Significance Greater objective ability is thought to lead to more confidence and success across domains. We investigated instead whether objective numeracy and numeric confidence might “mismatch” sometimes and, critically, interact in predicting financial and medical outcomes. The results of 2 studies (secondary analyses of a diverse internet panel and primary analysis of patients with systemic lupus erythematosus) revealed that being more objectively numerate benefits those who are more numerically confident, but not the less numerically confident. Enjoying good outcomes in finances and health appears to require the persistence of numeric confidence and also the human capital of objective numeracy. The patterns further suggest that improving 1 numerical competency without considering the other could cause harm.

Abstract 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.

People often laugh at being “no good at math,” as if innumeracy is unimportant. Unrecognized, however, is that about one-third of American adults are so innumerate (it’s like illiteracy but with numbers) that they likely cannot operate effectively in financial and health environments. According to the Organisation for Economic Co-operation and Development (OECD), 29% of American adults (about 73 million people in 2018; ref. 1) can do only simple numeric processes. They can count, sort, do simple arithmetic, and use simple percentages like 50%, but cannot do more complex numeric operations (2). As a result, they likely cannot select the health plan with the lowest cost based on annual premiums and deductibles for a family or calculate the difference in the percentage of patients who survive 1 treatment vs. another (3). Similar issues emerge in personal finances. For example, when told the amount owed on a credit card, monthly payments, and annual percentage rate charged, only 35% of people correctly answered that they could never pay off the debt (4).

Such numeric incomprehension is generally thought to be due to having low objective numeracy (defined as the ability to understand and use probabilistic and other mathematical concepts), but it could be due, in part, to having low numeric self-efficacy (defined as confidence in one’s objective numeracy abilities) (5⇓–7). Across domains from math to medicine, objective ability and confidence exist in a positive feedback loop, whereby objective success in solving relevant problems enhances confidence, and having more self-efficacy propels persistence and further learning and success (5, 8⇓–10). For example, arthritis patients more confident in carrying out necessary behaviors enjoyed better clinical outcomes (6, 11). As in other domains, objective numeracy and numeric confidence are related (average r = ∼0.45; refs. 12 and 13). Numeric-confidence measures are even used sometimes as proxies for objective numeracy because they are easier and less stressful for participants than objective numeracy measures (14). However, their correlation is imperfect, and, as reviewed below, they have independent effects on comprehension and decision making.

In the present paper, we considered whether they also have separate associations with medical and financial outcomes, a hypothesis mostly unexamined. In addition, we further reasoned that neither numeric competence would lead inevitably to better financial or medical outcomes. Instead, we posited an interaction hypothesis. Below, we first review correlational effects of objective numeracy and numeric confidence in comprehension, decisions, and outcomes. We then explain our interaction hypothesis and examine it in self-reported financial outcomes (a large diverse US internet panel; Study 1) and in the disease activity of systemic lupus erythematosus (SLE) patients (Study 2).

Objective Numeracy and Numeric Confidence Have Separate Relations with Comprehension and Decision Quality Objective Numeracy. Consistent with OECD data, the more objectively numerate have better comprehension of numeric information (controlling for demographics, numeric confidence, and nonnumeric intelligence; ref. 7). They also make better decisions than the less numerate when numeric information is involved (13, 15). In particular, the highly numerate think longer in numeric decisions (16, 17). They trust numeric information more (18) and do more (usually simple) numeric operations while attempting to understand what numbers, like dollar amounts, mean for a decision (19⇓–21). The highly numerate “have a numeric hammer,” and they use it. Decisions of the less objectively numerate instead are more vulnerable to decision heuristics, mental shortcuts used in judgments and choices (21⇓–23). For example, they succumb to framing effects and the compelling power of narratives, emotions, and concrete, easy-to-evaluate information (24⇓–26). As a result, the less objectively numerate tend to make worse decisions when numbers are involved, even after controlling for nonnumeric intelligence. Numeric Confidence. Drawing from self-efficacy theory, greater confidence is a major driver of behavior, behavior change, and persistence in the face of obstacles (8, 27). Across domains, it leads to better performance and outcomes (5, 11, 28, 29). Numeric confidence is no exception. The less numerically confident are thought to engage and persist less with numeric information. Ultimately, they understand numeric information less well and take fewer actions in number-heavy decisions (controlling for objective numeracy, demographics, and nonnumeric intelligence; refs. 7 and 12). They also make fewer normatively appropriate choices (30).

Numeric Competencies’ Relations with Financial and Health Outcomes Poorer comprehension and less sound decisions, then, may act as cumulative risk factors over time that exact financial and health tolls for the less objectively numerate and, separately, the less numerically confident. Personal-finance studies have examined objective numeracy, but not numeric confidence. In them, having more objective numeracy predicts better financial behaviors and outcomes, such as retirement planning and greater wealth, over and above general intelligence (23, 31⇓⇓⇓–35). Having greater objective numeracy also is related to better health behaviors and outcomes. The less objectively numerate adopted fewer protective health behaviors (e.g., exercise or condom usage), controlling for objective numeracy and nonnumeric intelligence (36, 37). They were 40% more likely to have at least 1 chronic disease and took 20% more prescription drugs (controlling for numeric confidence and demographics; ref. 38), but followed complex health regimens less well (39⇓–41). They also ended up in the hospital and emergency room more often (42, 43). Less numerically confident patients, on the other hand, perceived their physical and mental health to be worse (controlling for objective numeracy and demographics; ref. 38). In the only known experimental study, altering numeric confidence to improve objective numeracy in a required university statistics course caused positive effects on healthy-behavior maintenance and financial literacy (9).

The Current Studies Thus, greater objective numeracy and, independently, more numeric confidence tend to predict better comprehension, decision quality, and outcomes. We reasoned, however, that they should interact. In particular, among those with higher objective numeracy, having more vs. less numeric confidence should lead to better outcomes. This prediction is based on greater self-efficacy helping them persist in numeric tasks critical to making decisions about their finances and health. They then should succeed because they also have the numeric skills needed to support action. Those with higher ability but less numeric confidence, however, should persist less in numeric tasks and do less well as a result. Thus, despite high ability, those with less numeric confidence should suffer poorer outcomes. On the other hand, among less objectively numerate individuals, having more numeric confidence should lead to worse outcomes. This prediction is based on their confidence leading to numeric-task persistence but innumeracy leading to numeric mistakes that go unrecognized. For example, a patient may miscalculate how to reduce her medication dose over time, resulting in less-well-controlled disease. A consumer may make a financial mistake, resulting in late payments and fees (44). Thus, among the less objectively numerate, we predicted that having more numeric confidence would undermine financial and medical outcomes. We examined this interaction hypothesis in self-reported financial outcomes (Study 1) and SLE patient disease activity (Study 2). We chose these samples for several reasons. First, the Understanding America Study (UAS) included self-reported financial outcomes from a large, diverse sample of Americans who had previously responded to measures of objective numeracy and numeric confidence. Second, the SLE sample offered a clinical rather than self-reported outcome. Finally, examining our hypothesis across domains was key to testing generalizability. The studies also break ground in several ways. First, numeric confidence has been overlooked in financial research that focuses on objective abilities. The present research underscores the importance of self-efficacy and its associated motivation and persistence. Confidence in managing disease has seen some focus in medical research (e.g., rheumatoid arthritis; ref. 6). However, numeric confidence has not. Understanding more general abstract numeric competencies (objective numeracy and numeric confidence) should highlight psychological mechanisms underlying financial and health outcomes that require numeric persistence and ability. Finally, we questioned the “more is better” mantra of prior numeracy and self-efficacy research, which points toward interventions leading to greater objective numeracy or greater confidence, respectively. No known research has tested our alternative hypothesized interaction and its generalization across financial and health domains. Our results suggest that intervening on 1 numeric competency, without considering the other, may cause harm. Such data provide helpful evidence for those who wish to be (or help others to be) healthier and wealthier. Study 1—Self-Reported Financial Outcomes. We accessed a sample of n = 4,572 respondents from the UAS. Respondents had completed measures of positive financial outcomes, objective numeracy (45), numeric confidence (14), financial knowledge (46), and demographics.

Results Demographics, mean scores, and intercorrelations are in SI Appendix, Tables S4 and S5 (60). Multiple linear regression analysis was conducted to predict disease activity (SLEDAI scores) from objective numeracy, numeric confidence, their interaction, health literacy, patient activation, and demographics. In this initial planned test, the interaction of objective numeracy and numeric confidence was marginally significant [b(SE) = −0.27(0.14); P = 0.051]. We then removed nonsignificant covariates (P < 0.05) 1 at a time to attain a final parsimonious model (see SI Appendix, Table S6 for full and final models). Results supported the hypothesized interaction of objective numeracy and numeric confidence [b(SE) = −0.27(0.13); P = 0.037]; Fig. 2. Among patients with more numeric confidence (+1 SD), having greater objective numeracy was associated with lower SLEDAI scores [less disease activity, b(SE) = −0.66(0.29); P = 0.023]. However, objective-numeracy benefits again did not accrue among those with less numeric confidence (−1 SD) [b(SE) = 0.14(0.27); P = 0.61]. Based on this model, a patient higher in numeric confidence (+1 SD) was predicted to have a 44% vs. 7% chance of high disease activity (≥6) if she scored, respectively, the lowest vs. highest on objective numeracy. In contrast, a patient lower in numeric confidence (−1 SD) was predicted to be less likely to have high disease activity if she had the lowest vs. highest score in objective numeracy, 21% vs. 31%, respectively. Older age also was associated with less disease activity. Fig. 2’s numeric-confidence differences at the lowest and highest numeracy scores, however, did not attain significance (respectively, P = 0.12 and 0.08). Fig. 2. Predicted disease activity (SLEDAI scores) for individuals varying in objective numeracy and ±1 SD from the numeric confidence mean. Lower numbers are better, as they reflect less disease activity. Estimates are based on setting covariates to sample means.

General Discussion Comprehending and using numeric evidence in decisions appears to require 2 types of numeric competence—both objective numeracy to “run the numbers” well and numeric self-efficacy or confidence to persist when numeric tasks become tedious, difficult, or anxiety-provoking. From prior literature, the absence of either competency appeared to act as a risk factor, such that less of either one was associated with worse outcomes, and more of each one was better. Researchers have demonstrated such correlational effects with objective numeracy in financial and health domains and (less so) with numeric confidence in health. In the present studies, we questioned whether having more objective numeracy and more numeric confidence is always better. Results of these studies supported our hypothesis that objective numeracy interacts with numeric confidence to predict self-reported financial outcomes and a clinical outcome (SLE disease activity). Although medical and psychological studies demonstrate that greater self-efficacy leads to better performance and outcomes (5, 6, 29), these confidence benefits accrued only among those with adequate objective skills. In 2 studies, those with high objective numeracy and high numeric confidence had the best outcomes. Individuals who lacked objective numeracy skills but had high numeric confidence fared the worst, presumably because they persisted in doing numeric tasks critical to their finances and health, but made mistakes that went unnoticed. Consistent with this reasoning, they perceived their financial well-being as similar to those with high confidence and high objective numeracy, who actually experienced better financial outcomes (SI Appendix, SI Text and Fig. S1). As a result, opportunities to improve financial outcomes, including through receipt of help from others, may go unrecognized and/or be seen as lacking value. Thus, having high numeric confidence is insufficient and may be harmful when ability is low. Similarly, having high objective numeracy does not guarantee good outcomes. The benefits of objective numeracy did not accrue among those who were not numerically confident. In particular, those with greater objective numeracy and lower confidence appear to have disengaged, as they are much less likely to be the financial decision maker in their household compared to those with similar skills and more numeric confidence. These results are consistent with other research suggesting that having confidence can be beneficial (61), but overly positive self-beliefs can lead to negative consequences (62⇓⇓–65). In the present studies, it was not ideal to have low ability with high confidence or high ability with low confidence. These “mismatched” portions of the population are not small. In Study 1 (n = 4,572), we calculated median splits on objective numeracy (scores of 0–3 and 4–8) and numeric confidence (scores of 0–4 and 5–6). In this sample, 18% had greater objective numeracy and lower numeric confidence (we’ll call them the numerically underconfident). An additional 12% had lower objective numeracy and high confidence (the numerically overconfident). Using these same scale splits (scores of 0–3 for low objective numeracy and 0–4 for low numeric confidence), 20% and 13%, respectively, of SLE patients fell into these mismatched groups. Although our regression models explained small to medium amounts of variance, the effect sizes were not trivial (66). For example, for a person scoring highest on objective numeracy and numeric confidence (scores of 8 and 6, respectively), the predicted percentage of positive financial outcomes experienced was 83%, compared to only 74% for a person scoring highest on objective numeracy and lowest in numeric confidence (scores of 8 and 1, respectively), controlling for other variables. Considering the variety and severity of possible financial outcomes included in our study (e.g., bankruptcy, house foreclosures, or unpaid taxes), this difference could have a big impact. Similarly, uncontrolled SLE can cause irreversible organ damage and subsequent heart failure, stroke, or chronic kidney failure. Further research is needed on the precise psychological mechanisms underlying these effects. Past research indicates that those with less confidence lack persistence. In fact, having objective skills made little difference among those who lack numeric confidence, as if they did not even attempt numeric tasks important to their finances and health. Objective skills did matter among those high in numeric confidence, with the subset of individuals lower in objective skills presumably trying and failing in these same tasks. We did not measure task persistence or performance directly, however. Also unclear are the boundary conditions for when the “mismatch” of the 2 numeric competencies is associated with negative effects. More experimental research is needed, given our correlational results. Researchers have successfully altered objective numeracy and numeric self-efficacy in past studies, although doing so is difficult (9, 28). Indeed, manipulations of self-efficacy have been successful across domains ranging from snake phobias (67) to investment decisions (68). Nonetheless, in the present studies, we do not know if the combination of objective numeracy and numeric self-efficacy causally improved financial or health outcomes. Although we statistically controlled for various demographics (including education), financial knowledge (Study 1), and health literacy (Study 2), doing so reduced, but did not eliminate, the possibility of third-variable effects. Nonetheless, findings in 2 very different life domains clarified psychological and health-behavior theory and findings. First, they highlighted the importance of self-efficacy (numeric confidence in the present studies) and objective numeracy to life outcomes (6, 8, 13, 15) and likely to task persistence, comprehension, and decision quality. Instead of concluding that more of each competency is better, however, we demonstrated that their effects depend on each other. Being numerically underconfident and especially overconfident appeared to undermine patients’ medical status and consumers’ financial outcomes. The results further suggest that improving numeric confidence among individuals lower in objective numeracy paradoxically may cause them harm. At the same time, improving objective numeracy without ensuring that numeric confidence follows could also produce negative effects, although that effect was smaller. Overall, the results suggest that people can take better charge of their finances and health through numeric ability and numeric confidence, and both numeric competencies are required. The most potent assistance, then, would differ based on the individual’s combination of numeric confidence and objective numeracy, with discordant people needing the greatest assistance. Individuals should attempt to understand their own numeric competencies to ascertain whether they would be better off working on their numeric confidence (because their skills are adequate already) or their objective numeracy (either by building skills and/or asking for additional assistance in numeric tasks important to finances and health). For example, those with higher objective numeracy and lower numeric confidence may need the confidence boost that can come from psychological interventions such as values affirmation or expressive writing (9, 10, 69). Individuals with lower objective numeracy and lower numeric confidence likely would benefit from objective numeracy training in addition to these psychological interventions. Individuals with lower objective numeracy and higher numeric confidence may represent the biggest challenge because they may resist negative feedback. For them, practicing simple arithmetic with feedback should improve objective numeracy (70), so long as they take the task seriously. In addition, offering assistance in specific numeric tasks to anyone lower in objective numeracy would be useful. For example, in medication titration for patients, it may be helpful to provide them with a calendar that explicitly shows the number of pills to take each day of the week and have them set a goal to consult the calendar each day. Identifying and providing tailored communication or other assistance to subgroups of patients and consumers based on numeric confidence and objective ability may allow a more focused use of financial and health care dollars. It is also possible that such numeracy interventions may help patients with other chronic diseases in which lower objective numeracy has been associated with worse outcomes (e.g., chronic kidney disease, congestive heart failure, or diabetes). Breakthroughs in medical science have meant that we live longer and with fewer problems. The accumulation of financial wealth also allows our society greater economic security and independence, and it creates opportunities for the next generation (71). One’s status, however, depends at least in part on the decisions people make. They decide whether to save for retirement, adhere to a medication, follow a budget or their doctor’s advice, and do all of the many things that can promote one’s finances and health. Many of these decisions relate to how objectively numerate and numerically confident they are. Realizing one’s financial and medical potential appears to depend on both numeric competencies.

Acknowledgments We thank the Center for Economic and Social Research at USC for providing access to the UAS data (Study 1). We also thank The Ohio State’s Decision Psychology research colloquium and 2 anonymous reviewers for comments and suggestions; the National Science Foundation for a Graduate Student Professional Development Award; and the Consumer Financial Protection Bureau for a Graduate Research Internship, which helped make this project possible. This work was supported by NSF Grant SES-1558230. The views expressed are those of the authors and do not represent the views of the Consumer Financial Protection Bureau, the NSF, or the United States.

Footnotes Author contributions: E.P., M.K.T., M.A.Z.K., S.P.A., and A.S.M. designed research; A.S.M. performed research; M.K.T. and B.S.-R. analyzed data; and E.P., M.K.T., M.A.Z.K., S.P.A., B.S.-R., and A.S.M. wrote the paper.

Conflict of interest statement: E.P. has a conflict of interest with the patient activation measure; her husband owns a portion (<0.50%) of Insignia Health and receives some royalties.

This article is a PNAS Direct Submission.

Data deposition: All materials, data, and exact analysis syntax not already included in SI Appendix have been deposited in the Open Science Framework (https://osf.io/72feh/, https://osf.io/cd785/, and https://osf.io/m28ar/). Materials and data from Study 1 also are available at https://uasdata.usc.edu/index.php.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1903126116/-/DCSupplemental.