Numeracy—the ability to understand and use numeric information—is linked to good decision-making. Several problems exist with current numeracy measures, however. Depending on the participant sample, some existing measures are too easy or too hard; also, established measures often contain items well-known to participants. The current article aimed to develop new numeric understanding measures (NUMs) including a 1-item (1-NUM), 4-item (4-NUM), and 4-item adaptive measure (A-NUM). In a calibration study, 2 participant samples (n = 226 and 264 from Amazon’s Mechanical Turk [MTurk]) each responded to half of 84 novel numeracy items. We calibrated items using 2-parameter logistic item response theory (IRT) models. Based on item parameters, we developed the 3 new numeracy measures. In a subsequent validation study, 600 MTurk participants completed the new numeracy measures, the adaptive Berlin Numeracy Test, and the Weller Rasch-Based Numeracy Test, in randomized order. To establish predictive and convergent validities, participants also completed judgment and decision tasks, Raven’s progressive matrices, a vocabulary test, and demographics. Confirmatory factor analyses suggested that the 1-NUM, 4-NUM, and A-NUM load onto the same factor as existing measures. The NUM scales also showed similar association patterns to subjective numeracy and cognitive ability measures as established measures. Finally, they effectively predicted classic numeracy effects. In fact, based on power analyses, the A-NUM and 4-NUM appeared to confer more power to detect effects than existing measures. Thus, using IRT, we developed 3 brief numeracy measures, using novel items and without sacrificing construct scope. The measures can be downloaded as Qualtrics files (https://osf.io/pcegz/).

Many people exhibit inconsistent preferences when they make choices based on descriptive summaries as compared to choices based on prior experiences. Theoretically, factors that promote more deliberative and skilled decision making (e.g., statistical numeracy) should also tend to promote more consistent choices and preferences regardless of information presentation formats. To test this hypothesis, in two studies I investigated individual differences in information search strategies (e.g., the amount and direction of information search) while estimating the degree to which numeracy predicted risky choice consistency across (a) decisions-from-description and (b) the decisions-from-samples. Results from Study 1 revealed that numeracy was generally associated with more extensive sampling and greater choice consistency across paradigms. Instead of reflecting differences in logical maximizing strategies (e.g., calculating expected values), analyses indicated that highly-numerate participants largely generated consistent choices by relying on heuristic-type processes (e.g., alternated between options less and exploring options with higher outcome variability more). In Study 2, the relationship between numeracy and choice consistency was eliminated when all participants were forced to make choices after experiencing the same fixed amount of sampling (i.e., provided the same amount of information). Taken together, the results of both studies converge with and extend previous findings (e.g., Skilled Decision Theory), indicating that numerate participants may generally exhibit more consistent preferences and choices via deliberatative heuristic search during decision making.

People who possess greater mathematical skills (i.e., numeracy) are generally more accurate in interpreting numerical data than less numerate people. However, recent evidence has suggested that more numerate people may use their numerical skills to interpret data only if their initial interpretation conflicts with their worldview. That is, if an initial, intuitive (but incorrect) interpretation of data appears to disconfirm one’s beliefs, then numerical skills are used to further process the data and reach the correct interpretation, whereas numerical skills are not used in situations where an initial incorrect interpretation of the data appears to confirm one’s beliefs (i.e., motivated numeracy). In the present study, participants were presented with several data problems, some with correct answers confirming their political views and other disconfirming their views. The difficulty of these problems was manipulated to examine how numeracy would influence the rate of correct responses on easier vs. more difficult problems. Results indicated that participants were more likely to answer problems correctly if the correct answer confirmed rather than disconfirmed their political views, and this response pattern did not depend on problem difficulty or numerical skill. Although more numerate participants were more accurate overall, this was true both for problems in which the correct answer confirmed and disconfirmed participants’ political views.

The mathematics of downside financial risk can be difficult to understand: For example a 50% loss requires a subsequent 100% gain to break-even. A given percentage loss always requires a greater percentage gain to break-even. Instead, many non-expert investors may assume for example that a 50% gain is sufficient to offset a 50% loss. Over 3,498 participants and five experiments, the widespread illusion that a sequence of equal percentage gains and losses produces a zero overall return was demonstrated. Participants continued to err frequently, even with percentage returns of +/-100%, or when financially incentivized. Financial literacy, numeracy, and deliberation were all shown to independently contribute to accurate performance. These results have implications for promoting the understanding of downside financial risk.

It is important to understand the impact of individual differences in decision making from childhood to adulthood. This cohort-based study extends our knowledge by comparing decision making of children across the age range of 8 to 17 years and their parents. Based on prior research and theory focusing on different types of framing effects, we uncover several key differences across ages, including levels of risk taking and sensitivity to expected value differences between risky and riskless choices. Furthermore, we find that measures such as Numeracy and Surgency help explain both age-related and individual differences on our tasks, especially for decisions involving risk. We discuss the role of diverse task measures in understanding how individual difference factors affect different aspects of decision making, including the ability and effort to process numerical information and the ability to suppress affective reactions to stimulus labels.

Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills) consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations) also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a) perceived differences between numbers, b) the extent to which proportional differences are weighed in decisions, and, ultimately, c) the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.

Interval estimates are commonly used to descriptively communicate the degree of uncertainty in numerical values. Conventionally, low alpha levels (e.g., .05) ensure a high probability of capturing the target value between interval endpoints. Here, we test whether alpha levels and individual differences in numeracy influence distributional inferences. In the reported experiment, participants received prediction intervals for fictitious towns’ annual rainfall totals (assuming approximately normal distributions). Then, participants estimated probabilities that future totals would be captured within varying margins about the mean, indicating the approximate shapes of their inferred probability distributions. Results showed that low alpha levels (vs. moderate levels; e.g., .25) more frequently led to inferences of over-dispersed approximately normal distributions or approximately uniform distributions, reducing estimate accuracy. Highly numerate participants made more accurate estimates overall, but were more prone to inferring approximately uniform distributions. These findings have important implications for presenting interval estimates to various audiences.

The aim of the study was to test convergent/discriminant validity of two measures of cognitive reflection, cognitive reflection test (CRT) and belief bias syllogisms (BBS) and to investigate whether their distinctive characteristic of luring participants into giving wrong intuitive responses explains their relationships with various abilities and disposition measures. Our results show that the same traits largely account for performance on both non-lure task, the Berlin Numeracy Test (BNT), and CRT and explain their correlations with other variables. These results also imply that the predictive validity of CRT for wide range of outcomes does not stem from lures. Regarding the BBS, we found that its correlations with other measures were substantially diminished once we accounted for the effects of BNT. This also implies that the lures are not the reason for the correlation between BBS and these measure. We conclude that the lures are not the reason why cognitive reflection tasks correlate with different outcomes. Our results call into question an original definition of CRT as a measure of ability or disposition to resist reporting first response that comes to mind, as well as the validity of results of studies showing “incremental validity” of CRT over numeracy.

Donation requests often convey numerical information about the people in need. In two studies we investigated the effects of numeracy and presentation format on the underlying affective and cognitive mechanisms of donation decisions. In Study 1, participants were presented with information about a victim in need, either in a frequency format or in a percentage format. In Study 2, we manipulated the identifiability and number of target victims. Our results demonstrate that donations of individuals lower in numeracy were more susceptible to changes in numeric presentation format than those higher in numeracy. Importantly, the underlying mechanisms for donations differed by numeracy. Whereas the mental image of the victim influenced donation decisions of less numerate people only, the estimated impact of a donation was positively correlated with donation amounts for both more and less numerate individuals.

We conducted three studies to investigate how well pictographs communicate medical screening information to persons with higher and lower numeracy skills. In Study 1, we conducted a 2 (probability level: higher vs. lower) × 2 (reference information: yes vs. no) × 2 (subjective numeracy: higher vs. lower) between-subjects design. Persons with higher numeracy skills were influenced by probability level but not by reference information. Persons with lower numeracy tended to differentiate between a higher and a lower probability when there was no reference information. Study 2 consisted of interviews about the mental processing of pictographs. Higher numeracy was associated with counting the icons and relying on numbers depicted in the graph. Study 3 was an experiment with the same design as in Study 1, but, rather than using reference information, we varied the sequence of task type (counting first vs. non-counting first) to explore the role of the focus on numerical information. Persons with lower numeracy differentiated between higher and lower risk only when they were in the non-counting first condition. Task sequence did not influence the risk perceptions of persons with higher numeracy. In sum, our results suggest that pictographs may be useful for persons with higher and lower numeracy. However, these groups seem to process the graph differently. Persons with higher numeracy rely more on the numerical information depicted in the graph, whereas persons with lower numeracy seem to be confused when they are guided towards these numbers.

We investigated the relations between numeracy and superior judgment and decision making in two large community outreach studies in Holland (n=5408). In these very highly educated samples (e.g., 30–50% held graduate degrees), the Berlin Numeracy Test was a robust predictor of financial, medical, and metacognitive task performance (i.e., lotteries, intertemporal choice, denominator neglect, and confidence judgments), independent of education, gender, age, and another numeracy assessment. Metacognitive processes partially mediated the link between numeracy and superior performance. More numerate participants performed better because they deliberated more during decision making and more accurately evaluated their judgments (e.g., less overconfidence). Results suggest that well-designed numeracy tests tend to be robust predictors of superior judgment and decision making because they simultaneously assess (1) mathematical competency and (2) metacognitive and self-regulated learning skills.

Individual differences in cognitive abilities and skills can predict normatively superior and logically consistent judgments and decisions. The current experiment investigates the processes that mediate individual differences in risky choices. We assessed working memory span, numeracy, and cognitive impulsivity and conducted a protocol analysis to trace variations in conscious deliberative processes. People higher in cognitive abilities made more choices consistent with expected values; however, expected-value choices rarely resulted from expected-value calculations. Instead, the cognitive ability and choice relationship was mediated by the number of simple considerations made during decision making — e.g., transforming probabilities and considering the relative size of gains. Results imply that, even in simple lotteries, superior risky decisions associated with cognitive abilities and controlled cognition can reflect metacognitive dynamics and elaborative heuristic search processes, rather than normative calculations. Modes of cognitive control (e.g., dual process dynamics) and implications for process models of risky decision-making (e.g., priority heuristic) are discussed.

Right-wing ideology and cognitive ability, including objective numeracy, have been found to relate negatively. Although objective and subjective numeracy correlate positively, it is unclear whether subjective numeracy relates to political ideology in the same way. Replicating and extending previous research, across two samples of American adults (ns= 455, 406), those who performed worse on objective numeracy tasks scored higher on right-wing authoritarianism (RWA) and social dominance orientation (SDO), and they self-identified as more conservative on general, social, and economic continua. Controlling for objective numeracy, subjective numeracy related positively to measures of right-wing ideologies. In other words, those who strongly (vs. weakly) endorsed right-wing ideologies believed they are good with numbers yet performed worse on numeracy tasks. We discuss implications for the opposing direction of associations between ideology with objective versus subjective numeracy and similarities with literature on overconfidence.

The present study investigated skilled and adaptive strategy selection in risky decision making. We proposed that people with high objective numeracy, a strong predictor of general decision making skill, would have a broad repertoire of choice strategies andadaptively select these strategies depending on the importance of the decision. Thus more objectively numerate people would maximize their effort (e.g., invest more time) in important, high-payoff decisions and switch to a simple, fast heuristic strategy in trivial decisions. Subjective numeracy would, by contrast, be more closely related to interest in problem solving for its own sake and would not yield such an effect of importance. Participants made twelve high-payoff choices and twelve low-payoff choices in binary two-outcome gambles framed as gains. We measured objective and subjective numeracy using standard measures. Results showed that people with high subjective numeracy generally maximized the expected value (EV) in all decisions. In contrast, participants with high objective numeracy maximized EV only when choice problems were meaningful (i.e., they could result in high payoffs). When choice problems were trivial (i.e., choosing the normatively better option would not result in a large payoff), more objectively numerate participants made choices consistent with faster, more frugal heuristic strategies.

Proportion responding (PR) is the preference for proportionally higher gains, such that the same absolute quantity is valued more as the reference group decreases. This research investigated this kind of proportion PR in decisions about saving lives (e.g., saving 10/10 lives is preferred to saving 10/100 lives). The results of two studies suggest that PR does not stem from an overall tendency to choose higher proportions, but rather from faulty deliberative reasoning. In particular, people who display PR are less likely to engage in deliberative reflection as measured by response time, the Process Dissociation Procedure, the Cognitive Reflection Test, a numeracy test, and a task assessing denominator neglect. This association between faulty deliberation and PR was observed only when choosing the highest proportion was non-normative because it came at the expense of absolute gains (e.g., saving 10/10 lives is preferred to saving 11/100 lives). These results help to make sense of discrepant findings in previous research, pertaining to how PR relates to biased reasoning and decision making.

Previous research has demonstrated that Bayesian reasoning performance is improved if uncertainty information is presented as natural frequencies rather than single-event probabilities. A questionnaire study of 342 college students replicated this effect but also found that the performance-boosting benefits of the natural frequency presentation occurred primarily for participants who scored high in numeracy. This finding suggests that even comprehension and manipulation of natural frequencies requires a certain threshold of numeracy abilities, and that the beneficial effects of natural frequency presentation may not be as general as previously believed.

People often base judgments on stereotypes, even when contradictory base-rate information is provided. In a sample of 438 students from two state universities, we tested several hypotheses regarding why people would prefer stereotype information over base-rates when making judgments: A) People believe stereotype information is more diagnostic than base-rate information, B) people find stereotype information more salient than base-rate information, or C) even though people have some intuitive access to base-rate information, they may need to engage in deliberation before they can make full use of it, and often fail to do so. In line with the deliberative failure account, and counter to the diagnosticity account, we found that inducing deliberation by having people evaluate statements supporting the use of base-rates increased the use of base-rate information. Moreover, counter to the salience and diagnosticity accounts, asking people to evaluate statements supporting the use of stereotypes decreased reliance on stereotype information. Additionally, more numerate subjects were more likely to make use of base-rate information.

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 numeracy on information processing of two risk communication formats (percentage and pictograph) was examined using an eye tracker. A sample from the general population (N = 159) was used. In intuitive and deliberative decision conditions, the participants were presented with a hypothetical scenario presenting a test result. The participants indicated their feelings and their perceived risk, evoked by a 17% risk level. In the intuitive decision condition, a significant correlation (r = .30) between numeracy and the order of information processing was found: the higher the numeracy, the earlier the processing of the percentage, and the lower the numeracy, the earlier the processing of the pictograph. This intuitive, initial focus on a format prevailed over the first half of the intuitive decision-making process. In the deliberative decision condition, the correlation between numeracy and order of information processing was not significant. In both decision conditions, high and low numerates processed pictograph and percentage formats with similar depths and derived similar meanings from them in terms of feelings and perceived risk. In both conditions numeracy had no effects on the degree of attention on the percentage or the pictograph (number of fixations on formats and transitions between them). The results suggest that pictographs attract low numerates’ attention, and percentages attract high numerates’ attention in the first, intuitive, phase of numeric information processing. Pictographs thus ensure low numerates’ further elaboration on numeric risk information, which is an important precondition of risk understanding and decision making.