How numeracy influences risk comprehension and medical decision making

Socio-culturally mediated factors and lower level of education are the main influencers of functional cervical cancer literacy among women in Mayuge, Eastern Uganda

Background

Health literacy (HL) is the degree of an individual’s knowledge and capacity to seek, understand and use health information to make decisions on one’s health, yet information on the functional level of cervical cancer literacy in Mayuge and Uganda as a whole is lacking. We, therefore, assessed the level of functional cervical cancer literacy among women aged 18–65 years in Mayuge district in five functional HL domains; prior knowledge, oral, print, numeracy and e-health. Understanding the factors associated with cervical cancer literacy is also pertinent to cervical health communication programming, however, no study has documented this in Uganda and particularly in Mayuge. Mayuge is a rural population based cancer registry and one of the sites for piloting cancer control interventions in Uganda. We also assessed the factors associated with cervical cancer literacy and awareness about currently available cervical cancer preventive services.

Methods

The study protocol was approved by the Uganda Cancer Institute research and ethic committee (UCI-REC). In August 2017, we assessed five HL domains; cervical cancer knowledge, print literacy, oral literacy using audio-clip, numeral literacy and perceived e-HL among 400 women at household levels. Correct response was scored 1 and incorrect response was scored 0 to generate the mean percentage score for each domain. The mean scores were classified as limited, basic and proficient bands based on the McCormack HL cut-offs scale for knowledge, print, oral and e-health and Weiss cut-offs in the newest vital signs (NVS) for numeracy. We used the cervical cancer literacy scores to explore the effect of selected study variables on cervical cancer literacy. We also conducted five focus group discussions (FGDs) based on the theoretical constructs of the PEN-3 model.

Results

The majority (96.8%) of the participants demonstrated a limited level of cervical cancer literacy with a mean score of 42%. Women who had completed a primary level of education or lower (OR = 3.91; p = 0.044) were more likely to have limited cervical cancer literacy. The qualitative data indicated that the women had limited cervical cancer literacy coupled with limited decisional, social and financial support from their male partners with overall low locus of control. Most (92.3%) of the women were not aware of the available cervical cancer services and had no intention to screen (52.5%).

Conclusions

The women in Mayuge in general have limited cervical cancer literacy except oral HL domain. Limited cervical cancer literacy was highest among women with lower level of education and overall literacy seemed to be influenced on the higher side by socio-cultural constructs characterised by limited decisional, social and personal resources among the women with overall low locus of control. The Mayuge women further demonstrated scant knowledge about the available health services in their district and low intention to screen. Multi-strategy cervical health empowerment programme is needed to improve cervical HL using orally disseminated messages.

When Does the Incremental Risk Format Aid Informed Medical Decisions? The Role of Learning, Feedback, and Number of Treatment Options

Background. Informed medical decisions require understanding the benefits and risks of treatments. This entails comparing treatment outcomes to a control group. The incremental risk format has been recommended as it directly visualizes the differences between treatment and control group in 1 graph, whereas they have to be calculated from 2 separate graphs in the total risk format. We investigated when the incremental risk format aids understanding. Methods. In 2 experiments, participants received information about medical treatments, either as incremental or total risk format. We assessed verbatim knowledge (precise quantitative knowledge), gist knowledge (knowledge of essential meaning), and evaluations of the formats. Study 1 (N = 99) consisted of only 1 trial with medical information and also assessed recall. Study 2 (N = 222) assessed learning across multiple trials and also varied the presence of feedback and the number of treatment options. Results. In study 1, the incremental risk format (v. total risk format) led to worse knowledge, recall, and evaluations. In study 2, participants learned to understand the incremental risk format over time, resulting in comparable verbatim knowledge and evaluations as in the total risk format, as well as in even better gist knowledge. Feedback and number of treatment options did not moderate the effect of risk format. Limitations. The studies were conducted with nonpatient samples, and study 2 employed hypothetical treatments. Conclusions. The incremental risk format was initially less understandable than the total risk format. After a short learning period, however, the incremental risk format resulted in better gist knowledge and was comparable otherwise, which suggests that participants had to get used to that format. This has important implications for the study of new formats.

Intuitive symbolic magnitude judgments and decision making under risk in adults

Performance on an intuitive symbolic number skills task-namely the number line estimation task-has previously been found to predict value function curvature in decision making under risk, using a cumulative prospect theory (CPT) model. However there has been no evidence of a similar relationship with the probability weighting function. This is surprising given that both number line estimation and probability weighting can be construed as involving proportion judgment, that is, involving estimating a number on a bounded scale based on its proportional relationship to the whole. In the present work, we re-evaluated the relationship between number line estimation and probability weighting through the lens of proportion judgment. Using a CPT model with a two-parameter probability weighting function, we found a double dissociation: number line estimation bias predicted probability weighting curvature while performance on a different number skills task, number comparison, predicted probability weighting elevation. Interestingly, while degree of bias was correlated across tasks, the direction of bias was not. The findings provide support for proportion judgment as a plausible account of the shape of the probability weighting function, and suggest directions for future work.

PhenX: Host: Social/Cognitive measures for tobacco regulatory research

A working group (WG) of experts from diverse fields related to nicotine and tobacco addiction was convened to identify elements and measures from the Host: Social/Cognitive domain to include in the Tobacco Regulatory Research Collection in the PhenX Toolkit, a catalogue of measures for biomedical research. This paper describes the methods used to identify, select, approve and include measures in the toolkit with potential relevance to users of both conventional and newer tobacco products, such as electronic cigarettes (e-cigarettes). In addition to 25 complementary measures primarily focused on cigarette use already present in the PhenX Toolkit, the WG recommended 11 additional social/cognitive measures focused on children and adult users or potential users of tobacco products. Of these, 10 were self-administered measures: frequency of communication with parents about smoking, quality of communication with parents about smoking, susceptibility to tobacco use, behaviour economics/purchase behaviour, motivation to quit (both single and multi-item measures), hedonic tone or response to pleasurable situations, multigroup ethnic identity, peer and family influence on smoking, attentional control and house rules about tobacco use. The remaining selected measure was computer based (distress tolerance). Although validated tools for use in the Host: Social/Cognitive realm are available, much remains to be done to develop, standardise and validate the tools for application to users of e-cigarettes and other non-combusted tobacco products, non-English language speakers and adolescents.

Predictors of Undergoing Colonoscopy, Does Time Horizon Matter?

When talking to patients about undergoing diagnostic colonoscopy, their doctors can present the risk of developing colorectal cancer (CRC) in different time horizons. Studies on time horizons suggest that people have different psychological associations for the near and distant future, which potentially influence their judgments and actions. The aim of this study was to examine what factors predict patients’ intentions to undergo diagnostic colonoscopy. We particularly focused on examining the role of the time horizon in which the probability of developing malignant CRC was presented, when taking into account the following factors: the perception of risk (perceived susceptibility to and perceived severity of CRC), expected discomfort related to the procedure, a previous colonoscopy, and subjective numeracy. Using the Health Belief Model, we sought to determine whether the intention to undergo a preventive colonoscopy is affected by the time horizon. We hypothesized that the risk of developing CRC in a proximal time horizon would be more threatening to an individual than a distal one and would consequently increase an individual’s behavioral intention to undergo a colonoscopy. We examined the effects of two different time horizons: the risk of developing a disease in the next few years and total lifetime risk. A total of 144 respondents (77 women and 67 men) aged 50–59 years participated in the study. We found that risk perception and expected discomfort significantly affected participants’ intention to undergo a colonoscopy. No empirical evidence was found to confirm that presenting a person with the risk of developing malignant CRC in the coming years, as compared to their lifetime risk, increases the behavioral intention to undergo a diagnostic colonoscopy.

Overview of Data Visualization

This chapter will first address data visualization and then discuss the relationship between data visualization and aesthetics. It discusses the definition of data and information and the forms and characteristics of traditional data visualization, emphasizes on understanding of meaning of data in effectiveness and efficiency. And then this chapter outlines some key data visualizations, which includes Trees, Scatter plots, Charts, Tables, Diagram, Graphic, Waveform, Simulation and Volume.

When calculators lie: A demonstration of uncritical calculator usage among college students and factors that improve performance

Calculators are often unnecessary to solve routine problems, though they are convenient for offloading cognitively effortful processes. However, errors can arise if incorrect procedures are used or when users fail to monitor the output for keystroke mistakes. To investigate the conditions under which people's attention are captured by errant calculator outputs (i.e., from incorrectly chosen procedures or keystroke errors), we programmed an onscreen calculator to "lie" by changing the answers displayed on certain problems. We measured suspicion by tracking whether users explicitly reported suspicion, overrode calculator "lies", or re-checked their calculations after a "lie" was presented. In Study 1, we manipulated the concreteness of problem presentation and calculator delay between subjects to test how these affect suspicion towards "lies" (15% added to answers). We found that numeracy had no effect on whether people opted-in or out of using the calculator but did predict whether they would become suspicious. Very few people showed suspicion overall, however. For study 2, we increased the "lies" to 120% on certain answers and included questions with "conceptual lies" shown (e.g., a negative sign that should have been positive). We again found that numeracy had no effect on calculator usage, but, along with concrete formatting, did predict suspicion behavior. This was found regardless of "lie" type. For study 3, we reproduced these effects after offering students an incentive for good performance, which did raise their accuracy across the math problems overall but did not increase suspicion behavior. We conclude that framing problems within a concrete domain and being higher in numeracy increases the likelihood of spotting errant calculator outputs, regardless of incentive.

The Benefits and Challenges of Using Patient Decision Aids to Support Shared Decision Making in Health Care

Shared decision making (SDM) and patient-centered care require patients to actively participate in the decision-making process. Yet with the increasing number and complexity of cancer treatment options, it can be a challenge for patients to evaluate clinical information and make risk-benefit trade-offs to choose the most appropriate treatment. Clinicians face time constraints and communication challenges, which can further hamper the SDM process. In this article, we review patient decision aids (PDAs) as a means of supporting SDM by presenting clinical information and risk data to patients in a format that is accessible and easy to understand. We outline the benefits and limitations of PDAs as well as the challenges in their development, such as a lengthy and complex development process and implementation obstacles. Lastly, we discuss future trends and how change on multiple levels-PDA developers, clinicians, hospital administrators, and health care insurers-can support the use of PDAs and consequently SDM. Through this multipronged approach, patients can be empowered to take an active role in their health and choose treatments that are in line with their values.

The Effect of Including Quantitative Information on Multiple Endpoints in Direct-to-Consumer Prescription Drug Television Advertisements

Background. Previous research found that adding a single piece of quantitative information about prescription drug benefits to direct-to-consumer (DTC) ads helps consumers understand how well the drug works. However, drug information often includes quantitative information on multiple benefit outcomes and risks. Thus, we examined whether consumer understanding was similarly improved when DTC television ads include varying amounts of quantitative information. Methods. We randomly assigned participants (945 Internet panelists ≥ 60 years old) to view 1 of 9 fictitious prescription drug television ads that varied the presentation of quantitative information for benefits (none, single outcome, 2 outcomes) and risks (none, 1 risk category, 3 risk categories) and then measured gist and verbatim recall/estimation and drug perceptions. Results. Adding a single benefit outcome and a single risk category replicated past results. Compared with an ad containing no quantitative information, presenting 2 benefit outcomes and multiple risk categories increased gist and verbatim recall and affected drug perceptions. Compared with presenting a single benefit outcome, presenting 2 benefit outcomes increased verbatim recall for the second outcome but decreased verbatim recall for the first outcome. Likewise, compared with presenting a single risk category, presenting multiple risk categories increased gist and verbatim recall for the multiple risk categories but decreased gist recall for a concept more closely associated with the single risk category. Adding multiple risk categories decreased risk perceptions even more than did the single risk category. Limitations. This study may have limited generalizability because it examined an ad for only 1 medical condition. Conclusions. There are tradeoffs to adding multiple quantitative benefit outcomes in DTC ads. However, presenting multiple quantitative risk categories helps consumers better understand a drug's risks.

Despite high objective numeracy, lower numeric confidence relates to worse financial and medical outcomes

People often laugh about being "no good at math." Unrecognized, however, is that about one-third of American adults are likely too innumerate to operate effectively in financial and health environments. Two numeric competencies conceivably matter-objective numeracy (ability to "run the numbers" correctly; like literacy but with numbers) and numeric self-efficacy (confidence that provides engagement and persistence in numeric tasks). We reasoned, however, that attaining objective numeracy's benefits should depend on numeric confidence. Specifically, among the more objectively numerate, having more numeric confidence (vs. less) should lead to better outcomes because they persist in numeric tasks and have the skills to support numeric success. Among the less objectively numerate, however, having more (vs. less) numeric confidence should hurt outcomes, as they also persist, but make unrecognized mistakes. Two studies were designed to test the generalizability of this hypothesized interaction. We report secondary analysis of financial outcomes in a diverse US dataset and primary analysis of disease activity among systemic lupus erythematosus patients. In both domains, best outcomes appeared to require numeric calculation skills and the persistence of numeric confidence. "Mismatched" individuals (high ability/low confidence or low ability/high confidence) experienced the worst outcomes. For example, among the most numerate patients, only 7% of the more numerically confident had predicted disease activity indicative of needing further treatment compared with 31% of high-numeracy/low-confidence patients and 44% of low-numeracy/high-confidence patients. Our work underscores that having 1 of these competencies (objective numeracy or numeric self-efficacy) does not guarantee superior outcomes.

Individual and contextual influences on framing effect: Evidence from the Middle East

Framing effect occurs when decision makers choose inconsistent solutions for identical problems based on the way the problems are presented to them. Despite considerable scholarly investigations in this area, the majority of existing work tends to be western-centric and systematically overlooks the characteristics of decision makers and context. Using a sample of Iranian health-care providers, this article addresses these challenges in investigation of framing effect. The results based on responses of 62 decision makers to multiple decision scenarios indicate that framing has a very strong influence on Iranian experts’ choices. Additionally, the findings show that framing interacts with decision makers’ general risk-taking propensity and domain-specific expertise to shape choice. Theoretical and practical implications are discussed.

Numeracy Skills and Self-Reported Mental Health in People Aging Well

This study investigated the relationship between numerical accuracy (i.e, number comprehension and mental calculation) and self-reported depression in late adulthood. Whether social context (i.e., marital status) and very early cognitive decline symptoms impacted numerical performance was also examined. Ninety-four community-dwelling elderly participants were recruited in Sardinia, an Italian island characterized by increased longevity. All participants were presented a battery of tests and questionnaires assessing general cognitive efficiency, lifestyle, perceived physical health, numeracy, metacognitive and depressive responses. Number comprehension skills, time spent for gardening, metacognitive performance, and physical health predicted 26% of variance in CES-D index. Furthermore, married participants outperformed single/widowed ones in both number comprehension and mental calculation tasks. The same pattern of results was replicated when cognitively healthy controls were contrasted with participants with some signs of cognitive decline. The assessment of numeracy skills can be very informative in order to promote mental health and life quality in late adult span.

Age, numeracy, and cultural differences in Chinese and American adolescents' performance on the ratio bias task

Ratio bias occurs when low-probability events with large numerators are judged as more probable than identical or higher-probability ratios with small numerators. Chinese and American adolescents made judgments on ratio bias problems with identical winning probabilities and unequal winning probabilities and completed a test of numeracy. In general, older participants performed better than younger participants and Chinese participants performed subtly better than American participants. On both problem types, numeracy mediated the relationships between age and performance. Between-country differences on unequal ratio problems were moderated by numeracy, such that Chinese participants outperformed American adolescents only at the most numerate level. By contrast, numeracy neither mediated nor moderated the country-performance relationship on equal ratio problems; instead, Chinese adolescents outperformed American adolescents at each level of numeracy, although these differences were fairly small. Discussion focuses on transferring formal math skills to everyday judgments, the associations among age, culture, and numeracy from a dual-process perspective, and limitations and alternative interpretations of the findings.

New insights from children with early focal brain injury: Lessons to be learned from examining STEM-related skills

The study of cognitive development in children with early brain injury reveals crucial information about the developing brain and its plasticity. However, information on long-term outcomes of these children, especially in domains relevant to science, technology, engineering, and math (STEM) remains limited. In the current review, our goal is to address the existing research on cognitive development of children with pre- or perinatal focal brain lesion (PL) as it relates to children's STEM-related skills and suggest future work that could shed further light on the developmental trajectories of children with PL. We argue that examining STEM-related development in children with PL will have broader implications for our understanding of the nature of the plasticity children with PL exhibit as well as address theoretical questions in the field regarding the foundation skills for STEM, including visuospatial and mathematical skills.

Developing a Better and More User-Friendly Numeracy Scale for Patients

Background

A person's ability to work with and understand numerical information (i.e., numeracy) is increasingly important in everyday health and other decision-making contexts. Several survey measures of numeracy have been developed to address this trend, including the widely used General Numeracy Scale (GNS), which is thematically focused on health decision-making and is assumed to measure a unidimensional construct of numeracy.

Objective

The present research was designed to evaluate this proposed unidimensional structure of general numeracy, for which prior data have given mixed empirical support.

Methods

Three samples completed the GNS, in different forms, and responses were analyzed in terms of underlying factor structure.

Key Results

We show that both one-factor and four-factor models of numeracy are plausible based on the GNS (Study 1), and then develop a multiple-choice version of the GNS (i.e., the MC-GNS) that demonstrates some increased clarity in factor structure due to the consistent response format (Study 2). A further study evaluated the convergent and discriminant validity of the MC-GNS (Study 3), finding it to be as good as or better than the prior scale.

Conclusions

Additionally, the MC-GNS is easier for people to take, likely to be less stressful, and easier for practitioners to score. Collectively, this research identifies a problem with the GNS measure, develops improvements to help address this problem, and in the process creates a way to more easily measure numeracy in practical settings. [HLRP: Health Literacy Research and Practice. 2019;3(3):e174-e180.].

Plain Language Summary

Numeracy is important across health contexts. Prevalent numeracy scales assumedly measure a single construct but empirical support for this is lacking. We find both one- and four-factor models are consistent with one scale and develop a revision that clarifies this structure without sacrificing validity. This revised numeracy scale is easier to administer and score, and therefore preferable in practical settings.

Using HIV Risk Prediction Tools to Identify Candidates for Pre-Exposure Prophylaxis: Perspectives from Patients and Primary Care Providers

Clinical guidelines for HIV pre-exposure prophylaxis (PrEP) include risk prediction tools to identify appropriate candidates. We conducted a qualitative interview study to explore the potential acceptability, interpretation, and anticipated impact of such tools from the perspectives of men who have sex with men (MSM) and primary care providers (PCPs). Our purposive sample of English-speaking participants included: (1) MSM reporting HIV risk behaviors (n = 32; median age = 38 years; 53% non-Hispanic white; 22% high school degree or less education); (2) PCPs specializing in health care for MSM (n = 12); and (3) PCPs in general practice (n = 19). MSM participants questioned the ability of risk tools to predict HIV acquisition, and their perceptions of what might constitute a high HIV risk score varied widely. Many MSM participants believed that receiving a high score would prompt them to consider PrEP or other risk reduction strategies. Some believed that the data would be useful, particularly if discussed with their providers, whereas others anticipated feeling fear, anxiety, or mistrust. PCPs expressed more confidence in HIV risk prediction and imagined integrating tools with medical histories and their clinical judgment to assess risk. PCPs were most enthusiastic about adopting HIV risk prediction as a teaching tool to help patients visualize and reduce risk, their concerns about time constraints notwithstanding. In conclusion, our findings suggest that PCPs' views of HIV risk prediction tools are generally positive, whereas MSM participants' are more mixed. Given that both groups emphasized the value of contextualizing risk, shared decision making may be needed to implement HIV risk prediction tools effectively.

Numeracy and Interpretation of Prognostic Estimates in Intracerebral Hemorrhage Among Surrogate Decision Makers in the Neurologic ICU

OBJECTIVE

Clinicians caring for patients with intracerebral hemorrhage must often discuss prognosis and goals of care with their patients' surrogate decision makers, and may make numeric estimates of likelihood of survival and functional independence, informed by validated prediction models. Surrogates' prognostic estimates are often discordant with physicians', suggesting that physicians' numeric statements may not be accurately interpreted. We sought to assess the relationship between numeracy and interpretation of prognostic estimates in intracerebral hemorrhage among surrogate decision makers. We also assessed surrogates' application of prognostic estimates to decisions regarding goals of care.

DESIGN

Single-center, survey-based, cross-sectional study.

SETTING

Twenty-two-bed neurologic ICU at an urban, academic hospital.

SUBJECTS

Surrogate decision makers for patients admitted to the neurologic ICU.

INTERVENTIONS

Participants completed a survey containing five clinical vignettes describing patients with nontraumatic intracerebral hemorrhage. For each patient, numerical estimates of survival and functional independence were explicitly provided, based on the validated outcome risk stratification scale (intracerebral hemorrhage score) and the Prediction of Functional Outcome in Patients with Primary Intracerebral Hemorrhage score.

MEASUREMENTS AND MAIN RESULTS

Participants were asked to make their own prognostic estimates, as well as to describe their preferred goals of care for each hypothetical patient. Respondent demographics were collected, and numeracy was assessed using a modified Lipkus 11-item scale. Poor numeracy was common (42 of 96 total subjects) in this relatively highly educated population. Most prognostic estimates (55%) made by surrogates were discordant with the provided estimates. High numeracy correlated with better concordance (odds ratio, 23.9 [5.57-97.64]; p < 0.001), independent of several factors, including level of education and religion. Numeracy also affected goals-of-care decisions made by surrogates.

CONCLUSIONS

Poor numeracy is common among surrogate decision makers in an intensive care setting and poses a barrier to communication between surrogates and clinicians regarding prognosis and goals of care.

Not all who ponder count costs: Arithmetic reflection predicts utilitarian tendencies, but logical reflection predicts both deontological and utilitarian tendencies

Conventional sacrificial moral dilemmas propose directly causing some harm to prevent greater harm. Theory suggests that accepting such actions (consistent with utilitarian philosophy) involves more reflective reasoning than rejecting such actions (consistent with deontological philosophy). However, past findings do not always replicate, confound different kinds of reflection, and employ conventional sacrificial dilemmas that treat utilitarian and deontological considerations as opposite. In two studies, we examined whether past findings would replicate when employing process dissociation to assess deontological and utilitarian inclinations independently. Findings suggested two categorically different impacts of reflection: measures of arithmetic reflection, such as the Cognitive Reflection Test, predicted only utilitarian, not deontological, response tendencies. However, measures of logical reflection, such as performance on logical syllogisms, positively predicted both utilitarian and deontological tendencies. These studies replicate some findings, clarify others, and reveal opportunity for additional nuance in dual process theorist's claims about the link between reflection and dilemma judgments.

Cancer screening risk literacy of physicians in training: An experimental study

We investigated what factors may foster or hinder physicians' cancer screening risk literacy-specifically the ability to understand evidence regarding screening effectiveness and make evidence-based recommendations to patients. In an experiment, physicians in training (interns and residents) read statistical information about outcomes from screening for cancer, and had to decide whether to recommend it to a patient. We manipulated the effectiveness of the screening (effective vs. ineffective at reducing mortality) and the demand of the patient to get screened (demand vs. no demand). We assessed participants' comprehension of the presented evidence and recommendation to the patient, as well as a-priori screening beliefs (e.g., that screening is always a good choice), numeracy, science literacy, knowledge of screening statistics, statistical education, and demographics. Stronger positive a-priori screening beliefs, lower knowledge of screening statistics, and lower numeracy were related to worse comprehension of the evidence. Physicians recommended against the ineffective screening but only if they showed good comprehension of the evidence. Physicians' recommendations were further based on the perceived benefits from screening but not on perceived harms, nor the patient's demands. The current study demonstrates that comprehension of cancer screening statistics and the ability to infer the potential benefits for patients are essential for evidence-based recommendations. However, strong beliefs in favor of screening fostered by promotion campaigns may influence how physicians evaluate evidence about specific screenings. Fostering physician numeracy skills could help counteract such biases and provide evidence-based recommendations to patients.

The decision paradoxes motivating Prospect Theory: The prevalence of the paradoxes increases with numerical ability

Prospect Theory (PT: Kahneman & Tversky, 1979) of risky decision making is based on psychological phenomena (paradoxes) that motivate assumptions about how people react to gains and losses, and how they weight outcomes with probabilities. Recent studies suggest that people’s numeracy affect their decision making. We therefore conducted a large-scale conceptual replication of the seminal study by Kahneman and Tversky (1979), where we targeted participants with larger variability in numeracy. Because people low in numeracy may be more dependent on anchors in the form of other judgments we also manipulated design type (within-subject design, vs. single-stimuli design, where participants assess only one problem). The results from about 1,800 participants showed that design type had no effect on the modal choices. The rate of replication of the paradoxes in Kahneman and Tversky was poor and positively related to the participants’ numeracy. The Probabilistic Insurance Effect was observed at all levels of numeracy. The Reflection Effects were not fully replicated at any numeracy level. The Certainty and Isolation Effects explained by nonlinear probability weighting were replicated only at high numeracy. No participant exhibited all 9 paradoxes and more than 50% of the participants exhibited at most three of the 9 paradoxes. The choices by the participants with low numeracy were consistent with a shift towards a cautionary non-compensatory strategy of minimizing the risk of receiving the worst possible outcome. We discuss the implications for the psychological assumptions of PT.

The Influence of Health Numeracy and Health Warning Label Type on Smoking Myths and Quit-Related Reactions

INTRODUCTION

Health numeracy helps individuals understand risk information, but limited data exist concerning numeracy's role in reactions to varying types of health warning labels (HWLs) for cigarettes.

METHODS

A nationally representative online panel of adult current smokers received two exposures (1 week apart) to nine HWLs with either text-only or pictorial images with identical mandated text. Following the second exposure, participants (n = 594) rated their beliefs in smoking myths (eg, health-promoting behaviors can undo the risks of smoking) and how much the warnings made them want to quit smoking. Generalized estimating equation regression examined the relation of objective health numeracy and its interaction with HWL type to smoking-myth beliefs and quit-related reactions.

RESULTS

Health numeracy was not significantly associated with smoking-myth beliefs; the interaction with HWL type was also nonsignificant. Adult smokers with lower health numeracy had higher quit-related reactions than those with higher numeracy following exposure to HWLs. The type of HWL significantly modified numeracy's associations with quit-related reactions; no significant association existed between text-only HWLs and quit-related reactions, whereas among those who viewed the pictorial warnings, lower numeracy was associated with greater quit-related reactions (β = -.23; p < .001).

CONCLUSIONS

Lower as compared to higher health numeracy was significantly associated with higher quit-related reactions to HWLs and especially with pictorial HWLs. Health numeracy and HWL type were not associated with the endorsement of smoking myths. The role of health numeracy in effectively communicating risks to smokers warrants thoughtful consideration in the development of tobacco HWLs.

IMPLICATIONS

Health numeracy plays an important role in an individual's ability to understand and respond to health risks. Smokers with lower health numeracy had greater quit-related reactions to pictorial health warnings than those who viewed text-only warning labels. Development and testing of health warning labels should consider health numeracy to most effectively communicate risk to US smokers.

Positive Effects of Openness on Cognitive Aging in Middle-Aged and Older Adults: A 13-Year Longitudinal Study

The relationship between openness (a psychological trait of curiosity) and a cognitive change was examined in middle-aged and older adults. Participants were 2214 men and women (baseline age range: 40 to 81 years). They were tested up to seven times over approximately 13 years. Openness at the baseline was assessed by the NEO Five-Factor Inventory. Cognitive abilities were assessed at each examination using the Wechsler adult intelligence scale-revised short form, which includes information, similarities, picture completion, and digit symbol subscales. General linear mixed models comprised fixed effects of openness, age at the baseline, follow-up time, their interactions, and the covariates. The results indicated that the main effects of openness were significant for all scores. Moreover, the interaction term openness × age × time was significant for the information and similarities test scores, indicating that changes in the information and similarities scores differed depending on the level of openness and baseline age. The estimated trajectory indicated that the differences in slopes between participants with high and low openness were significant after 60 years of age for the information, and after 65 years of age for the similarities scores. It is concluded that openness has a protective effect on the decline in general knowledge and logical abstract thinking in old age.

How does information on the harms and benefits of cervical cancer screening alter the intention to be screened?: a randomized survey of Norwegian women

Cervical cancer (CC) is the 13th most frequent cancer among women in Norway, but the third most common among women aged 25-49 years. The national screening program sends information letters to promote screening participation. We aimed to evaluate how women's stated intention to participate in screening and pursue treatment changed with the provision of additional information on harms associated with screening, and to assess women's preferences on the timing and source of such information. We administered a web-based questionnaire to a panel of Norwegian women aged 25-69 years and randomized into three groups on the basis of when in the screening process additional information was introduced: (i) invited for routine screening, (ii) recommended an additional test following detection of cellular abnormalities, and (iii) recommended precancer treatment. A fourth (control) group did not receive any additional information. Results show that among 1060 respondents, additional information did not significantly alter women's stated intentions to screen. However, it created decision uncertainty on when treatment was recommended (8.76-9.09 vs. 9.40; 10-point Likert scale; P=0.004). Over 80% of women favored receiving information on harms and 59% preferred that information come from a qualified public health authority. Nearly 90% of women in all groups overestimated women's lifetime risk of CC. In conclusion, additional information on harms did not alter Norwegian women's stated intention to screen for CC; yet, it resulted in greater decision uncertainty to undergo precancer treatment. Incorporating information on harms into invitation letters is warranted as it would increase women's ability to make informed choices.

Probability range and probability distortion in a gambling task

In decision making under risk, adults tend to overestimate small and underestimate large probabilities (Tversky & Kahneman, 1992). This inverse S-shaped distortion pattern is similar to that observed in a wide variety of proportion judgment tasks (see Hollands & Dyre, 2000, for review). In proportion judgment tasks, distortion patterns tend not to be fixed but rather to depend on the reference points to which the targets are compared. Here, we tested the novel hypothesis that probability distortion in decision making under risk might also be influenced by reference points-in this case, references implied by the probability range. Adult participants were assigned to either a full-range (probabilities from 0-100%), upper-range (50-100%), or lower-range (0-50%) condition, where they indicated certainty equivalents for 176 hypothetical monetary gambles (e.g., "a 50% chance of $100, otherwise $0"). Using a modified cumulative prospect theory model, we found only minimal differences in probability distortion as a function of condition, suggesting no differences in use of reference points by condition, and broadly demonstrating the robustness of distortion pattern across contexts. However, we also observed deviations from the curve across all conditions that warrant further research.

Patients' and Clinicians' Perceptions of Antibiotic Prescribing for Upper Respiratory Infections in the Acute Care Setting

Reducing inappropriate prescribing is key to mitigating antibiotic resistance, particularly in acute care settings. Clinicians' prescribing decisions are influenced by their judgments and actual or perceived patient expectations. Fuzzy trace theory predicts that patients and clinicians base such decisions on categorical gist representations that reflect the bottom-line understanding of information about antibiotics. However, due to clinicians' specialized training, the categorical gists driving clinicians' and patients' decisions might differ, which could result in mismatched expectations and inefficiencies in targeting interventions. We surveyed clinicians and patients from 2 large urban academic hospital emergency departments (EDs) and a sample of nonpatient subjects regarding their gist representations of antibiotic decisions, as well as relevant knowledge and expectations. Results were analyzed using exploratory factor analysis (EFA) and multifactor regression. In total, 149 clinicians (47% female; 74% white), 519 online subjects (45% female; 78% white), and 225 ED patients (61% female; 56% black) completed the survey. While clinicians demonstrated greater knowledge of antibiotics and concern about side effects than patients, the predominant categorical gist for both patients and clinicians was "why not take a risk," which compares the status quo of remaining sick to the possibility of benefit from antibiotics. This gist also predicted expectations and prior prescribing in the nonpatient sample. Other representations reflected the gist that "germs are germs" conflating bacteria and viruses, as well as perceptions of side effects and efficacy. Although individually rational, reliance on the "why not take a risk" representation can lead to socially suboptimal results, including antibiotic resistance and individual patient harm due to adverse events. Changing this representation could alter clinicians' and patients' expectations, suggesting opportunities to reduce overprescribing.

Reducing complexity of patient decision aids for community-based older adults with dementia and their caregivers: multiple case study of Decision Boxes

OBJECTIVES

To identify patient decision aids' features to limit their complexity for older adults with dementia and their family caregivers.

DESIGN

Mixed method, multiple case study within a user-centred design (UCD) approach.

SETTING

Community-based healthcare in the province of Quebec in Canada.

PARTICIPANTS

23 older persons (aged 65+ years) with dementia and their 27 family caregivers.

RESULTS

During three UCD evaluation-modification rounds, participants identified strengths and weaknesses of the patient decision aids' content and visual design that influenced their complexity. Weaknesses of content included a lack of understanding of the decision aids' purpose and target audience, missing information, irrelevant content and issues with terminology and sentence structure. Weaknesses of visual design included critics about the decision aids' general layout (density, length, navigation) and their lack of pictures. In response, the design team implemented a series of practical features and design strategies, comprising: a clear expression of the patient decision aids' purpose through simple text, picture and personal stories; systematic and frequent use of pictograms illustrating key points and helping structure patient decision aids' general layout; a glossary; removal of scientific references from the main document; personal stories to clarify more difficult concepts; a contact section to facilitate implementation of the selected option; GRADE ratings to convey the quality of the evidence; a values clarification exercise formatted as a checklist and presented at the beginning of the document to streamline navigation; involvement of a panel of patient/caregiver partners to guide expression of patient priorities; editing of the text to a sixth grade reading level; UCD process to optimise comprehensiveness and relevance of content and training of patients/caregivers in shared decision-making.

CONCLUSIONS

The revised template for patient decision aids is designed to meet the needs of adults living with dementia and their caregivers better, which may translate into fewer evaluation-modification rounds.

Multi-method brain imaging reveals impaired representations of number as well as altered connectivity in adults with dyscalculia

Two hypotheses have been proposed about the etiology of neurodevelopmental learning disorders, such as dyslexia and dyscalculia: representation impairments and disrupted access to representations. We implemented a multi-method brain imaging approach to directly investigate these representation and access hypotheses in dyscalculia, a highly prevalent but understudied neurodevelopmental disorder in learning to calculate. We combined several magnetic resonance imaging methods and analyses, including univariate and multivariate analyses, functional and structural connectivity. Our sample comprised 24 adults with dyscalculia and 24 carefully matched controls. Results showed a clear deficit in the non-symbolic magnitude representations in parietal, temporal and frontal regions, as well as hyper-connectivity in visual brain regions in adults with dyscalculia. Dyscalculia in adults was thereby related to both impaired number representations and altered connectivity in the brain. We conclude that dyscalculia is related to impaired number representations as well as altered access to these representations.

The Roles of Education, Literacy, and Numeracy in Need for Health Information during the Second Half of Adulthood: A Moderated Mediation Analysis

We examine complex pathways that link health information seeking behavior with education and health literacy (decomposed into general literacy and numeracy), and how these pathways differ by perceived health status (need) among a nationally representative sample of Americans age 50 and older (n = 2,750). Data come from the Program for International Assessment of Adult Competencies (PIAAC). Multi-group structural equation models were used to examine the use of eight health information sources (newspapers, magazines, internet, radio, TV, books, friends/family, and health professionals). Findings partially support the long-standing notion that health seeking behaviors are directly linked to educational attainment, and provide some of the first nationally representative evidence for how education functions through distinct health literacy components to shape health information seeking behaviors by health status. Findings from this moderated mediation analysis point to the importance of examining, and addressing, health literacy disparities in access to and use of health information.

Data visualization literacy: Definitions, conceptual frameworks, exercises, and assessments

In the information age, the ability to read and construct data visualizations becomes as important as the ability to read and write text. However, while standard definitions and theoretical frameworks to teach and assess textual, mathematical, and visual literacy exist, current data visualization literacy (DVL) definitions and frameworks are not comprehensive enough to guide the design of DVL teaching and assessment. This paper introduces a data visualization literacy framework (DVL-FW) that was specifically developed to define, teach, and assess DVL. The holistic DVL-FW promotes both the reading and construction of data visualizations, a pairing analogous to that of both reading and writing in textual literacy and understanding and applying in mathematical literacy. Specifically, the DVL-FW defines a hierarchical typology of core concepts and details the process steps that are required to extract insights from data. Advancing the state of the art, the DVL-FW interlinks theoretical and procedural knowledge and showcases how both can be combined to design curricula and assessment measures for DVL. Earlier versions of the DVL-FW have been used to teach DVL to more than 8,500 residential and online students, and results from this effort have helped revise and validate the DVL-FW presented here.

Use of a Decision Aid for Patients Considering Peritoneal Dialysis and In-Center Hemodialysis: A Randomized Controlled Trial

RATIONALE & OBJECTIVE

Annually, about 100,000 US patients face the difficult choice between the most common dialysis types, in-center hemodialysis and peritoneal dialysis. This study evaluated the value of a new decision aid to assist in the choice of dialysis modality.

STUDY DESIGN

A parallel-group randomized controlled trial to test the efficacy of the decision aid on decision-making outcomes.

SETTING & PARTICIPANTS

English-speaking US adults with advanced chronic kidney disease and internet access enrolled in 2015.

INTERVENTION

Participants randomly assigned to the decision aid intervention received information about chronic kidney disease, peritoneal dialysis, and hemodialysis and a value clarification exercise through the study website using their own electronic devices. Participants in the control arm were only required to complete the control questionnaire. Questionnaire responses were used to assess differences across arms in decision-making outcomes.

OUTCOMES

Treatment preference, decisional conflict, decision self-efficacy, knowledge, and preparation for decision making.

RESULTS

Of 234 consented participants, 94 (40.2%) were lost to follow-up before starting the study. Among the 140 (70 in each arm) who started the study, 7 were subsequently lost to follow-up. Decision aid users had lower decisional conflict scores (42.5 vs 29.1; P<0.001) and higher average knowledge scores (90.3 vs 76.5; P<0.001). Both arms had high decisional self-efficacy scores independent of decision aid use. Uncertainty about choice of dialysis treatment declined from 46% to 16% after using the decision aid. Almost all (>90%) users of the decision aid reported that it helped in decision making.

LIMITATIONS

Limited generalizability from the study of self-selected study participants who had to have internet access, speak English, and have computer literacy. High postrandomization loss to follow-up. Evaluation of only short-term outcomes.

CONCLUSIONS

The decision aid improves decision-making outcomes immediately after use. Implementation of the decision aid in clinical practice may allow further assessment of its effects on patient engagement and empowerment in choosing a dialysis modality.

FUNDING

This study was funded through a Patient Centered Outcomes Research Institute (PCORI) award (#1109).

TRIAL REGISTRATION

Registered at ClinicalTrials.gov with study number NCT02488317.

Using the Short Graph Literacy Scale to Predict Precursors of Health Behavior Change

BACKGROUND

Visual displays can facilitate risk communication and promote better health choices. Their effectiveness in improving risk comprehension is influenced by graph literacy. However, the construct of graph literacy is still insufficiently understood, partially because existing objective measures of graph literacy are either too difficult or too long.

OBJECTIVES

We constructed a new 4-item Short Graph Literacy (SGL) scale and examined how SGL scores relate to key cognitive, affective, and conative precursors of health behavior change described in common health behavior theories.

METHODS

We performed secondary analyses to adapt the SGL scale from an existing 13-item scale. The initial construction was based on data collected in a laboratory setting in Germany ( n = 51). The scale was then validated using data from nationally representative samples in Germany ( n = 495) and the United States ( n = 492). To examine how SGL scores relate to precursors of health behavior change, we performed secondary analyses of a third study involving a nationwide US sample with 47% participants belonging to racial/ethnic minorities and 46% with limited formal education ( n = 835).

RESULTS

Graph literacy was significantly associated with cognitive precursors in theoretically expected ways (e.g., positive associations with risk comprehension and response efficacy and a negative association with cognitive risk perception). Patterns for affective precursors generally mirrored those for cognitive precursors, although numeracy was a stronger predictor than graph literacy for some affective factors (e.g., feelings of risk). Graph literacy had predictive value for most cognitive and affective precursors beyond numeracy. In addition, graph literacy (but not numeracy) predicted key conative precursors such as defensive processing.

CONCLUSIONS

Our data suggest that the SGL scale is a fast and psychometrically valid method for measuring objective graph literacy. Our findings also highlight the theoretical and practical relevance of graph literacy.

Reaping the Benefits and Avoiding the Risks: Unrealistic Optimism in the Health Domain

People's perceptions of benefits and risks play a key role in their acceptance or rejection of medical interventions, yet these perceptions may be poorly calibrated. This online study with N = 373 adults aged 19-76 years focused on unrealistic optimism in the health domain. Participants indicated how likely they were to experience benefits and risks associated with medical conditions and completed objective and subjective numeracy scales. Participants exhibited optimistic views about the likelihood of experiencing the benefits and the side effects of treatment options described in the scenarios. Objective and subjective numeracy were not associated with more accurate ratings. Moreover, participants' underestimation of the risks was significantly greater than their overestimation of the benefits. From an applied perspective, these results suggest that clinicians may need to ensure that patients do not underestimate risks of medical interventions, and that they convey realistic expectations about the benefits that can be obtained with certain procedures.

Understanding Patients' Preferences: A Systematic Review of Psychological Instruments Used in Patients' Preference and Decision Studies

BACKGROUND

Research has been mainly focused on how to elicit patient preferences, with less attention on why patients form certain preferences.

OBJECTIVES

To assess which psychological instruments are currently used and which psychological constructs are known to have an impact on patients' preferences and health-related decisions including the formation of preferences and preference heterogeneity.

METHODS

A systematic database search was undertaken to identify relevant studies. From the selected studies, the following information was extracted: study objectives, study population, design, psychological dimensions investigated, and instruments used to measure psychological variables.

RESULTS

Thirty-three studies were identified that described the association between a psychological construct, measured using a validated instrument, and patients' preferences or health-related decisions. We identified 33 psychological instruments and 18 constructs, and categorized the instruments into 5 groups, namely, motivational factors, cognitive factors, individual differences, emotion and mood, and health beliefs.

CONCLUSIONS

This review provides an overview of the psychological factors and related instruments in the context of patients' preferences and decisions in healthcare settings. Our results indicate that measures of health literacy, numeracy, and locus of control have an impact on health-related preferences and decisions. Within the category of constructs that could explain preference and decision heterogeneity, health locus of control is a strong predictor of decisions in several healthcare contexts and is useful to consider when designing a patient preference study. Future research should continue to explore the association of psychological constructs with preference formation and heterogeneity to build on these initial recommendations.

Numeracy and Risk Literacy: What Have We Learned so Far?

Numerical skills are essential to make informed decisions in our daily life. Unfortunately, many people lack basic numeracy, which limits their ability to accurately interpret risks (i.e., risk literacy). In this paper, we provide an overview of research investigating the role of numeracy in two prominent domains, where most research was concentrated, health and finance. We summarize what has been learned so far in these domains and suggest promising venues for future research. We conclude that it is important to conduct interventions to improve numeracy in less numerate individuals and to help them make informed decisions and achieve better life outcomes.

Women's preferences for and experiences with prenatal genetic testing decision making: Sociodemographic disparities in preference-concordant decision making

OBJECTIVE

To investigate women's preferred approach to prenatal genetic testing decision making and assess concordance between preference and experience.

METHODS

We conducted a secondary analysis of data from two randomized trials conducted between 2007-2012. Survey items assessed participants' preferred approach to decision making and whether they experienced a preference-concordant decision process. Logistic regression estimated relationships between patient characteristics and these outcomes.

RESULTS

56% of women preferred autonomous decision making, 39% preferred shared decision making, and 5% preferred a provider-driven approach. Only 57% experienced preference-concordant decision making. On bivariate analysis, black women, Spanish-speaking Latinas and women with less education were less likely to experience this outcome than white, more educated women. Numeracy and preferring a provider-driven approach fully mediated observed disparities in preference-concordant decision making for most participants, except for Spanish-speaking Latinas, who were still less likely to have experienced this outcome after accounting for these factors.

CONCLUSION

Numeracy, preference for provider-driven decision processes, and language barriers were key drivers of disparities in preference-concordant decision making.

PRACTICE IMPLICATIONS

Given the values-sensitive and quantitative nature of prenatal testing decisions, nuanced counseling and interventions to address language barriers, numeracy gaps, and decision-making preferences are needed to tailor counseling to patient's backgrounds and desires.

Aiding Risk Information learning through Simulated Experience (ARISE): A Comparison of the Communication of Screening Test Information in Explicit and Simulated Experience Formats

OBJECTIVE

To determine whether the use of Aiding Risk Information learning through Simulated Experience (ARISE) to communicate conditional probabilities about maternal serum screening results for Down syndrome promotes more accurate positive predictive value (PPV) estimates and conceptual understanding of screening, compared with explicitly providing individuals with this information via numerical summary or icon array.

METHOD

In experiment 1, 582 participants completed an online study in which they were asked to estimate the PPV and rate their attitudes toward a screening test when information was presented in either a description (required calculation of the PPV), explicit (PPV was provided and had to be identified), or an ARISE format (PPV was inferred through experience-based learning). In experiment 2, 316 participants estimated the PPV and rated their attitudes toward screening based on information presented in either an icon array (identify the icons that represent the PPV) or ARISE format.

RESULTS

In experiment 1, ARISE elicited the most accurate PPV estimates compared with the description and explicit formats, and both the explicit and ARISE formats led to more unfavorable attitudes toward screening. In experiment 2, both the icon array and ARISE resulted in similar PPV estimates; however, ARISE led to more negative attitudes toward screening.

CONCLUSIONS

These findings suggest that ARISE may be superior to other formats in the communication of PPV information for screening tests. However, differences in the complexity of the formats vary and require further investigation.

Linear Spatial-Numeric Associations Aid Memory for Single Numbers

Memory for numbers improves with age. One source of this improvement may be learning linear spatial–numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial–numeric mappings from other numeric abilities, such as counting or number word-cardinality mapping. To obviate the influence of memory span on numerical memory, we examined 39 3- to 5-year-olds’ ability to recall one spontaneously produced number (1–20) after a delay, and the relation between numeric recall (controlling for non-numeric recall) and quality of mapping between symbolic and non-symbolic quantities using number-line estimation, give-a-number estimation, and counting tasks. Consistent with previous reports, mapping of numerals to space, to discrete quantities, and to numbers in memory displayed a logarithmic-to-linear shift. Also, linearity of spatial–numeric mapping correlated strongly with multiple measures of numeric recall (percent correct and percent absolute error), even when controlling for age and non-numeric memory. Results suggest that linear spatial–numeric mappings may aid memory for number over and above children’s other numeric skills.

Enumeration and Alertness in Developmental Dyscalculia

Enumeration, the ability to report an amount of elements, differs as a function of range. Subitizing (quantities 1–4) is an accurate and quick process with reaction times (RTs) minimally affected by the number of presented elements within its range. In the counting range (range of 5–9 elements), RTs increase linearly. Subitizing was considered to be a pre-attentive process for many years. However, recently we found that subitizing could be facilitated by improving engagement of attention. Specifically, brief alerting cues increase attentional engagement and reduced RTs in the subitizing range. Moreover, previous studies found that students with developmental dyscalculia (DD) have a smaller than normal subitizing range (3 vs. 4) and their alerting attentional system is impaired. In the current study, we explored whether an alerting cue would increase the subitizing range of adults suffering from DD from 3 to 4. For controls, alerting increased accuracy rates and facilitated enumeration of quantities only in the subitizing range. Participants with DD presented a larger alerting effect; an alerting cue enhanced their RTs in all ranges, but did not increase their smaller than normal subitizing range or accuracy. Our results suggest that both domain-general and domain-specific abilities contribute to the mechanism of enumeration and related to developmental dyscalculia.

Predicting Age of Becoming a Cardinal Principle Knower

Children's first mathematics concept is their understanding of the quantities represented by number words (cardinal value), and the age at which they achieve this insight predicts their readiness for mathematics learning in school. We provide the first exploration of the factors that influence the age of becoming a cardinal principle knower (CPK), with a longitudinal study of 197 (94 boys) children from the beginning to the end of two years of preschool. Core symbolic and non-symbolic quantitative competencies at the beginning of preschool, as well as measures of intelligence, executive function, preliteracy skills, and parental education were used to predict timing of CPK status. Children who achieved early CPK status had higher IQ scores, knew more count words and numerals, and had a better intuitive understanding of relative quantity than their peers. Children who were delayed CPKs, in contrast, had deficits in executive function and poor preliteracy skills. The results add to our understanding of children's conceptual development in mathematics and have implications for the identification of at-risk children and design of interventions for them.

The experience-based format of probability improves probability estimates: The moderating role of individual differences in numeracy

People with low statistical numeracy have difficulties understanding numerical information. For instance, they often misunderstand the probability of experiencing side effects, which could reduce adherence to medical treatments. We investigated whether presenting information about probability using a method based on the direct experience of events influences the accuracy of probability estimates compared to viewing a static numerical description of the same information. Participants completed a numeracy test and were randomly assigned to one of two conditions. In the description-based probability condition, participants were presented with 24 binomial distributions consisting of a target stimulus "X" and a distractor stimulus "·" in the form of odds (the distribution "7 × 13 ·" is an example of a 35% probability: here the target [distractor] stimulus was present 7[13] times in a 20-stimulus distribution). In the experience-based probability condition, participants observed the same information but the stimuli were randomly arranged and displayed sequentially. Participants in both conditions estimated the probability of the target stimulus in each trial. In the experience-based format participants with low numeracy made more accurate probability estimates in comparison to the description-based format. In contrast, accuracy in participants with high numeracy was similar in the two formats.

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

Our ability to represent temporal, spatial, and numerical information is critical for understanding the world around us. Given the prominence of quantitative representations in the natural world, numerous cognitive, neurobiological, and developmental models have been proposed as a means of describing how we track quantity. One prominent theory posits that time, space, and number are represented by a common magnitude system, or a common neural locus (i.e., Bonn & Cantlon in Cognitive Neuropsychology, 29(1/2), 149-173, 2012; Cantlon, Platt, & Brannon in Trends in Cognitive Sciences, 13(2), 83-91, 2009; Meck & Church in Animal Behavior Processes, 9(3), 320, 1983; Walsh in Trends in Cognitive Sciences, 7(11), 483-488, 2003). Despite numerous similarities in representations of time, space, and number, an increasing body of literature reveals striking dissociations in how each quantity is processed, particularly later in development. These findings have led many researchers to consider the possibility that separate systems may be responsible for processing each quantity. This review will analyze evidence in favor of a common magnitude system, particularly in infancy, which will be tempered by counter evidence, the majority of which comes from experiments with children and adult participants. After reviewing the current data, we argue that although the common magnitude system may account for quantity representations in infancy, the data do not provide support for this system throughout the life span. We also identify future directions for the field and discuss the likelihood of the developmental divergence model of quantity representation, like that of Newcombe (Ecological Psychology, 2, 147-157, 2014), as a more plausible account of quantity development.