and decisions are frequently biased by attribute framing, presenting either positive or negative attributes of an object. This paper focused on two factors previously shown to moderate the attribute‐framing bias: mode of presentation and participants' numeric ability. Whereas many studies demonstrated that graphical display reduced the bias, recent findings suggest that graphical manipulation can nevertheless elicit significant framing bias. Numeracy has been shown to moderate attribute‐framing bias when the quantitative information was represented by numbers. The present study examined to what extent numeracy would still moderate the framing bias when it is graphically elicited. The results showed a significant framing bias for graphically as well as for numerically represented framing scenarios. Critically, whereas numeracy moderated the framing bias in numerically represented scenarios, it did not have a similar moderating effect when the quantitative information in the scenario was graphically represented. Theoretical and practical implications of the findings are discussed.     

Numeracy Predicts More Effortful and Elaborative Search Strategies in a Complex Risky Choice Context: A Process‐Tracing Approach

The goal of the current study was to explore information search and processing differences between individuals who are less and more numerate in an attempt to better understand the mechanisms that might differentiate the choices they make. We did so using a computerized process‐tracing system known as MouseTrace, which presented monetary gambles in an alternative × attribute matrix with outcome (dollar amount) and probability information as attributes. This information was initially occluded but could be revealed by clicking on the cell that contained the desired information. Beginning with nine gambles offering the chance of gaining or losing a specified amount, participants (N = 110) narrowed down the options (to three and then one) using an inclusion or exclusion strategy. Consistent with previous research, inclusion was a more effortful strategy, and individuals who were higher in numeracy were more likely to select prospects with the highest expected value. Process measures revealed these individuals expended more effort (i.e., attended to and sought out more information and processed it in greater depth) and exhibited more compensatory processing than those who were lower in numeracy, but this sometimes depended on whether one was asked to include or exclude. These results serve as further evidence that individuals with higher levels of numeracy often engage in more elaborative processing of the decision task, which tends to lead to more optimal choices. However, they also suggest that individuals are adaptive and that the specific situation can matter. Copyright © 2016 John Wiley & Sons, Ltd.     

The loss‐bet paradox: Actuaries,accountants, and other numerate people rate numerically inferior gambles as superior

Psychologists have convincingly demonstrated that preferences are not always stable and, instead, are often “constructed” based on information available in the judgment or decision context. In 4 studies with experts (accountants and actuaries in Studies 1 and 2, respectively) and a diverse lay population (Studies 3 and 4), the evidence was consistent with the highly numerate being more likely than the less numerate to construct their preferences by rating a numerically inferior bet as superior (i.e., the bets effect). Thus, the effect generalizes beyond a college student sample, and preference construction differs by numeracy. Contrary to prior thinking about preference construction, however, high expertise and high ability (rather than low) consistently related to the paradoxical phenomenon. Results across studies including Study 3's experimental modifications of the task supported the hypothesized number comparison process (and not a lack of expertise with monetary outcomes and probabilities or numeracy‐related differences in attention to numbers) as the effect's underlying cause. The bets effect was not attenuated by Study 4's instructions to think about what would be purchased with bet winnings. Task results combined with free‐response coding supported the notion that highly numerate participants have a systematic and persistent inclination for doing simple and complex number operations that drive their judgments (even after controlling for nonnumeric intelligence). Implications for 3 types of dual‐process theories are discussed. The results were inconsistent with default‐interventionist theories, consistent or unclear with respect to fuzzy trace theory, and consistent with interactive theories.     

Numeracy and decision making

A series of four studies explored how the ability to comprehend and transform probability numbers relates to performance on judgment and decision tasks. On the surface, the tasks in the four studies appear to be widely different; at a conceptual level, however, they all involve processing numbers and the potential to show an influence of affect. Findings were consistent with highly numerate individuals being more likely to retrieve and use appropriate numerical principles, thus making themselves less susceptible to framing effects, compared with less numerate individuals. In addition, the highly numerate tended to draw different (generally stronger or more precise) affective meaning from numbers and numerical comparisons, and their affective responses were more precise. Although generally helpful, this tendency may sometimes lead to worse decisions. The less numerate were influenced more by competing, irrelevant affective considerations. Analyses showed that the effect of numeracy was not due to general intelligence. Numerical ability appears to matter to judgments and decisions in important ways.     

Numeracy as a Predictor of Adaptive Risky Decision Making

Numeracy or one's ability to appropriately process and use numerical information has been shown to be an important individual difference factor in decision making. The current study utilized a risky decision‐making task (called the “cups task”) in which choices are made to both earn and avoid losing hypothetical money. Critically, this design allowed investigators to examine numeracy‐related differences in adaptive decision‐making as measured by sensitivity to expected value (EV) differences over 54 paired‐choice trials—some in which it was advantageous to take a risk and some in which it was not. Results showed that in an undergraduate sample of 114 individuals, the less numerate took more risks and were less sensitive to varying EV levels than the more numerate, especially when it was disadvantageous to take a risk and when the choice involved a potential loss (rather than a gain). These results are consistent with a dual processing account in which the more numerate are much better than the less numerate at extracting the precise affective “gist” of the numerical information, which is then used to determine the goodness or badness of a particular choice. Copyright © 2012 John Wiley & Sons, Ltd.     

The Role of Inference in Attribute Framing Effects

Previous research has shown that a speaker's choice between logically equivalent frames is influenced by reference point information, and that listeners draw accurate inferences based on the frame. Less clear, however, is whether these inferences play a causal role in generating attribute framing effects. Two experiments are reported, which suggest that frame‐dependent inferences are sufficient to generate attribute framing effects, and that blocking such inferences may block framing effects. Experiment 1 decomposed the typical framing design into two parts: One group of participants saw a target described in one of two attribute frames and reported their estimates (inferences) of the typical attribute value. These estimates were then given to a second group of yoked participants, who evaluated the target. Although this latter group was not exposed to different attribute frames, they nevertheless exhibited a “framing effect” as a result of receiving systematically different inferences. In contrast, Experiment 2 shows that experts—who are familiar with an attribute's distribution and are therefore less likely to draw strong frame‐based inferences—exhibit a diminished framing effect. Together, these findings underscore the role of inferences in the generation and attenuation of attribute framing effects. Copyright © 2017 John Wiley & Sons, Ltd.     

The pros and cons of funnel plots as an aid to risk communication and patient decision making

Funnel plots, which simultaneously display a sample statistic and the corresponding sample size for multiple cases, have a range of applications. In medicine, they are used to display treatment outcome rates and caseload volume by institution, which can inform strategic decisions about health care delivery. We investigated lay people's understanding of such plots and explored their suitability as an aid to individual treatment decisions. In two studies, 172 participants answered objective questions about funnel plots representing the surgical outcomes (survival or mortality rates) of institutions varying in caseload, and indicated their preferred institutions. Accuracy for extracting objective information was high, unless question phrasing was inconsistent with the plot's survival/mortality framing, or participants had low numeracy levels. Participants integrated caseload‐volume and outcome‐rate data when forming preferences, but were influenced by reference lines on the plot to make inappropriate discriminations between institutions with similar outcome rates. With careful choice of accompanying language, funnel plots can be readily understood and are therefore a useful tool for communicating risk. However, they are less effective as a decision aid for individual patient's treatment decisions, and we recommend refinements to the standard presentation of the plots if they are to be used for that purpose.     

Development and Testing of an Abbreviated Numeracy Scale: A Rasch Analysis Approach

Research has demonstrated that individual differences in numeracy may have important consequences for decision making. In the present paper, we develop a shorter, psychometrically improved measure of numeracy—the ability to understand, manipulate, and use numerical information, including probabilities. Across two large independent samples that varied widely in age and educational level, participants completed 18 items from existing numeracy measures. In Study 1, we conducted a Rasch analysis on the item pool and created an eight‐item numeracy scale that assesses a broader range of difficulty than previous scales. In Study 2, we replicated this eight‐item scale in a separate Rasch analysis using data from an independent sample. We also found that the new Rasch‐based numeracy scale, compared with previous measures, could predict decision‐making preferences obtained in past studies, supporting its predictive validity. In Study, 3, we further established the predictive validity of the Rasch‐based numeracy scale. Specifically, we examined the associations between numeracy and risk judgments, compared with previous scales. Overall, we found that the Rasch‐based scale was a better linear predictor of risk judgments than prior measures. Moreover, this study is the first to present the psychometric properties of several popular numeracy measures across a diverse sample of ages and educational level. We discuss the usefulness and the advantages of the new scale, which we feel can be used in a wide range of subject populations, allowing for a more clear understanding of how numeracy is associated with decision processes. Copyright © 2012 John Wiley & Sons, Ltd.     

What shapes the probability weighting function? Influence of affect,numeric competencies,and information formats

Research suggests that people are less sensitive to variations in probability in affect‐rich compared with affect‐poor risky choices. This effect is modeled by a more curved probability weighting function (PWF). We investigated the role of different numeric competencies and the effectiveness of several intervention strategies to decrease this affect‐laden probability distortion. In two experiments, we manipulated the affect‐richness of a risky prospect. In Experiment 1 (N = 467), we measured numeracy and symbolic‐number mapping (i.e., the ability to accurately map numbers onto their underlying magnitudes). The affect‐based manipulations showed the expected effects only in participants with more accurate symbolic‐number mapping, who also reported more differentiated emotional reactions to the various probabilities and displayed more linear PWFs. Instructions to focus on the probability information decreased probability distortion and revealed differences in the use of probability information on the basis of symbolic‐number mapping ability. In Experiment 2 (N = 417), we manipulated the format in which the probability information was presented: using visual aids versus no visual aids and a positive frame (e.g., one person wins) versus combined frame (e.g., one person wins and 99 persons do not win). The affect‐based manipulations had no effect but both the visual aids and combined frame decreased probability distortion. Whereas affect‐richness manipulations require further research, results suggest that probability weighting is at least partially driven by the inability to translate numerical information into meaningful and well‐calibrated affective intuitions. Visual aids and simple framing manipulations designed to calibrate these intuitions can help decision makers extract the gist and increase sensitivity to probabilities.     

Numeracy in the jury box: Numerical ability,meaningful anchors,and damage award decision making

This project employs an experimental design to test theoretical predictions regarding how numeracy can assist jurors in determining damage awards to compensate a plaintiff for pain and suffering and how the use of meaningful numerical anchors may produce similar benefits. Mock jurors (N = 345) reviewed a legal case and were asked to give a dollar award to compensate the plaintiff for pain and suffering. The presence and nature of a numerical anchor and the duration of pain and suffering were manipulated. Participants' numeracy was measured. Results provided support for predictions. Jurors higher in numeracy gave awards that more appropriately reflected the duration of pain and suffering and showed less variability in awards. Similar benefits were obtained by exposing jurors to meaningful numerical anchors to help them contextualize dollar amounts. Thus, introducing meaningful anchors to jurors may provide similar benefits to numeracy, without the drawbacks associated with selecting only numerate jurors.     

The Role of Numeracy and Intelligence in Health‐Risk Estimation and Medical Data Interpretation

Despite ample evidence that numeracy is an important influence on patient understanding and use of health‐related information, there is a dearth of studies examining the concept's relationship to other individual differences measures that may underlie complex judgments in the health domain. In this study, we compared the relative contributions of selected extant numeracy measures and general intelligence and other measures to varied judgment and decision‐making outcomes. Two hundred participants completed numeracy items, subscales of the Wechsler Adult Intelligence Scales, the need for cognition scale, and four relevant outcome measures including risk estimation and medical data interpretation. A numeracy scale constructed using item response and confirmatory factor analyses was consistently the strongest predictor across all outcome measures and accounted for unique variance over and above general intelligence. The results support the concept of numeracy as an independent construct that merits consideration in patient communication. Copyright © 2013 John Wiley & Sons, Ltd.     

The role of procedural memory in grammar and numeracy skills

The objective of this study was to examine the contribution of procedural memory to grammar and numeracy skills, which both involve the manipulation of abstract patterns. Seventy-six typically developing children between 5 and 7 years of age were assessed on grammar with a past tense production task and a sentence comprehension task, on numeracy with a counting task and a calculation task, and on procedural memory with a serial reaction time task. Moderate correlations were found between the measures of grammar and numeracy. Moreover, 4 hierarchical linear regressions indicated that procedural memory was associated with calculation but not with counting or grammar skills when age and working memory were taken into account. These novel findings suggest that procedural memory may have a role to play in the development of some numeracy skills. Several possible explanations for the absence of contribution to grammar are considered.     

Staying fit and staying well: physical fitness as a moderator of life stress

Previous research suggests that physical fitness moderates the adverse effects of stressful life events. However, a reliance on self-reports of fitness and health may limit the validity of prior investigations. The present research tested the stress-buffering effect of fitness with subjective and objective indicators of exercise, fitness, and physical well-being. For self-reports of health, both self-reports of exercise and objective measures of fitness showed the buffering effect; however, only objective fitness levels buffered stress when visits to a health facility were considered. Additional evidence indicated that this effect was largely independent of measures of psychological distress. Implications for understanding the link between fitness, stress, and health status are discussed.     

特征框架效应的心理机制与影响因素

特征框架效应是指当分别以积极框架和消极框架来描述给定情境中某一事物或事件的关键特征时, 一般情况下人们更偏好以积极框架来描述其关键特征的事物或事件的现象。特征框架效应广泛的存在于消费、医学及政治等领域。目前, 它的解释机制主要包括效价加工的认知机制、参照依赖、查询理论以及认知神经机制。它的影响因素主要包括经验、人格特质、计算能力以及认知闭合需要等。未来的研究应该从深入探索特征框架效应的产生根源和影响因素, 拓展其应用研究, 深入探索偏好消极框架下的特征框架效应以及探讨该现象与其它现象之间的关系等五方面展开。     

Looking at Both Sides of the Coin: Mixed Representation Moderates Attribute‐framing Bias in Written and Auditory Messages

Objects and events are often evaluated more favourably when presented in a positive frame than when presented in the complementary negative framing. Recent studies show that this attribute‐framing bias can be moderated when both positive and negative frames are represented in the message. Most attribute‐framing studies used written messages, although important messages are often conveyed auditorily. Unlike written messages, recipients cannot reread auditory messages and have to rely on their memory when evaluating them; consequently, the moderating effect of mixed representation may depend on memory constraints. The current study compared the framing bias in single‐attribute versus mixed‐attribute representations in written and auditory messages. In both written and auditory messages, single‐attribute representation yielded substantial framing bias whereas mixed‐attribute representation moderated the bias. The results are discussed in terms of the role of memory and attention in the attribute‐framing bias. Theoretical and practical implications are considered, and future research is suggested. Copyright © 2016 John Wiley & Sons, Ltd.     

A Swedish validation of the Berlin Numeracy Test

Recent research has highlighted the importance of considering an individual's level of numeracy, that is their numerical abilities, in a vast variety of judgment and decision making tasks. To accurately evaluate the influence of numeracy requires good and valid measures of the construct. In the present study we validate a Swedish version of the Berlin Numeracy Test (Cokely, Galesic, Schulz, Ghazal & Garcia‐Retamero, 2012). The validation was carried out on both a student sample and a sample representative of the Swedish population. The Swedish BNT showed sound psychometrical properties in both samples. Further, in both samples the BNT had satisfactory convergent and discriminant validity when correlating with other measures of numeracy, while not being significantly related to measures of personality. With respect to predictive validity the results indicated divergent patterns in the two samples. In the student sample, participants scoring highest on the BNT outperformed those in the other three levels, which did not differ in performance. In contrast, in the population sample participants scoring lowest on the BNT performed worse than those in the other three levels, which did not differ in performance. Taken together, however, the results suggest that the Swedish version of the BNT should be considered a valid measure of numeracy in both Swedish student and population representative samples.     

Graph‐Framing Effects in Decision Making

This study manipulated the graphical representation of options by framing the physical characters in figures and found that preferences could be affected even when the words and numbers of the problem were constant. Based on attribute substitution theory and an equate‐to‐differentiate approach, we proposed a two‐process model of graph‐framing effects. In the first mental process, the graph‐editing process, the physical features (e.g., distance, size) represented in the graph are visually edited, and the perceived numerical difference between the options is judged based on its physical features. The second mental process, the preferential choice process, occurs by an equate‐to‐differentiate approach in which people seek to equate the difference between options on the dimension on which the difference is smaller, thus leaving the greater other‐dimensional difference to be the determinant of the final choice. Four experiments were tested for graph‐framing effects. Experiment 1 found a graph‐framing effect in coordinate graphs resting on the (de)compression of the scales employed in the figures. Experiment 2 revealed additional graph‐framing effects in other question scenarios and showed that preference changes were mediated by perceived numerical distances. Experiment 3 further confirmed the presence of graph‐framing effects in sector graphs similar to those found in coordinate ones. Experiment 4 suggested that such graph‐framing effects could be eliminated when logical processing (e.g., introducing a mathematical operation before a choice task) was encouraged. This paper discusses related research and a possible substrate basis for graph‐framing effects. Copyright © 2011 John Wiley & Sons, Ltd.     

The Effect of Transparency on Framing Effects in Within‐Subject Designs

A long‐lasting assumption about the framing effect is that if the participants discover the purpose of the experiment in a within‐subject design, then this test transparency would trigger them to override their initial answer and make coherent choices. For this reason, researchers try to mask the connection between the two parts of the test by inserting filling questions or a time delay between the two parts of the test. In this research, we explored the extent to which these customarily used masking solutions are effective in increasing test sensitivity for the framing effect. In three experiments, we assessed the effect of masking on the tests of the attribute framing and the risky‐choice framing effects. Contradicting the general belief, our results indicate that these effects are already measurable without any masking or delay and we found no convincing evidence that the attempts to decrease task transparency provide worthwhile benefits for general tests of the effect. Beyond their practical relevance, the results question whether the test is a good measure of coherence rationality and better suit those accounts that suggest that the two parts of the framing tasks cannot be regarded as identical. Copyright © 2017 John Wiley & Sons, Ltd.