en pl
en pl


Show issue
Year 6/2021 
Issue 35

Sensitivity of numerate individuals to large asymmetry in outcomes: A registered replication of Traczyk et al. (2018)

Supratik Mondal
SWPS University of Social Sciences and Humanities

6/2021 (35) Decyzje

DOI 10.7206/DEC.1733-0092.150a


The main aim of this study is to replicate the effect shown by Traczyk et al. (2018), where individuals with higher statistical numeracy, compared to individuals with lower statistical numeracy, employed a more effortful choice strategy when outcomes were meaningful. I hypothesize that participants with higher numeracy will be more likely to make choices predicted by Cumulative Prospect Theory and Expected Value theory (CPT/EV) in high-payoff problems than in low-payoff problems. Data collection was done online by appointing 73 participants. Participants’ preference, fluid intelligence, objective and subjective numeracy were measured using thirteen high and eleven low payoff choice problems, International Cognitive Ability Resource (ICAR), Berlin Numeracy Test (BNT), and Subjective Numeracy Scale (SNS), respectively. All the measures mentioned above were presented randomly. Results showed that all participants, in high-payoff condition, on average maximized EV; however, participants with high BNT scores were more likely to make choices consistent with CPT/EV predictions than individuals with low BNT scores. Furthermore, compared to less numerate participants, highly numerate participants were less likely to make choices consistent with CPT/EV predictions in low-payoff condition. Highly numerate individuals
adjusted their choice strategy by modulating their response time, indicating
their discernible sensitivity towards large asymmetry in payoff. In conclusion, the effect shown by Traczyk et al. (2018) was successfully replicated.


  1. Arnold, B. F., Hogan, D. R., Colford, J. M., & Hubbard, A. E. (2011). Simulation methods to estimate design power: An overview for applied research. BMC Medical Research Methodology, 11(1), 94. doi: 10.1186/1471-2288-11-94 [Google Scholar]
  2. Ashby, N. J. S. (2017). Numeracy predicts preference consistency: Deliberative search heuristics increase choice consistency for choices from description and experience. Judgment and Decision Making, 12(2), 128–139. [Google Scholar]
  3. Becker, A., Deckers, T., Dohmen, T., Falk, A., & Kosse, F. (2012). The Relationship Between Economic Preferences and Psychological Personality Measures. Annual Review of Economics, 4(1), 453–478. doi: 10.1146/annurev-economics-080511-110922 [Google Scholar]
  4. Bernoulli, D. (1954). Exposition of a New Theory on the Measurement of Risk. Econometrica, 22(1), 23–36. doi: 10.2307/1909829 [Google Scholar]
  5. Brandstätter, E., Gigerenzer, G., & Hertwig, R. (2006). The priority heuristic: Making choices without trade-offs. Psychological Review, 113(2), 409–432. doi: 10.1037/0033-295X.113.2.409 [Google Scholar]
  6. Brysbaert, M., & Stevens, M. (2018). Power Analysis and Effect Size in Mixed Effects Models: A Tutorial. Journal of Cognition, 1(1), 9. doi: 10.5334/joc.10 [Google Scholar]
  7. Cacioppo, J. T., & Petty, R. E. (1982). The need for cognition. Journal of Personality and Social Psychology, 42(1), 116–131. doi: 10.1037/0022-3514.42.1.116 [Google Scholar]
  8. Cirillo, P., & Taleb, N. N. (2016). On the statistical properties and tail risk of violent confl icts. Physica A: Statistical Mechanics and its Applications, 452, 29–45. doi: https://doi.org/10.1016/j.physa.2016.01.050 [Google Scholar]
  9. Cokely, E. T., Galesic, M., Schulz, E., Ghazal, S., & Garcia-Retamero, R. (2012). Measuring Risk Literacy: The Berlin Numeracy Test. Judgment and Decision Making, 7(1), 23. [Google Scholar]
  10. Cokely, E. T., & Kelley, C. M. (2009). Cognitive abilities and superior decision making under risk: A protocol analysis and process model evaluation. Judgment and Decision Making, 4(1), 20–33. [Google Scholar]
  11. Condon, D. M., & Revelle, W. (2014). The international cognitive ability resource: Development and initial validation of a public-domain measure. Intelligence, 43, 52–64. doi: 10.1016/j.intell.2014.01.004 [Google Scholar]
  12. Davids, S. L., Schapira, M. M., McAuliffe, T. L., & Nattinger, A. B. (2004). Predictors of pessimistic breast cancer risk perceptions in a primary care population. Journal of General Internal Medicine, 19(4), 310–315. doi: 10.1111/j.1525-1497.2004.20801.x [Google Scholar]
  13. Estrada-Mejia, C., de Vries, M., & Zeelenberg, M. (2016). Numeracy and wealth. Journal of Economic Psychology, 54, 53–63. doi: 10.1016/j.joep.2016.02.011 [Google Scholar]
  14. Fagerlin, A., Zikmund-Fisher, B. J., Ubel, P. A., Jankovic, A., Derry, H. A., & Smith, D. M. (2007). Measuring Numeracy without a Math Test: Development of the Subjective Numeracy Scale. Medical Decision Making, 27(5), 672–680. doi: 10.1177/0272989X07304449 [Google Scholar]
  15. Ghazal, S., Cokely, E. T., & Garcia-Retamero, R. (2014). Predicting biases in very highly educated samples: Numeracy and metacognition. Judgment and Decision Making, 9(1), 15–34. [Google Scholar]
  16. Gigerenzer, G. (2007). Gut feelings: The intelligence of the unconscious. Penguin. Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103(4), 650–669. doi: 10.1037/0033-295X.103.4.650 [Google Scholar]
  17. Gurmankin, A. D., Baron, J., & Armstrong, K. (2004). The Effect of Numerical Statements of Risk on Trust and Comfort with Hypothetical Physician Risk Communication. Medical Decision Making, 24(3), 265–271. doi: 10.1177/0272989X04265482 [Google Scholar]
  18. Hands, D. W. (2015). Normative Rational Choice Theory: Past, Present, and Future (SSRN Scholarly Paper No. ID 1738671). Rochester, NY. doi: 10.2139/ssrn.1738671 [Google Scholar]
  19. Horn, S., & Freund, A. M. (2021). Adult age differences in monetary decisions with real and hypothetical reward. Journal of Behavioral Decision Making. doi: 10.1002/bdm.2253 [Google Scholar]
  20. Jasper, J. D., Bhattacharya, C., & Corser, R. (2017). Numeracy Predicts More Effortful and Elaborative Search Strategies in a Complex Risky Choice Context: A Process-Tracing Approach. Journal of Behavioral Decision Making, 30(2), 224–235. doi: 10.1002/bdm.1934 [Google Scholar]
  21. Jasper, J. D., Bhattacharya, C., Levin, I. P., Jones, L., & Bossard, E. (2013). Numeracy as a predictor of adaptive risky decision making. Journal of Behavioral Decision Making, 26(2), 164–173. doi: 10.1002/bdm.1748 [Google Scholar]
  22. John, & Raven, J. (2003). Raven Progressive Matrices. In R. S. McCallum (Ed.), Handbook of Nonverbal Assessment (pp. 223–237). Boston, MA: Springer US. doi: 10.1007/978-1-4615-0153-4_11 [Google Scholar]
  23. Johnson, P. C. D., Barry, S. J. E., Ferguson, H. M., & Müller, P. (2015). Power analysis for generalized linear mixed models in ecology and evolution. Methods in Ecology and Evolution, 6(2), 133–142. doi: 10.1111/2041-210X.12306 [Google Scholar]
  24. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291. doi: 10.2307/1914185 [Google Scholar]
  25. Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). General Performance on a Numeracy Scale among Highly Educated Samples. Medical Decision Making, 21(1), 37–44. doi:10.1177/0272989X0102100105 [Google Scholar]
  26. Lüdecke, D. (2018). Ggeffects: Tidy Data Frames of Marginal Effects from Regression Models. Journal of Open Source Software, 3(26), 772. doi: 10.21105/joss.00772 [Google Scholar]
  27. Lusardi, A. (2012). Numeracy, financial literacy, and financial decision-making (Tech. Rep. No.w17821). National Bureau of Economic Research. doi: 10.3386/w17821 [Google Scholar]
  28. Małecka, M. (2020). The normative decision theory in economics: A philosophy of science perspective. The case of the expected utility theory. Journal of Economic Methodology, 27(1), 36–50. doi:10.1080/1350178X.2019.1640891 [Google Scholar]
  29. McElreath, R. (2018). Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Chapman and Hall/CRC. doi: 10.1201/9781315372495 [Google Scholar]
  30. McGrew, K. S. (2021). CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 37(1), 1–10. doi: 10.1016/j.intell.2008.08.004 [Google Scholar]
  31. Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133–142. doi:10.1111/j.2041-210x.2012.00261.x [Google Scholar]
  32. Pachur, T., Hertwig, R., Gigerenzer, G., & Brandstätter, E. (2013). Testing process predictions of models of risky choice: A quantitative model comparison approach. Frontiers in Psychology, 4.doi: 10.3389/fpsyg.2013.00646 [Google Scholar]
  33. Peters, E., & Bjalkebring, P. (2015). Multiple numeric competencies: When a number is not just a number. Journal of Personality and Social Psychology, 108(5), 802–822. doi: 10.1037/pspp0000019 [Google Scholar]
  34. Reyna, V. F., Nelson, W. L., Han, P. K., & Dieckmann, N. F. (2009). How numeracy influences risk comprehension and medical decision making. Psychological Bulletin, 135(6), 943–973. doi:10.1037/a0017327 [Google Scholar]
  35. Rothman, R. L., Housam, R., Weiss, H., Davis, D., Gregory, R., Gebretsadik, T., ... Elasy, T. A. (2006). Patient Understanding of Food Labels: The Role of Literacy and Numeracy. American Journal of Preventive Medicine, 31(5), 391–398. doi:10.1016/j.amepre.2006.07.025 [Google Scholar]
  36. Russell, S., & Norvig, P. (2002). Artifi cial intelligence: A modern approach. Schönbrodt, F. D., & Wagenmakers, E.-J. (2018). Bayes factor design analysis: Planning for compelling evidence. Psychonomic Bulletin & Review, 25(1), 128–142. doi: 10.3758/s13423-017-1230-y [Google Scholar]
  37. Schwartz, L. M., Woloshin, S., Black, W. C., & Welch, H. G. (1997, December). The Role of Numeracy in Understanding the Benefi t of Screening Mammography. Annals of Internal Medicine, 127(11), 966–972. doi: 10.7326/0003-4819-127-11-199712010-00003 [Google Scholar]
  38. Sherry, A., & Henson, R. K. (2005). Conducting and Interpreting Canonical Correlation Analysis in Personality Research: A User-Friendly Primer. Journal of Personality Assessment, 84(1), 37–48. doi: 10.1207/s15327752jpa8401_09 [Google Scholar]
  39. Sobkow, A., Garrido, D., & Garcia-Retamero, R. (2020). Cognitive Abilities and Financial Decision Making. In T. Zaleskiewicz & J. Traczyk (Eds.), Psychological Perspectives on Financial Decision Making (pp. 71–87). Springer, Cham. doi: 10.1007/978-3-030-45500-2_4 [Google Scholar]
  40. Sobkow, A., Olszewska, A., & Traczyk, J. (2020). Multiple numeric competencies predict decision outcomes beyond fl uid intelligence and cognitive refl ection. Intelligence, 80, 101452. doi:10.1016/j.intell.2020.101452 [Google Scholar]
  41. Taleb, N. N. (2020). Statistical Consequences of Fat Tails: Real World preasymptotics, epistemology, and applications. arXiv:2001.10488. [Google Scholar]
  42. Thaler, R. (1980). Toward a positive theory of consumer choice. Journal of Economic Behavior & Organization, 1(1), 39–60. doi: 10.1016/0167-2681(80)90051-7 [Google Scholar]
  43. Traczyk, J., & Fulawka, K. (2016). Numeracy moderates the infl uence of task-irrelevant affect on probability weighting. Cognition, 151, 37–41. doi: 10.1016/j.cognition.2016.03.002 [Google Scholar]
  44. Traczyk, J., Sobkow, A., Fulawka, K., Kus, J., Petrova, D., & Garcia-Retamero, R. (2018). Numerate decision makers don’t use more effortful strategies unless it pays: A process tracing investigation of skilled and adaptive strategy selection in risky decision making. Judgment and Decision Making, 13(4), 372–381. [Google Scholar]
  45. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323. doi: 10.1007/BF00122574 [Google Scholar]

Full metadata record

Cite this record

APA style

Mondal, Supratik (2021). Sensitivity of numerate individuals to large asymmetry in outcomes: A registered replication of Traczyk et al. (2018). (2021). Sensitivity of numerate individuals to large asymmetry in outcomes: A registered replication of Traczyk et al. (2018). Decyzje, (35), 5-26. https://doi.org/ 10.7206/DEC.1733-0092.150a (Original work published 6/2021AD)

MLA style

Mondal, Supratik. “ Sensitivity Of Numerate Individuals To Large Asymmetry In Outcomes: A Registered Replication Of Traczyk Et Al. (2018)”. 6/2021AD. Decyzje, no. 35, 2021, pp. 5-26.

Chicago style

Mondal, Supratik. “ Sensitivity Of Numerate Individuals To Large Asymmetry In Outcomes: A Registered Replication Of Traczyk Et Al. (2018)”. Decyzje, Decyzje, no. 35 (2021): 5-26. doi: 10.7206/DEC.1733-0092.150a.