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Front Psychol . 2018 Jul 13;9:1202. doi: 10.3389/fpsyg.2018.01202 Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy Silke M Mueller Silke M Mueller 1 General Psychology: Cognition and Center for Behavioral Addiction Rese... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.838 | ["decision_making", "education"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.730039 | [
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gy: Cognition and Center for Behavioral Addiction Research, University of Duisburg-Essen, Duisburg, Germany 2 Erwin L. Hahn Institute for Magnetic Resonance Imaging, Essen, Germany Find articles by Matthias Brand 1, 2, * Author information Article notes Copyright and License information 1 General Psychology: Cognition ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.385 | 0.816 | ["education", "philosophy"] | 424 | Decision Making | topic | 2026-03-21T00:51:19.730121 | [
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y of Duisburg-Essen, Duisburg, Germany 2 Erwin L. Hahn Institute for Magnetic Resonance Imaging, Essen, Germany Edited by: Petko Kusev, University of Huddersfield, United Kingdom Reviewed by: Ronald Hübner, Universität Konstanz, Germany; Marcus Lindskog, Uppsala University, Sweden ✉ *Correspondence: Silke M. Mueller, s... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.682 | ["education"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730168 | [
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d, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. PMC Copyright notice PMCID: PMC6053537 PMID: 30057562 Abstract Research on the cognitive abilities involved in decision making has shown that, under objective risk conditions (i.e.... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.842 | ["decision_making", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730217 | [
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s and exact number processing skills, also referred to as objective numeracy. So far, decision-making research has mainly focused on exact number processing skills, such as performing calculations or transformations of symbolic numbers. There is evidence that such exact numeric skills are based on approximate number pr... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.987 | 0.828 | ["philosophy", "decision_making"] | 437 | Decision Making | topic | 2026-03-21T00:51:19.730256 | [
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non-symbolic numbers (e.g., Chen and Li, 2014 ). Very few studies, however, have investigated ANP skills in the context of risky decision making and have analyzed direct associations among the aforementioned sub functions. Possible interactions between the closely related skills have not been considered. The current st... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.991 | 0.834 | ["decision_making", "education"] | 456 | Decision Making | topic | 2026-03-21T00:51:19.730296 | [
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ve numeracy, in predicting risky choice behavior. ANP skills are represented by the accuracy in a dot-comparison task. Decision making is measured by two versions of the Game of Dice Task (GDT), which place different emphases on the reflection of potential risks. The results show two-way as well as three-way interactio... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.991 | 0.84 | ["decision_making"] | 454 | Decision Making | topic | 2026-03-21T00:51:19.730332 | [
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predicting risky decisions in both GDT versions. The riskiest decisions were most frequently made in case of low scores in all of the three competencies, while good performance in any one of them resulted in significant reductions of disadvantageous decisions. The findings indicate that high ANP skills can positively a... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.992 | 0.834 | ["decision_making", "philosophy"] | 462 | Decision Making | topic | 2026-03-21T00:51:19.730368 | [
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amely executive functions and objective numeracy. Potential compensatory effects and mechanisms of ANP in decision making are discussed. Keywords: decision making under risk, approximate number system, number processing, executive functions, numeracy, GDT Introduction Processing numbers is essential for many kinds of d... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.903 | 0.834 | ["decision_making", "philosophy"] | 487 | Decision Making | topic | 2026-03-21T00:51:19.730402 | [
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to assess expected outcomes prior to a decision. However, numbers can be present in various contexts (e.g., finance or health risks), forms, and abstractions levels, e.g., as fractions (¼), percentages (25%), non-symbolic quantities (⋅/::), or absolute values (30 in 120). These different types of numerical information ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.687 | 0.674 | ["philosophy", "decision_making", "ethics", "crisis"] | 437 | Decision Making | topic | 2026-03-21T00:51:19.730438 | [
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terpretation requires different processing steps. Examples of different skills required for understanding numerical information are having knowledge about symbolic representations of numbers (that ‘4’ equals ‘::’), relating numbers to one another (that 120 is four times 30), or transforming different numeric informatio... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.296 | 0.704 | ["philosophy", "communication", "education"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.730472 | [
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eracy’ ( Peters et al., 2006 ; Reyna et al., 2009 ). Studies have shown that even highly educated professionals have deficits in numeracy and thus lack understanding probabilistic numeric information ( Estrada et al., 1999 ; Hoffrage et al., 2000 ; Lipkus et al., 2001 ). Research on the positive impact of numeracy on d... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.895 | 0.718 | ["philosophy", "decision_making", "career"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730506 | [
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of formal mathematical competence regarding symbolic numbers, such as basic calculation skills, and comprehension of different ratio formats as described above. However, recent theories and results of neurocognitive studies promote a differentiation between exact and approximate number processing ( Piazza et al., 2004 ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.4 | 0.852 | ["philosophy"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.730546 | [
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e not only processed by the same but also by distinct brain regions ( Sokolowski et al., 2017 ). However, the two competencies seem to be associated with one another (see Chen and Li, 2014 for a review). So far, research on decision making under risk has focused on the involvement of (symbolic) exact number processing ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.987 | 0.842 | ["decision_making"] | 433 | Decision Making | topic | 2026-03-21T00:51:19.730584 | [
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r processing skills has rarely been investigated. The current study aims to fill this gap by focusing approximate number processing skills, more precisely approximate non-symbolic number discrimination precision, and their potential interactions with numeracy and executive functions in the context of decision making un... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.842 | ["decision_making", "education", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730618 | [
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rent numeracy measures see Cokely et al., 2014 ). In such tasks, subjects are asked to make ordinal judgments of risk (e.g., 1 in 10 represents a bigger risk than 1 in 100 or 1 in 1000), to convert frequencies into percentages or vice versa (e.g., 10% risk is the same as 100 in 1000), or to demonstrate knowledge about ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.31 | 0.724 | ["decision_making", "education"] | 459 | Decision Making | topic | 2026-03-21T00:51:19.730651 | [
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l six-sided die is twice as high as tossing a 3). In the following, for reasons of clarity and consistency, we will use the term ‘objective numeracy’ for the ability to accurately handle probabilistic numeric information in terms of exact symbolic numbers, as measured by tests as described above (e.g., the task by Lipk... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.726 | ["philosophy", "decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730686 | [
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10 ; for reviews see Reyna and Brainerd, 2007 ; Reyna et al., 2009 ) as well as on decision making in general, even when controlling for measures of general intelligence ( Peters et al., 2006 , 2007 ; Peters, 2012 ). Convergent results, obtained by use of laboratory gambling tasks, such as the Game of Dice Task (GDT; B... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.878 | ["decision_making", "economy", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730722 | [
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: ±200; four digits: ±100), all given explicitly. In the GDT-Double, participants are also asked whether they want to double the amount of their bet or not. Executive functions were shown to correlate with performance in the GDT and GDT-Double ( Brand et al., 2005 , 2006 , 2007 , 2014 ) as well as with performance in o... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.874 | ["philosophy", "decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730757 | [
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robability-Associated Gambling Task ( Schiebener et al., 2011 ). In these tasks executive functions are assumed to enable the categorization of given information as well as strategy application and feedback inclusion. That is why models of decision making under objective risk consider executive functions to be a centra... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.683 | 0.828 | ["decision_making", "strategy", "resume", "philosophy"] | 416 | Decision Making | topic | 2026-03-21T00:51:19.730791 | [
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rand et al., 2006 ; Schiebener and Brand, 2015 ). Linking numeracy and executive functions, it was found that ‘processing probabilities’ (measured by tests of probability knowledge and objective numeracy as mentioned above) mediate the effect of executive functions ( Brand et al., 2014 , Study 2) and mental calculation... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.925 | 0.832 | ["education", "decision_making", "philosophy"] | 413 | Decision Making | topic | 2026-03-21T00:51:19.730825 | [
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he decision-making performance in the GDT-Double. Basic calculation skills are supposed to be relevant, e.g., for calculating expected values and thus for comparing different attributes and evaluating risks in a normative way (e.g., Cokely and Kelley, 2009 ; Brand et al., 2014 ). This assumption has recently been suppo... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.901 | 0.698 | ["philosophy", "decision_making", "ethics"] | 497 | Decision Making | topic | 2026-03-21T00:51:19.730859 | [
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r in the GDT-Double than average math performers. Thus, objective numeracy skills and executive functions act together in the process of decision making under objective risk. However, besides careful consideration of the given (numeric) facts, decision makers also need to be able to extract and comprehend the meaning t... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.912 | 0.844 | ["decision_making", "philosophy"] | 452 | Decision Making | topic | 2026-03-21T00:51:19.730894 | [
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a and Brainerd, 1995 ; Lipkus and Peters, 2009 ). There is evidence that this ability might be even more relevant than exact numeric skills. For example, Cokely and Kelley (2009) showed by verbal protocol analysis that most decisions that were consistent with expected values did not originate from expected-value calcul... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.854 | ["decision_making", "ethics", "economy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730936 | [
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ere more inclined to extract and integrate the very essence from the given numeric information when making decision, which contributes to more accurate choice behavior ( Cokely and Kelley, 2009 ). Accordingly, Peters et al. (2006) showed that individuals with higher objective numeracy could derive more affective meanin... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.854 | ["philosophy", "decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730970 | [
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umeric information can sometimes lead to an overuse of exact numbers resulting in non-optimal evaluations ( Peters et al., 2006 ; Kleber et al., 2013 , Study 4). Approximate Number Processing Besides numeracy, which concerns the processing of exact numbers, there is strong evidence that humans (and also other non-human... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.862 | ["education", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.730998 | [
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or approximate way as vague mental magnitudes ( Dehaene, 1997 ; Feigenson et al., 2004 ). The so-called Approximate Number System is supposed to enable rough but quick estimations and comparisons between such non-symbolic numbers. While some researchers assume other systems than the Approximate Number System to be resp... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.858 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731022 | [
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NP precision (i.e., accuracy) is ratio dependent. Further, ANP precision increases from infancy to adulthood ( Xu and Spelke, 2000 ; Halberda and Feigenson, 2008 ; Libertus and Brannon, 2010 ; Halberda et al., 2012 ). While two quantities with a ratio of 1:2 (e.g., 16 versus 32 dots) can be easily distinguished by adul... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.726 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731047 | [
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ratios of about 9:10, e.g., 36 versus 40 dots ( Halberda and Feigenson, 2008 ). Dot comparison tasks exist in many different versions (see Dietrich et al., 2015 ). Thereby the to-be-compared sets of dots are presented either sequentially, or simultaneously as separate pairs, or simultaneously intermixed, e.g., in diffe... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.702 | [] | 511 | Decision Making | topic | 2026-03-21T00:51:19.731072 | [
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emory, inhibitory control, or visual resolution ( Price et al., 2012 ; Gilmore et al., 2014 ). Although ANP skills and objective numeracy are substantively different, research suggests that both abilities are related to one another. Having high ANP precision, i.e., being good at discriminating even close-together quant... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.384 | 0.678 | [] | 419 | Decision Making | topic | 2026-03-21T00:51:19.731096 | [
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sed a paired dot-comparison task. Dietrich et al. (2015) recommend the use of these kinds of tasks for measuring ANP precision, because of their frequent usage, the consistent correlations with other ANP tasks, and the low involvement of other cognitive processes. In the context of decision making, research relating AN... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.924 | 0.83 | ["decision_making", "philosophy"] | 415 | Decision Making | topic | 2026-03-21T00:51:19.731123 | [
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g tasks is still rare (see Winman et al., 2014 ). Regarding symbolic number mapping, there is first evidence suggesting that ANP skills play a distinct role. Studies by Peters and colleagues demonstrate that the precision of mental-number-line representations (e.g., symbolic number mapping) influences numerical reasoni... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.902 | 0.85 | ["communication", "decision_making", "philosophy"] | 490 | Decision Making | topic | 2026-03-21T00:51:19.731164 | [
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nd Peters, 2014 ; Peters and Bjalkebring, 2015 ). Such mapping skills were further assumed to have a compensatory effect for individuals who lack the time, motivation, or capacity to perform formal number calculations ( Peters and Bjalkebring, 2015 ). Non-symbolic number processing has been studied in the context of pr... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.852 | ["decision_making", "philosophy", "motivation"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731195 | [
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omparison task) made more realistic judgments about their own performance. However, ANP precision, in contrast to objective numeracy, did not predict the calibration of probability judgments. Similarly, Patalano et al. (2015) demonstrated that objective numeracy but not ANP precision was associated with number distorti... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.698 | ["decision_making", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731227 | [
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i in an intermixed format (i.e., blue and yellow dots). In a recent study ( Mueller et al., 2018 ), using a paired dot-comparison task, we did not find any direct association between ANP precision and the decision-making performance under objective risk measured with the GDT-Double. Rather, more integrative skills, suc... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.901 | 0.852 | ["decision_making", "philosophy", "education"] | 496 | Decision Making | topic | 2026-03-21T00:51:19.731257 | [
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the effects of executive functions and numeracy. What has not yet been investigated systematically, is the possible interplay between non-symbolic number processing skills (ANP precision), symbolic numeric skills (objective numeracy) and executive functions. The latter two have already been shown to constantly predict ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.998 | 0.83 | ["decision_making"] | 488 | Decision Making | topic | 2026-03-21T00:51:19.731285 | [
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bly not directly related) moderate these effects. Objectives and Hypotheses of the Study The above mentioned findings from decision-making and numerical-cognition research let assume that numeric information can be processed, on the one hand, in an exact manner, and, on the other hand, inexactly or approximately as rou... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.918 | 0.836 | ["communication", "decision_making", "education", "philosophy"] | 433 | Decision Making | topic | 2026-03-21T00:51:19.731313 | [
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; Pica et al., 2004 ; Reyna and Brainerd, 2011 ). Irrespective of which processing mode may comprise which aspect of numerical information processing (for different dual-processing accounts of decision making see Reyna and Brainerd, 1995 , 2011 ; Sloman, 1996 ; Stanovich and West, 2000 ; Schiebener and Brand, 2015 ) it... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.868 | ["decision_making", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731339 | [
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ately in terms of rough estimations or other rather simple considerations. This assumption can be transferred to complex decision-making situations. For example, the most optimal decisions in the GDT are those for combinations of four digits as possible die-roll results, rather than choosing combinations of three or tw... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.856 | ["decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731366 | [
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the chances and risks of the different decision options exactly (⅙ vs. ⅚; vs. ; vs. ; vs. ) in order to compare them or to further calculate expected values for each option by additionally taking the possible gains/losses into account (e.g., 1000 × [⅙ - ⅚] vs. 100 × [ - ]). On the other hand, one can also simply consid... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.696 | 0.728 | ["decision_making", "ethics"] | 481 | Decision Making | topic | 2026-03-21T00:51:19.731401 | [
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the options with the highest quantity of digits. Both strategies would lead to the same (optimal) decision, i.e., choosing the most advantageous option. However, in the latter case, the individual could have come to this decision without having performed any calculations and without having considered any exact number o... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.911 | 0.838 | ["decision_making", "education", "philosophy"] | 455 | Decision Making | topic | 2026-03-21T00:51:19.731440 | [
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with objective numeracy and executive functions. Objective numeracy, as an exact numeric processing skill, and executive functions have already been shown to (interactively) predict decision making under objective risk. Non-symbolic ANP skills were shown to be linked to numeracy. Based on previous findings, no direct e... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.85 | ["decision_making"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.731471 | [
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tory effect, as we suggested that advantageous decisions under risk can also result from the integration of non-exact considerations involving ANP, e.g., quick comparisons of item quantities representing risk information without the need for processing exact symbolic numbers. Thus, the current study examined ANP skills... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.925 | 0.664 | ["decision_making", "education", "philosophy"] | 412 | Decision Making | topic | 2026-03-21T00:51:19.731505 | [
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umbers (i.e., numerosities) can be discriminated. We hypothesized interaction effects between ANP skills and executive functions as well as between ANP skills and objective numeracy in predicting risky decision making in the GDT. Furthermore, it can be assumed that ANP is particularly relevant when reflective processin... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.846 | ["decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731532 | [
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functions, numeracy, and ANP skills in predicting GDT decision making. The current study used two slightly different versions of the GDT as measures of decision making under objective risk. The group variable (GDT version) served as between-subject factor in order to examine whether the hypothesized interactions apply ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.902 | 0.84 | ["decision_making", "crisis", "education"] | 492 | Decision Making | topic | 2026-03-21T00:51:19.731562 | [
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ly challenge reflection about risks (GDT-Double). Moreover, equal variables of both GDT versions allowed combined data analyzes across the whole sample. Materials and Methods Study Sample The sample analyzed in the current study consisted of a total of 128 subjects (73 females, 55 males), aged from 18 to 62 years ( M =... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.878 | ["education", "crisis", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731593 | [
0.038987912237644196,
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of the GDT as well as the other tasks mentioned below. This group stemmed from a new streamlined data collection. The other group ( n = 64; 37 females, 27 males) consisted of age- and gender-matched participants from the sample reported in Mueller et al. (2018) , which performed the GDT-Double instead of the original G... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.862 | ["philosophy"] | 503 | Decision Making | topic | 2026-03-21T00:51:19.731620 | [
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led out in the breaks between two computer tasks. Participants were free to choose their preferred distance from the screen. The instructions for each of the tests were given in a standardized manner. Number-Comparison Task We used the first subtask of the Risk Approximation Task (RAT; Mueller et al., 2018 ) as a measu... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.315 | 0.844 | ["philosophy"] | 442 | Decision Making | topic | 2026-03-21T00:51:19.731650 | [
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011) . The trials were presented in random order. Each stimulus pair was used twice to counterbalance the side on which the array with more dots is presented. Thereby, the stimulus pictures were rotated and/or mirrored when presented for the second time, in order to avoid recognition effects but to keep the visual prop... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.856 | ["crisis", "philosophy"] | 500 | Decision Making | topic | 2026-03-21T00:51:19.731677 | [
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o one of four decks, according to specific rules. The to-be-sorted cards are presented separately with symbols that vary in shape, color, and quantity. By pressing button ‘1’ to ‘4’ the participant sorts the respective card to one of the four decks. The participant then receives auditory and visual feedback about wheth... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.866 | ["philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731706 | [
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rocessing of risks and ratios as described below. GDT original The GDT ( Brand et al., 2005 ) is a computer task where subjects shall maximize a virtual capital of €1000 by betting on the results of multiple die rolls. In each of the 36 rounds, the subject can either bet on a single digit or on different combinations o... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.884 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731731 | [
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g., ‘5’) or combination of digits (e.g., ‘1 2 3 4’). Betting on a single digit reveals the highest gain/loss amount, but the lowest winning probability. Bets on combinations of two, three, or four digits are linked to, respectively, lower gain/loss amounts. Overall, the decision for one single digit is the riskiest cho... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.868 | ["decision_making"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.731760 | [
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advantageous in the long run because of a winning probability of more than 50% and a positive expected value (see Table 1 for exact winning chances, gain/loss amounts, and expected values). The probabilities and amounts of gains/losses stay stable and are constantly displayed on the screen during the entire game. After... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.691 | 0.84 | ["decision_making", "ethics"] | 456 | Decision Making | topic | 2026-03-21T00:51:19.731794 | [
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in/loss) and the actual account balance. Table 1. Winning chances, gains/losses, and expected values of each type of decision option for the GDT and the GDT-Double. GDT (original) GDT-Double (if doubled) Options Winning chance (%) Gain/Loss EV Gain/Loss EV One single digit 16.67 1000 –666.67 2000 –1333.33 Two digits 33... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.73 | ["decision_making", "ethics"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731835 | [
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se the bet is not doubled in the GDT-Double, the gain/loss amounts and expected values (EV) of each option are the same as in the original GDT. GDT-double The GDT-Double (for a more detailed description see Brand et al., 2014 ) is based on the same game principle as the original GDT. The only difference is that, in the... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.691 | 0.864 | ["decision_making", "ethics"] | 453 | Decision Making | topic | 2026-03-21T00:51:19.731862 | [
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r the expected values of the GDT and GDT-Double). Furthermore, the questions following each choice (whether to double or not) encourage subjects to (again) think about ratios and potential risks, which potentially triggers more reflective processing ( Schiebener and Brand, 2015 ). For both the GDT and the GDT-Double, t... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.854 | ["decision_making", "ethics"] | 510 | Decision Making | topic | 2026-03-21T00:51:19.731890 | [
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for the riskiest alternatives (one single digit). Results Statistical analyses were carried out with SPSS 24.0 (IBM SPSS Statistics, released 2016). Pearson product-moment correlation coefficients (Pearson’s r ) were calculated to test for bivariate correlations, with r ≥ 0.1 indicating a small, r ≥ 0.3 indicating a me... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.706 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.731915 | [
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s were run in order to test the first hypothesis. The third block of analyses tested the hypothesized three-way interaction between the three predictors, namely executive functions (MCST errors), objective numeracy (correct responses in the numeracy task), and ANP skills (accuracy in the number-comparison task). Descri... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.312 | 0.834 | [] | 450 | Decision Making | topic | 2026-03-21T00:51:19.731939 | [
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parameters, except the net score (see Table 2 ). Subjects who played the original GDT had higher net scores than those who played the GDT-Double, however, the mean GDT-Double net score was generally low compared to other studies (see Brand et al., 2014 ; Pertl et al., 2017 ). The groups did not differ in the mean numbe... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.696 | 0.866 | ["decision_making"] | 478 | Decision Making | topic | 2026-03-21T00:51:19.731967 | [
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yses as the measure of risky GDT decision making. The performance scores in the number-comparison task were also statistically equal for both groups (see Table 2 ). Overall, a typical ratio effect could be observed, i.e., the closer-together the to-be-compared quantities were, the poorer was the accuracy (ratio ¼: M = ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.693 | 0.724 | ["decision_making", "philosophy"] | 466 | Decision Making | topic | 2026-03-21T00:51:19.731996 | [
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.723, SD = 0.165; ratio : M = 0.565, SD = 0.178). Accordingly, the highest variability in discrimination precision across subjects was found for dot-arrays of ratio . Accuracy at ratios ½ and ¼ were non-normally distributed with skewness of -4.38 ( SE = 0.214) and -2.33 ( SE = 0.214) indicating ceiling effects ( Koedel... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.724 | ["crisis"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732023 | [
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effects (i.e., including trials with ratio ¾ or larger) in order to have an additional measure that is more sensitive to individual differences in ANP precision. Following this approach, we additionally took an even more sensitive score. As adults from typically educated cultures can discriminate quantities of ratios u... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.296 | 0.87 | ["crisis"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.732051 | [
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t ratio (i.e., the most difficult trials in the number-comparison task used in this study, M = 0.565, SD = 0.178). Thus, the following analyses were conducted on all three measures of ANP skills, respectively, namely number-comparison (1) total accuracy, (2) accuracy at ratios ≥ ¾, and (3) accuracy at ratio . Table 2. ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.738 | ["crisis", "education"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732084 | [
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D ) M ( SD ) t p Age 18 62 28.56 (12.50) 28.56 (11.82) <0.01 >0.999 MCST (total errors) 0 32 8.91 (8.34) 7.23 (6.67) 1.25 0.213 Numeracy task (total correct) 1 12 10.08 (2.19) 10.03 (1.79) 0.13 0.895 Number-comparison task (accuracy) Total 0.600 0.930 0.793 (0.070) 0.791 (0.066) 0.13 0.897 Ratio ≥ ¾ 0.389 0.889 0.674 (... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.738 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732109 | [
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7 (10.46) 2.05 0.043 One single digit 0 18 1.19 (3.18) 1.59 (2.99) –0.74 0.458 Open in a new tab MCST, Modified Card Sorting Test . Correlation Analyses The results of the correlation analysis (see Table 3 ) show that in both groups (i.e., both GDT versions) decision-making performance is associated in similar patterns... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.914 | 0.688 | ["decision_making", "philosophy"] | 445 | Decision Making | topic | 2026-03-21T00:51:19.732135 | [
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vely with correct responses in the numeracy task. There is no direct correlation between GDT performance and the accuracy in the number-comparison task in neither group. Table 3. Bivariate correlations between measures of executive functions, numeracy, ANP precision, and decision making under risk, separately for the t... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.874 | ["decision_making", "philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732161 | [
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ect) –0.297* – –0.329** – (3) Number-comparison (total accuracy) 0.074 –0.065 – –0.089 0.250* – (4) GDT (net score) –0.269* 0.378** 0.007 – –0.294* 0.201 –0.099 – (5) GDT (one single digit) 0.229 –0.637** –0.053 –0.742** 0.308* –0.306* 0.008 –0.671** Open in a new tab GDT, Game of Dice Task; MCST = Modified Card Sortin... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.724 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732185 | [
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ANP skills with measures of executive functions and objective numeracy, moderated regression analyses were performed. First, the interactions between the measures of executive functions and ANP abilities were analyzed. The group variable ‘GDT version’ was included as an additional predictor in order to control for grou... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.313 | 0.828 | ["philosophy"] | 449 | Decision Making | topic | 2026-03-21T00:51:19.732212 | [
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Here again, the group variable was also included. Thirdly, we examined three-way interactions between the measures of executive functions, objective numeracy, and ANP skills in predicting overall GDT performance. All analyses were conducted with number-comparison ‘total accuracy’ as well as with the two more sensitive ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.32 | 0.818 | ["philosophy"] | 425 | Decision Making | topic | 2026-03-21T00:51:19.732239 | [
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)’ and ‘number-comparison (accuracy at ratio )’]. Interactions Between Executive Functions and ANP Skills The first hierarchical regression analysis included the group variable ‘GDT version’ in the first step, followed by ‘MCST’ (total errors) and ‘number-comparison’ (accuracy) in the second and third steps. Then, all ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.4 | 0.844 | ["decision_making"] | 506 | Decision Making | topic | 2026-03-21T00:51:19.732268 | [
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GDT one single digit) was the dependent variable. The results of the analysis including ‘number-comparison (total accuracy)’ as ANP-skill measure show no significant interactions. MCST was the only predictor of GDT performance (for the model summary see Appendix Table A1 ). The equivalent analysis with ‘number-comparis... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.4 | 0.846 | ["philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732294 | [
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er-comparison’ (step 6) significantly explains additional variance in the GDT score, Δ R 2 = 0.044, Δ F = 6.19, p = 0.014. The three-way interaction with group is not significant, Δ R 2 < 0.001, Δ F = 0.02, p = 0.888. Besides the interaction with number-comparison, the MCST is the only predictor with a significant coef... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.73 | ["decision_making"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.732321 | [
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ison still has no direct effect on GDT decisions, Δ R 2 = 0.013, Δ F = 1.72, p = 0.192. As in the previous analyses, no interactions with the group variable are present, neither with MCST, Δ R 2 = 0.002, Δ F = 0.33, p = 0.570, nor with number-comparison, Δ R 2 = 0.001, Δ F = 0.19, p = 0.663, nor with both (three-way), ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.658 | ["decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732353 | [
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% of the variance in ‘GDT one single digit’, Δ R 2 = 0.110, Δ F = 16.55, p < 0.001. The final model accounts for almost 20% of the variation in GDT decision making, total R 2 = 0.199, F (7,127) = 4.26, p < 0.001 (for the coefficients of the final model see Appendix Table A2 ). Figure 1A visualizes the interaction effec... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.744 | ["decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732410 | [
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ne single digit) is barely chosen, irrespective of MCST performance. However, if number-comparison (accuracy at ratio ) is low (see Figure 1 , black lines), subjects of both groups make significantly more of the riskiest choices when they show weak rather than good MCST performance (weak performance is indicated by a h... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.862 | ["philosophy", "decision_making"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.732439 | [
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ion), executive functions (errors in the Modified Card Sorting Test; MCST), and ANP skills (number-comparison accuracy; NC accuracy) as well as between (B) group, objective numeracy, and ANP skills on risky decision making in the Game of Dice Task (GDT one single digit). The ‘high’ and ‘low’ data points represent value... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.866 | ["decision_making", "ethics"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.732467 | [
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ith the difference that ‘numeracy’ (total correct responses in the numeracy task) was included instead of ‘MCST’. Results of the analysis including ‘number-comparison (total accuracy)’ show no significant predictors, except numeracy in the second step, which accounted for about 24% of the variance in GDT performance (f... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.4 | 0.85 | ["philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732494 | [
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ificant interactions of number-comparison with numeracy, neither two-way (step 6), Δ R 2 = 0.016, Δ F = 2.69, p = 0.103, nor three-way with group (step 7), Δ R 2 = 0.008, Δ F = 21.38, p = 0.243. However, performing the same analysis with the score ‘number-comparison (accuracy at ratio )’ reveals significance for the in... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.744 | ["philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732523 | [
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ses no additional changes, Δ R 2 = 0.002, Δ F = 0.29, p = 0.594. The final model accounts for one third of the variance in risky GDT decisions, total R 2 = 0.333, F (7,127) = 8.57, p < 0.001 (for the coefficients of the final model see Appendix Table A4 ). The mentioned interaction between numeracy and number-compariso... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.7 | 0.726 | ["decision_making"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.732550 | [
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ion ‘Interactions Between Executive Functions and ANP Skills’), subjects with low numeracy show more of the riskiest GDT decisions than those with high numeracy. However, this difference is only significant in case number-comparison accuracy at ratio is additionally low (see Figure 1 , black lines). Accordingly, in bot... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.909 | 0.84 | ["decision_making", "philosophy"] | 463 | Decision Making | topic | 2026-03-21T00:51:19.732579 | [
0.07281758636236191,
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racy task and the number-comparison task are low. However, we like to note that the accuracy at ratio is based on only a few number of trials, which is why these results should to be treated with caution, as discussed later. Interactions Between Executive Functions, Numeracy, and ANP Skills The third analysis tested in... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.384 | 0.832 | ["crisis"] | 418 | Decision Making | topic | 2026-03-21T00:51:19.732606 | [
0.061016689985990524,
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0.047076236456632614,
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0.... | ||
ve functions, objective numeracy, and ANP skills. Because ‘GDT version’ did not have any effect in the previous analyses (neither a direct effect, nor two-way or three-way interaction effects with the other predictors), the two groups were considered together for the following analyses. The number of choices for ‘one s... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.856 | ["decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732635 | [
0.025535181164741516,
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0.03754601627588272,
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ect) as the second, and ‘number-comparison’ (accuracy) as the third predictor, followed by the respective interaction-terms in steps four to seven. The results reveal that, in addition to the effect of MCST performance (Δ R 2 = 0.064, Δ F = 8.59, p = 0.004), numeracy has a significant direct effect on ‘GDT one single d... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.75 | ["philosophy"] | 511 | Decision Making | topic | 2026-03-21T00:51:19.732666 | [
0.024163179099559784,
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0.01, p = 0.928; accuracy at ratios ≥ ¾ : Δ R 2 < 0.002, Δ F = 0.28, p = 0.596; accuracy at ratio : Δ R 2 = 0.014, Δ F = 2.40, p = 0.124). The interaction of ‘MCST × numeracy’ explains additional 12% of variance in GDT performance (in the analysis including number-comparison total accuracy: Δ R 2 = 0.123, Δ F = 24.24, ... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.295 | 0.752 | ["philosophy"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732693 | [
0.06949502229690552,
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CST × number-comparison’: Δ R 2 = 0.004, Δ F = 0.88, p = 0.351; ‘numeracy × number-comparison’: Δ R 2 < 0.001, Δ F = 0.09, p = 0.764). The respective three-way interaction fails to reach significance, Δ R 2 = 0.018, Δ F = 3.62, p = 0.060. Interestingly, looking at the results of the same analysis with the two more sens... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.322 | 0.698 | [] | 421 | Decision Making | topic | 2026-03-21T00:51:19.732717 | [
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eractions accounting for additional GDT variance. In detail, the interaction of ‘MCST × numeracy × number-comparison (accuracy at ratios ≥ ¾)’ explains additional 3.5%, Δ F = 7.36, p = 0.008, while the three-way interaction with the most sensitive ANP score (number-comparison accuracy at ratio ) accounts for almost 4%,... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.724 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732741 | [
0.06182936951518059,
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ccuracy at ratios ≥ ¾: F (7,127) = 13.20, p < 0.001] and 49.8% [number-comparison accuracy at ratio : F (7,127) = 16.98, p < 0.001] of ‘GDT one single digit’. The coefficients (see Table 4 ) show that MCST, numeracy, and the interaction of both have incremental effects on risky GDT decisions, with numeracy having the h... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.697 | 0.716 | ["decision_making"] | 487 | Decision Making | topic | 2026-03-21T00:51:19.732770 | [
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fficients of the most predictive model). Table 4. Statistics of the coefficients in the final step of the moderated regression analysis examining interaction effects between measures of executive functions (MCST), objective numeracy (numeracy task), and ANP skills (number-comparison accuracy) on risky decision making i... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 1 | 0.702 | ["decision_making"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732796 | [
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tal correct) –0.46 0.11 –0.300 –4.07*** <0.001 Number-comparison task (accuracy at ratio –0.29 1.21 –0.017 –0.24 0.813 2-way interactions MCST × Numeracy –0.05 0.02 –0.258 –3.48*** ≤0.001 MCST × Number-comparison –0.33 0.17 –0.145 –1.95 0.053 Numeracy × Number-comparison 0.83 0.63 0.097 1.32 0.188 3-way interaction MCS... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.71 | [] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732821 | [
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se note that the positive beta value of MCST errors indicates an association between weak executive functions (more errors) and weak GDT performance (more risky choices). Negative beta values indicate a positive effect of the respective predictor (high value) on good GDT performance (less risky choices); ∗ p < 0.05, ∗∗... | https://pmc.ncbi.nlm.nih.gov/articles/PMC6053537/ | Approximate Number Processing Skills Contribute to Decision Making Under Objective Risk: Interactions With Executive Functions and Objective Numeracy - PMC | pmc.ncbi.nlm.nih.gov | public_domain | false | 0.1 | 0.874 | ["decision_making", "philosophy", "ethics"] | 512 | Decision Making | topic | 2026-03-21T00:51:19.732849 | [
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0.028270183131098747,
0.07675100117921829,
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-0.0388050116... |
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