Revisiting the Links Between Numeracy and Decision Making: Replication Registered Report of Peters et al. (2006) With an Extension Examining Confidence
Collabra: Psychology
Abstract and Figures
Numeracy is individuals’ capacity to understand and process basic probability and numerical information required to make decisions. We conducted a Replication Registered Report of Peters et al. (2006) examining numeracy as a predictor of positive-negative framing effect (Study 1), frequency-percentage effect (Study 2), ratio effect (Study 3), and bets effect (Study 4). With an online US American Amazon Mechanical Turk sample (N = 860), our replication using the target’s dichotomizing of the numeracy measure found support for the original findings regarding interactions between numeracy and three decision-making effects. Numeracy was associated with weaker framing effect (η2p = 0.01, 90% CI [0.00, 0.02]), weaker ratio bias (Cramer’s V = 0.17, 95% CI [0.10, 0.24]), and stronger bets effect (η2p = 0.02, 90% CI [0.01, 0.04]), yet we found no support for the frequency-percentage effect (η2p = 0.00, 90% CI [0.00, 0.01]). However, we found support for associations with all four studies when treating numeracy as a continuous variable. We extended the replication to examine confidence, yet the results were mixed with support found for only three conditions (Study 1 positive framing condition: r = -0.11, 95% CI [-0.20, -0.02]; Study 3: r = 0.15, 95% CI [0.08, 0.21]; Study 4 no-loss bet condition: r = 0.10, 95% CI [0.01, 0.20]), suggesting a much weaker and more complex relationship than anticipated. Materials, data, and code are available on: https://osf.io/4hjck/.
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... This limitation hinders the self-correcting process initiated in response to the replication crisis, as observed in social and personality psychology (Vazire & Nosek, 2023). To our knowledge, only a handful of replication projects have revisited the relationship between numeracy and different aspects of decision making (Mondal et al., 2021;Persson et al., 2021;Sobkow et al., 2022;Zhu & Feldman, 2023). For example, Sobkow et al. (2022) and Mondal (2021) undertook preregistered replications of effects initially observed by Traczyk et al. (2018). ...
... Another previous project focused on a direct replication of seminal studies by Peters et al. (2006), pioneering the in-corporation of numeracy into the field of judgment and decision making. In this endeavor, Zhu and Feldman (2023) found consistent support for the original findings regarding numeracy's interactions with three decision-making effects: weaker framing effect (Study 1), weaker ratio bias (Study 3), and stronger bets effect (Study 4). However, the exploration of the interaction between objective numeracy and the frequency-percentage effect (Study 2) yielded mixed results, making the understanding of numeracy's role in decision-making dynamics more complex. ...
... Nevertheless, similarly to our replication attempt, several studies (e.g., Lohre et al., 2019;Mandel & Kapler, 2018;Peters et al., 2011) found no significant moderation effect of numeracy on modified framing tasks, including both objective and subjective numeracy. Finally, recent replication by Zhu and Feldman (2023), conducted with a large sample of MTurk users (N = 860), found evidence for significant framing and numeracy effects, but the interaction effect was negligible (η 2 p = .01). Similarly, regarding loss/no-loss bets, previous research has produced inconsistent results. ...
Numeracy, representing the ability to understand and process information related to probabilities and numbers, is crucial for accurate decision making. This study evaluates the replicability of eleven effects that underscore the pivotal role of numeracy in judgment and decision making, with successful replication defined as a statistically significant effect in the same direction as reported in the original study. Furthermore, the study explores the potential impact of employing diverse objective numeracy measures on the replicability of the tested effects. Additionally, we investigated correlations with various numeric competencies beyond objective numeracy, including subjective numeracy and approximate numeracy. We ran an online study on Polish-speaking Prolific users (N = 209). Six correlational effects were successfully replicated using the same numeracy measures as the original studies (decision rules, financial knowledge, consistency in risk perception, medical risk comprehension, maximizing the expected value, and preference for suboptimal options). Another two correlational effects were replicated using subjective instead of objective numeracy measures (resistance to sunk cost and financial well-being). Findings regarding the role of numeracy as a moderator variable were mixed. Numeracy was not a statistically significant moderator of the strength of the framing effect, the attractiveness ratings of bets, and performance in the diagnostic inference task. Nevertheless, our exploratory analyses revealed that individuals with higher numeracy found the loss bet more attractive compared to the no-loss bet. Additionally, visual aids improved diagnostic inferences among participants with lower objective numeracy. This comprehensive examination provides valuable insights into the multifaceted interplay between numeracy and decision-making processes. Materials, data, and scripts are available at: https://osf.io/927bx/
... This limitation hinders the self-correcting process initiated in response to the replication crisis, as observed in social and personality psychology (Vazire & Nosek, 2023). To our knowledge, only a handful of replication projects have revisited the relationship between numeracy and different aspects of decision making (Mondal, 2021;Persson et al., 2021;Sobkow et al., 2022;Zhu & Feldman, 2023). For example, Sobkow et al. (2022) and Mondal (2021) undertook preregistered replications of effects initially observed by Traczyk et al. (2018). ...
... Another previous project focused on a direct replication of seminal studies by Peters et al. (2006), pioneering the incorporation of numeracy into the field of judgment and decision making. In this endeavor, Zhu and Feldman (2023) found consistent support for the original findings regarding numeracy's interactions with three decision-making effects: weaker framing effect (Study 1), weaker ratio bias (Study 3), and stronger bets effect (Study 4). However, the exploration of the interaction between objective numeracy and the frequency-percentage effect (Study 2) yielded mixed results, making the understanding of numeracy's role in decision-making dynamics more complex. ...
Numeracy, representing the ability to understand and process information related to probabilities and numbers, is crucial for accurate decision making. This study evaluates the replicability of eleven effects that underscore the pivotal role of numeracy in judgment and decision making. Furthermore, the study explores the potential impact of employing diverse objective numeracy measures on the replicability of the tested effects. Additionally, we investigated correlations with various numeric competencies beyond objective numeracy, including subjective numeracy and approximate numeracy. We ran an online study on Polish-speaking Prolific users (N = 209). Six correlational effects were successfully replicated using the same numeracy measures as the original studies (decision rules, financial knowledge, consistency in risk perception, medical risk comprehension, maximizing the expected value, and preference for optimal options). Another two correlational effects were replicated using subjective instead of objective numeracy measures (resistance to sunk cost and financial well-being). Findings regarding the role of numeracy as a moderator variable were mixed. We found no evidence for the impact of numeracy on the strength of the framing effect. Nevertheless, more numerate individuals preferred the loss over the no-loss bet, and visual aids improved diagnostic inferences among participants with lower objective numeracy. This comprehensive examination provides valuable insights into the multifaceted interplay between numeracy and decision-making processes.
... We ran the four studies together in a single data collection. Combining several studies from a single target article in a single data collection has previously been successfully tested in several replications and extensions conducted by our team (e.g., Chen et al., 2023;Petrov et al., 2023;Vonasch et al., 2023;Yeung & Feldman, 2022;Zhu & Feldman, 2023), and is especially powerful in addressing concerns about the target sample (naivety, attentiveness, etc.) when some studies replicate successfully whereas others do not, as well as in the potential in drawing inferences about the links between the different studies and consistency in participants' responding to similar decision-making paradigms. Unless explicitly noted, our measures are identical to those employed in Norton et al. (2007). ...
Norton et al. (2007) demonstrated a counterintuitive phenomenon that knowing other people better and/or having more information about them is associated with decreased liking. They summarized it as - ambiguity leads to liking, whereas familiarity can breed contempt. In a Registered Report with a US Prolific undergraduate student sample (N = 801), we directly replicated Studies 1a, 1b, and 2, and conceptually replicated Studies 3 and 4 from Norton et al. (2007). Extending their research, we also proposed that curiosity provides an alternative path to liking, hypothesizing that curiosity mediates the relationship between knowledge and liking. Overall, we found weak support for the original findings. Consistent with the original article, participants believed they would like someone who they knew more about (original: h = 0.52 to 0.70; replication: h = 0.55 to 0.75) and that knowledge positively predicts liking (original: h = 0.21 to 0.45; replication: h = 0.57 to 0.76). However, we found no indication for number of traits known influencing liking (original: r = -0.43 to -0.005; replication: r = -0.05 to 0.06) or perceived similarity to the target (d = 0.00), for a mediating effect of perceived similarity, for a dissimilarity cascade effect, or for changes in liking or perceived similarity as a factor of learning more about the target. In our extensions, we found support for a positive relationship between curiosity and liking (r = 0.62 to 0.70), but not for knowledge and curiosity (r = -0.06 to 0.05). Overall, our findings suggest that learning more about others may not influence perceptions of liking, similarity, or curiosity towards them. Materials, data, and code are available on: https://osf.io/j6tqr/ . This Registered Report has been officially endorsed by Peer Community in Registered Reports: https://doi.org/10.24072/pci.rr.100947
... All three scenarios were presented in random order, and participants were randomly and evenly assigned to different conditions in Scenarios 2 and 3. This unified design combining replications of several studies into a singular data collection was previously tested successfully in many of the replications and extensions conducted by our team (e.g., Petrov et al., 2023;Vonasch et al., 2023;Yeung & Feldman, 2022;Zhu & Feldman, 2023), and is especially powerful in addressing concerns about the target sample (e.g., naivety and attentiveness) when some studies replicate successfully whereas others do not, as well as in allowing for drawing inferences about links between the different studies and consistency in participants' responding to similar decision-making paradigms. In case we fail to find support for the target article's hypotheses, we will test for order effects (order as a moderator) and for effects for each scenario when it is displayed first. ...
Arkes (1996) demonstrated a phenomenon of wastefulness avoidance, showing that people’s decisions are impacted by wastefulness, making decisions that avoid appearing wasteful. In a Registered Report with a Prolific sample (N = 659), we conducted a replication and extensions of Studies 1, 2, and 3 from Arkes (1996). We found empirical support for the impact of waste on evaluations of decisions in the movie package scenario in Study 1 (original: h=0.43[0.03, 0.83]; replication: h=0.26[0.10,0.42]) and on hypothetical decisions in the tent project scenario in Study 3 (original: w = 0.23 [0.00, 0.52]; replication: w = 0.09 [0.00, 0.17]), but with no support in the tax program scenario in Study 2 (original: w = .27 [0.00, 0.55]; replication: w = 0.03 [0.00, 0.12]). Our extension employing a continuous willingness measure, to supplement the scenarios’ dichotomous choice, showed similar results. We added a manipulation check extension which showed that the manipulation worked as expected in Scenarios 1 and 3, but not in Scenario 2. In our extension examining reasons, in the successfully replicated scenarios we found that in Scenario 1 utility maximization was not rated as the most important and in Scenario 3 minimizing waste was rated as the most important reason. Overall, we concluded a mixed replication, with a successful replication of two of the three tested studies. Materials, data, and code are available on: https://osf.io/gf8rc/ . This Registered Report has been officially endorsed by Peer Community in Registered Reports: https://doi.org/10.24072/pci.rr.100801
... Replications allow reassessing, validating, and adjusting the original's measurement, examining appropriateness and alignment with theory, and retesting using better validated measures. For example, in our replications of studies with scale predictors we often run the original's alongside different types of measurement or more comprehensive scales in random order and then test them all with comparisons against each other (e.g., Koppel et al., 2023;Zhu and Feldman, 2023). ...
Commentary on Isager et al. (2021) [https://doi.org/10.31222/osf.io/knjea].
Main arguments:
- Replications are very rare: We just do not do replications
- Replication value is tied to research value
- Replications go beyond replicability
... Participants answered the seven decision scenarios from the seven studies in random order, and the conditions assigned in each study were also randomized. This unified design combining replications of several studies into a singular data collection was previously tested successfully in many of the replications and extensions conducted by our team (e.g., Petrov et al., 2023;Vonasch et al., 2023;Yeung & Feldman, 2022;Zhu & Feldman, 2023), and is especially powerful in addressing concerns about the target sample (e.g., naivety and attentiveness) when some studies replicate successfully whereas others do not, as well as in allowing for drawing inferences about links between the different studies and consistency in participants' responding to similar decision-making paradigms. ...
Choice partitioning refers to the phenomenon when the same choice set yields different decision-making behaviour when they are grouped into sets (broadly bracketed) or evaluated separately (narrowly bracketed). In a Registered Report experiment with a US sample recruited online through Prolific (N = 896), we conducted a replication of seven studies reviewed in Read et al. (Read et al. 1999 J. Risk Uncertain. 19, 99 (doi:10.1023/A:1007879411489)). We concluded a mostly successful replication: out of the seven studies, we found support for six (Studies 1, 3, 4 and 6: Cramer’s V > 0.31; Studies 2 and 7: Cohen’s d > 0.29) and no empirical support for one (Study 5: Cramer’s V = 0.02). Extending the replication, we added new conditions in Studies 6 and 7, further expanding the manipulation’s scope range, yet failed to find any impact. In our replication, we came across many challenges, both conceptual and empirical, and we therefore call bracketing scholars to better define bracketing in relation to other phenomena in decision-making (joint versus separate mode, framing effects, mental accounting, etc.), with falsifiable hypotheses, examining overlap with other constructs, and clearer mapping between theory and empirics. Materials, data and code are available on: https://osf.io/vdqek/.
... Previous studies have shown that low numeracy reduces adherence to medication, skews perceptions of the benefits and risks of screening, hinders access to treatment, undermines risk communication (restricting prevention initiatives for the most vulnerable), and seems to have a negative effect on medical outcomes [44]. Low numeracy is also associated with higher sensitivity to external factors that do not affect objective numerical data but are linked to biases in judgment and decision-making (eg, the influence of framing and ratio bias effects) [45]. Thus, in France, health promotion actions should consider this specifically and should target the improvement of numeracy. ...
Background
In 2022, the World Health Organization highlighted the alarming state of oral health (OH) worldwide and urged action to include OH in initiatives on noncommunicable diseases. The population needs improved OH skills and attitudes and an adequate level of OH literacy (OHL) and general health literacy (HL). The implementation of health promotion actions in the workplace, which is a part of most people’s lives, appears to be an opportunity. In France, civil servants have several socioprofessional levels and represent an excellent model with results transposable to the population.
Objective
This study aimed at determining the OHL and HL level of civil servants in France in order to implement specific prevention actions in their workplaces.
Methods
A cross-sectional study of French civil servants was conducted in France from October 2023 to February 2024. Participants completed three validated questionnaires in French: (1) a questionnaire on OH knowledge, (2) the Oral Health Literacy Instrument, French version (OHLI-F; this is composed of reading comprehension and numeracy sections) to assess the OHL level, and (3) the Short Test of Functional Health Literacy in Adults, French version (s-TOFHLA-F) to assess the HL level. The scores for OH knowledge, the OHLI-F, and the s-TOFHLA-F were reported as means (SD) and the 95% CI. These scores were classified into 3 categories: adequate (75-100), marginal (60-74) and inadequate (0-59). ANOVA and binary logistic regression were performed. The OHLI-F reading comprehension and OHLI-F numeracy scores were compared using the Welch 2-sample t test and a paired t test (both 2-tailed). For the correlation matrix, the Pearson correlation and related tests were computed.
Results
A total of 1917 persons completed the 3 questionnaires, with adequate levels of OHL (n=1610, 84%), OH knowledge (n=1736, 90.6%), and HL (n=1915, 99.9%). The scores on the s-TOFHLA-F (mean 98.2, SD 2.8) were higher than the OHLI-F (mean 80.9, SD 7.9) and OH knowledge (mean 87.6, SD 10.5). The OHLI-F was highly correlated with OH knowledge ( P< .001), but the OHLI-F and OH knowledge had a low correlation with s-TOFHLA-F ( P =.43). The OHLI-F reading comprehension score was significantly higher than the OHLI-F numeracy score ( P <.001). Age, education level, and professional category impacted the 3 scores ( P <.001). The professional category was a determinant of adequate OHLI-F and OH knowledge scores.
Conclusions
Some French civil servants had inadequate or marginal levels of OH knowledge (n=181, 9.5%) and OHL (n=307, 16%) but none had an inadequate level of HL. Results highlighted the relevance of implementing OH promotion programs in the workplace. They should be nonstandardized, adapted to the literacy level of professional categories of workers, and focused on numeracy skills. Thus, appropriate preventive communication and improved literacy levels are the means to achieve greater disease equity and combat the burden of noncommunicable diseases.
... Replications allow reassessing, validating, and adjusting the original's measurement, examining appropriateness and alignment with theory, and retesting using better validated measures. For example, in our replications of studies with scale predictors we often run the original's alongside more comprehensive scales in random order and then test them all with comparisons against each other (e.g., Koppel et al., 2023;Zhu & Feldman, 2023). ...
The value of replications goes beyond replicability and is associated with the value of the research it replicates: Commentary on Isager et al. (2021)
... However, this argument is weaker for Wong and Kwong (2007) which is more recent. Additionally, other studies in the field of judgement and decision making have been successfully replicated despite a similar time-lag (Zhu & Feldman, 2023;Ziano, Xiao, et al., 2021). ...
The present study is a pre-registered replication of three influential studies in the field of escalation of commitment and regret aversion. In Study 1 [N = 595, MTurk], we failed to find empirical support for Wong and Kwong’s (2007) original paper examining the effect of personal responsibility (ηp2 = 0.001 [0, 0.011]) and regret possibility (ηp2 = 0.001 [0, 0.009]) on escalation of commitment. Moreover, the extension of study 1 found no support for individual differences in neuroticism on escalation of commitment (r = -0.04, 95% CI = [-0.12, 0.05]). Study 2 [N = 452, MTurk] failed to replicate Zeelenberg’s et al.’s (1996) paper examining the role of feedback on risk preferences (ηp² = 0.005, 90% CI = [0, 0.018]). In the extension to study 2, we found small correlation between the tendency to experience regret and risk preferences of participants in the Safe ONLY condition. Study 3 [N = 403, MTurk] found partial support for Staw’s (1976) paper on effects of personal responsibility (n2p = 0.040 [0.014, 0.076]) and consequences (n2p = 0.067 [0.032, 0.109]) on escalation to commitment. The impact of this replication on our understanding of decision-making processes and the factors that contribute to individuals' commitment to their choices will be discussed.
... Participants were first randomly allocated to either the case-prime or the class-prime condition. This unified design combining replications of several studies into a singular data collection was previously tested successfully in many of the replications and extensions conducted by our team (e.g., Petrov et al., 2023;Vonasch et al., 2023;Yeung & Feldman, 2022;Zhu & Feldman, 2023), also with one successful replication Registered ...
Partition dependence is the phenomenon in which individuals' evaluations of probabilities are influenced by the partitioning of the information in the way the information is presented or framed. In a Registered Report experiment with an American online Prolific sample (N = 603), we conducted a replication and extension of Studies 1a, 1b, 3, and 4 from a classic article by Fox and Rottenstreich (2003) demonstrating the phenomenon. They showed that participants’ estimations of an event’s likelihood shifted based on minor adjustments of the framing that suggested a change in partitioning perspective (“ignorance prior” priming). Based on a pre-registered replication evaluation criterion, we concluded a mostly successful replication of Fox and Rottenstreich (2003)’s findings. Specifically, we found support for partition dependence in scenarios from Study 1a items 1 and 2, Study 1b, and Study 3, with weaker effects, yet with no consistent support for Study 1a item 3 and Study 4. Our extensions further explored the robustness of partition dependence by examining participants’ probability evaluations of complementary events (happen vs. not happen) and the impact of task order on judgment and decision-making. Overall, the findings suggest support for partition dependence yet as more nuanced and context-dependent than expected, and the need for further research to understand its mechanisms, robustness, and implications across different contexts. Materials, data, and code are available on: https://osf.io/g9czs/ . This Registered Report has been officially endorsed by Peer Community in Registered Reports: https://doi.org/10.24072/pci.rr.100877
The temporal pattern of regret is the phenomenon that people perceive or experience stronger regret over action compared to inaction in the short-term, yet stronger regret over inaction compared to action in the long term. Following mixed and null findings in the literature, we conducted replications and extension of Studies 1, 3, 4, and 5 in the classic Gilovich and Medvec (1994) which first demonstrated this phenomenon, with a single combined data collection in randomized display order with an online sample of Americans on MTurk (N = 988). We found support for the original findings using different designs in Studies 1, 3, and 4, yet with weaker effects. We failed to find support for such a pattern in Study 5. We discuss possible interpretations for these differences: our replication adjustments, the change in the meaning of action and inaction, or change in hypothetical versus real-life personal experiences. Extending the replications, we found support for stronger responsibility for action compared to inaction both in the short-term and the long-term. We conclude overall support for the effects, yet with follow-up work necessary to resolve the inconsistencies in the findings of the Study 5 replication. Pre-registration, materials, data, and code were made available on: https://osf.io/7m3q2/
We attempted a pre-registered replication and extension of Studies 1, 2, and 3 from Pronin and Ross (2006) regarding the effects of social and temporal distance on trait attributions with an online American Amazon MTurk sample (N = 911). We concluded mixed findings. We found support for the original findings: participants attributed more dispositional traits to others compared to themselves, although with weaker effects (original: f = 0.35, 95% CI [0.09, 0.61]; replication: f = 0.10, 95% CI [0.03, 0.16]). Also, similar to the original, we found that participants tended to attribute a favorable ratio of positive traits when making self-assessments (original: f = 0.77, 95% CI [0.29, 1.25]; replication: f = 0.87, 95% CI [0.50, 1.24]). However, unlike the original, we failed to find support for the core hypothesis that participants would ascribe more dispositional traits to their temporally distant selves compared to their present self (original: f = 0.54, 95% CI [0.27, 0.77]; replication: f = 0.01, 95% CI [0.00, 0.05]). Furthermore, in contrast to the original, we found that the positive traits ratio increases with temporal distance (original: f = 0.15, 95% CI [0.00, 0.31]; replication: f = 0.32, 95% CI [0.22, 0.41] in opposite direction). Contrary to our hypothesis, in an extension we found that people were more likely to ascribe a greater ratio of positive traits to their friends than to themselves (ξ=0.3, 95% CI [0.21, 0.38]). All materials, data, and code are provided on: https://osf.io/gs2rx/.
This study estimates empirically derived guidelines for effect size interpretation for research in social psychology overall and sub-disciplines within social psychology, based on analysis of the true distributions of the two types of effect size measures widely used in social psychology (correlation coefficient and standardized mean differences). Analysis of empirically derived distributions of 12,170 correlation coefficients and 6,447 Cohen's d statistics extracted from studies included in 134 published meta-analyses revealed that the 25th, 50th, and 75th percentiles corresponded to correlation coefficient values of 0.12, 0.24, and 0.41 and to Cohen's d values of 0.15, 0.36, and 0.65 respectively. The analysis suggests that the widely used Cohen's guidelines tend to overestimate medium and large effect sizes. Empirically derived effect size distributions in social psychology overall and its sub-disciplines can be used both for effect size interpretation and for sample size planning when other information about effect size is not available.
We conducted a preregistered close replication and extension of Studies 1, 2, and 4 in Hsee (1998). Hsee found that when evaluating choices jointly, people compare and judge the option higher on desirable attributes as better ("more is better"). However, when people evaluate options separately, they rely on contextual cues and reference points, sometimes resulting in evaluating the option with less as being better ("less is better"). We found support for "less is better" across all studies (N=403; Study 1 original d=0.70 [0.24,1.15], replication d=0.99 [0.72,1.26]; Study 2 original d=0.74 [0.12,1.35], replication d=0.32 [0.07,0.56]; Study 4 original d=0.97 [0.43,1.50], replication d=0.76 [0.50,1.02]), with weaker support for "more is better" (Study 2 original d=0.92 [0.42,1.40], replication d=0.33 [.23,.43]; Study 4 original d=0.37 [0.02,0.72], replication d=0.09 [-0.05,0.23]). Some results of our exploratory extensions were surprising, leading to open questions. We discuss remaining implications and directions for theory and measurement relating to economic rationality and the evaluability hypothesis. Materials/data/code: https://osf.io/9uwns/
A growing body of research has indicated a relationship between numeracy and decision making and that lower numerate people display more disadvantageous decisions. In the domain of intertemporal choice, researchers have long been using impulsivity to address choice preference. To further illuminate the psychological mechanisms of making intertemporal choices, the present study examined the role of impulsivity and numeracy in intertemporal choice, in the presence of each other. The study adopted both subjective and numeracy scales. These scales correlated with each other and with intertemporal choice preference. Moreover, it was found that after controlling for impulsivity, the object numeracy was significantly associated with choice preference, with higher numerate participants showing a stronger preference toward the later larger gains over the sooner smaller gains. Thus, the study indicated that intertemporal choice preference could be attributed to both impulsivity and numeracy.
Background. Numeracy skills are important for medical decision making as lower numeracy is associated with misinterpreting statistical health risks. Math anxiety, characterized by negative emotions about numerical tasks, and lower subjective numeracy (i.e., self-assessments of numerical competence) are also associated with poor risk comprehension. Objective. To explore independent and mediated associations of math anxiety, numerical ability, and subjective numeracy with risk comprehension and to ascertain whether their associations are specific to the health domain. Methods. Objective numeracy was measured with a 14-item test. Math anxiety and subjective numeracy were assessed with self-report scales. Risk comprehension was measured with a 12-item test. In experiment 1, risk comprehension items were limited to scenarios in the health domain. In experiment 2, participants were randomly assigned to receive numerically equivalent risk comprehension items in either a health or nonhealth domain. Results. Linear regression analyses revealed that individuals with higher objective numeracy were more likely to respond correctly to the risk comprehension items, as were individuals with higher subjective numeracy. Higher math anxiety was associated with a lower likelihood of correct responding when controlling for objective numeracy but not when controlling for subjective numeracy. Mediation analyses indicated that math anxiety may undermine risk comprehension in 3 ways, including through 1) objective numeracy, 2) subjective numeracy, and 3) objective and subjective numeracy in serial, with subjective numeracy mediating the association between objective numeracy and risk comprehension. Findings did not differ by domain. Conclusions. Math anxiety, objective numeracy, and subjective numeracy are associated with risk comprehension through unique pathways. Education initiatives for improving health risk comprehension may be most effective if jointly aimed at tackling numerical ability as well as negative emotions and self-evaluations related to numeracy.
The importance of replication is becoming increasingly appreciated, however, considerably less consensus exists about how to evaluate the design and results of replications. We make concrete recommendations on how to evaluate replications with more nuance than what is typically done currently in the literature. We highlight six study characteristics that are crucial for evaluating replications: replication method similarity, replication differences, investigator independence, method/data transparency, analytic result reproducibility, and auxiliary hypotheses’ plausibility evidence. We also recommend a more nuanced approach to statistically interpret replication results at the individual-study and meta-analytic levels, and propose clearer language to communicate replication results.
Background
Objective numeracy appears to support better medical decisions and health outcomes. The more numerate generally understand and use numbers more and make better medical decisions, including more informed medical choices. Numeric self-efficacy—an aspect of subjective numeracy that is also known as numeric confidence—also relates to decision making via emotional reactions to and inferences from experienced difficulty with numbers and via persistence linked with numeric comprehension and healthier behaviors over time. Furthermore, it moderates the effects of objective numeracy on medical outcomes.
Purpose
We briefly review the numeracy and decision-making literature and then summarize more recent literature on 3 separable effects of numeric self-efficacy. Although dual-process theories can account for the generally superior decision making of the highly numerate, they have neglected effects of numeric self-efficacy. We discuss implications for medical decision-making (MDM) research and practice. Finally, we propose a modification to dual-process theories, adding a “motivational mind” to integrate the effects of numeric self-efficacy on decision-making processes (i.e., inferences from experienced difficulty with numbers, greater persistence, and greater use of objective-numeracy skills) important to high-quality MDM.
Conclusions
The power of numeric self-efficacy (confidence) has been little considered in MDM, but many medical decisions and behaviors require persistence to be successful over time (e.g., comprehension, medical-recommendation adherence). Including numeric self-efficacy in research and theorizing will increase understanding of MDM and promote development of better decision interventions.
Highlights
Research demonstrates that objective numeracy supports better medical decisions and health outcomes. The power of numeric self-efficacy (aka numeric confidence) has been little considered but appears critical to emotional reactions and inferences that patients and others make when encountering numeric information (e.g., in decision aids) and to greater persistence in medical decision-making tasks involving numbers. The present article proposes a novel modification to dual-process theory to account for newer findings and to describe how numeracy mechanisms can be better understood. Because being able to adapt interventions to improve medical decisions depends in part on having a good theory, future research should incorporate numeric self-efficacy into medical decision-making theories and interventions.
Innumeracy in the Wild explains how numeric ability supports the quality of the decisions we make and, ultimately, the life outcomes we experience. It dissects three ways that people can be good or bad with numbers and how each of these numeric competencies matter to decision making. Furthermore, it delves into how we can use this knowledge to improve decision making. Understanding the roles of numeric ability (often called numeracy ) is particularly important today due to widespread innumeracy. In addition, policies in health and financial domains have shifted toward giving consumers and patients more information (which is often numeric). These changes are intended to empower individuals to take charge of their own welfare. The evidence is clear, however, that not everybody is prepared to use this information effectively and that those who are less numerate tend to make worse decisions unless provided adequate support. The book discusses four main points: the complex and systematic psychological mechanisms that underlie objective numeracy’s effects in judgment and decision making; the importance of numeracy to experiencing positive life outcomes especially in health and finances; the decision-making support provided by two additional ways of knowing and using numbers; and the methods that exploit existing evidence and enable those who are less comfortable with numbers to use them more effectively and make better choices in an often numeric world.
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.