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Original Articles

The power of representation and interpretation: Doubling statistical reasoning performance with icons and frequentist interpretations of ambiguous numbers

Pages 81-97 | Received 07 May 2013, Accepted 29 Oct 2013, Published online: 03 Dec 2013

REFERENCES

  • Ancker, J. S., Senathirajah, Y., Kukafka, R., & Starren, J. B. (2006). Design features of graphs in health risk communication: A systematic review. Journal of the American Medical Informatics Association, 13, 608–618. doi:10.1197/jamia.M2115
  • Barbey, A. K., & Sloman, S. A. (2007). Base-rate respect: From ecological rationality to dual processes. Behavioral and Brain Sciences, 30, 241–254.
  • Barrett, H. C. (2005). Enzymatic computation and cognitive modularity. Mind and Language, 20, 259–287. doi:10.1111/j.0268-1064.2005.00285.x
  • Barrett, H. C., & Kurzban, R. (2006). Modularity in cognition: Framing the debate. Psychological Review, 113, 628–647. doi:10.1037/0033-295X.113.3.628
  • Brase, G. L. (2002). Ecological and evolutionary validity: Comments on Johnson-Laird, Legrenzi, Girotto, Legrenzi, & Caverni's (1999) mental model theory of extensional reasoning. Psychological Review, 109, 722–728. doi:10.1037/0033-295X.109.4.722
  • Brase, G. L. (2008). Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning. Psychonomic Bulletin & Review, 15, 284–289. doi:10.3758/PBR.15.2.284
  • Brase, G. L. (2009). Pictorial representations in statistical reasoning. Applied Cognitive Psychology, 23, 369–381. doi:10.1002/acp.1460
  • Brase, G. L., Cosmides, L., & Tooby, J. (1998). Individuation, counting, and statistical inference: The roles of frequency and whole object representations in judgment under uncertainty. Journal of Experimental Psychology: General, 127(1), 3–21. doi:10.1037/0096-3445.127.1.3
  • Chapman, G. B., & Liu, J. (2009). Numeracy, frequency, and Bayesian reasoning. Judgment and Decision Making, 4, 34–40.
  • Cokely, E. T., Galesic, M., Schulz, E., Ghazal, S., & Garcia-Retamero, R. (2012). Measuring risk literacy: The Berlin numeracy test. Judgment & Decision Making, 7, 25–47.
  • Cosmides, L., & Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition, 58(1), 1–73. doi:10.1016/0010-0277(95)00664-8
  • Evans, J. S. B. T. (2007). Hypothetical thinking: Dual processes in reasoning and judgement. New York, NY: Psychology Press.
  • Fagerlin, A., Wang, C., & Ubel, P. A. (2005). Reducing the influence of anecdotal reasoning on people's health care decisions: Is a picture worth a thousand statistics? Medical Decision Making, 25, 398–405. doi:10.1177/0272989X05278931
  • Feldman-Stewart, D., Brundage, M. D., Hayter, C., Groome, P., Nickel, J. C., Downes, H., & Mackillop, W. J. (2000). What questions do patients with curable prostate cancer want answered? Medical Decision Making, 20(1), 7–19. doi:10.1177/0272989X0002000102
  • Feldman-Stewart, D., Brundage, M. D., & Zotov, V. (2007). Further insight into the perception of quantitative information: Judgments of gist in treatment decisions. Medical Decision Making, 27(1), 34–43. doi:10.1177/0272989X06297101
  • Gaissmaier, W., Wegwarth, O., Skopec, D., Müller, A.-S., Broschinski, S., & Politi, M. C. (2012). Numbers can be worth a thousand pictures: Individual differences in understanding graphical and numerical representations of health-related information. Health Psychology, 31, 286–296. doi:10.1037/a0024850
  • Garcia-Retamero, R., & Cokely, E. T. (2011). Effective communication of risks to young adults: Using message framing and visual aids to increase condom use and STD screening. Journal of Experimental Psychology: Applied, 17, 270–287. doi:10.1037/a0023677
  • Garcia-Retamero, R., & Galesic, M. (2010). How to reduce the effects of framing on messages about health. Journal of General Internal Medicine, 25, 1323–1329. doi:10.1007/s11606-010-1484-9
  • Garcia-Retamero, R., & Galesic, M. (2013). Transparent communication of health risks: Overcoming cultural differences. New York, NY: Springer.
  • Garcia-Retamero, R., Galesic, M., & Gigerenzer, G. (2010). Do icon arrays help reduce denominator neglect? Medical Decision Making, 30, 672–684. doi:10.1177/0272989X10369000
  • Garcia-Retamero, R., & Hoffrage, U. (2013). Visual representation of statistical information improves diagnostic inferences in doctors and their patients. Social Science and Medicine, 83, 27–33. doi:10.1016/j.socscimed.2013.01.034
  • Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest, 8, 53–96.
  • Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102, 684–704. doi:10.1037/0033-295X.102.4.684
  • Gigerenzer, G., Todd, P. M., & The ABC Research Group. (1999). Simple heuristics that make us smart. Oxford: Oxford University Press.
  • Girotto, V., & Gonzalez, M. (2001). Solving probabilistic and statistical problems: A matter of information structure and question form. Cognition, 78, 247–276. doi:10.1016/S0010-0277(00)00133-5
  • Girotto, V., & Gonzalez, M. (2008). Children's understanding of posterior probability. Cognition, 106, 325–344. doi:10.1016/j.cognition.2007.02.005
  • Girotto, V., & Gonzalez, M. (2011). Probability evaluations, expectations, and choices. In K. Manktelow, D. Over, & S. Elqayam (Eds.), The science of reason: A festschrift for Jonathan St B. T. Evans (pp. 37–51). New York, NY: Psychology Press.
  • Girotto, V., & Johnson-Laird, P. N. (2010). Conditionals and probability. In M. Oaksford & N. Chater (Eds.), Cognition and conditionals: Probability and logic in human thinking (pp. 103–115). New York, NY: Oxford University Press.
  • Hill, W. T., & Brase, G. L. (2012). When and for whom do frequencies facilitate performance? On the role of numerical literacy. The Quarterly Journal of Experimental Psychology, 65, 2343–2368. doi:10.1080/17470218.2012.687004
  • Hoffrage, U., & Gigerenzer, G. (1998). Using natural frequencies to improve diagnostic inferences. Academic Medicine, 73, 538–540. doi:10.1097/00001888-199805000-00024
  • Hoffrage, U., Gigerenzer, G., Krauss, S., & Martignon, L. (2002). Representation facilitates reasoning: What natural frequencies are and what they are not. Cognition, 84, 343–352. doi:10.1016/S0010-0277(02)00050-1
  • Hoffrage, U., Lindsey, S., Hertwig, R., & Gigerenzer, G. (2000). Communicating statistical information. Science, 290, 2261–2262. doi:10.1126/science.290.5500.2261
  • Ichikawa, S. (1989). The role of isomorphic schematic representation in the comprehension of counterintuitive Bayesian problems. Journal of Mathematical Behavior, 8, 269–281.
  • Johnson-Laird, P. N. (2006). How we reason. New York, NY: Oxford University Press.
  • Kleiter, G. (1994). Natural sampling: Rationality without base rates. In G. H. Fischer & D. Laming (Eds.), Contributions to mathematical psychology, psychometrics, and methodology (pp. 375–388). New York, NY: Springer.
  • Lindsey, S., Hertwig, R., & Gigerenzer, G. (2003). Communicating statistical DNA evidence. Jurimetrics, 43, 147–163.
  • Lipkus, I. M. (2007). Numeric, verbal, and visual formats of conveying health risks: Suggested best practices and future recommendations. Medical Decision Making, 27, 696–713. doi:10.1177/0272989X07307271
  • McCloy, R., Byrne, R. M. J., & Johnson-Laird, P. N. (2010). Understanding cumulative risk. The Quarterly Journal of Experimental Psychology, 63, 499–515. doi:10.1080/17470210903024784
  • Moro, R., Bodanza, G. A., & Freidin, E. (2011). Sets or frequencies? How to help people solve conditional probability problems. Journal of Cognitive Psychology, 23, 843–857. doi:10.1080/20445911.2011.579072
  • Neace, W. P., Michaud, S., Bolling, L., Deer, K., & Zecevic, L. (2008). Frequency formats, probability formats, or problem structure? A test of the nested-sets hypothesis in an extensional reasoning task. Judgment and Decision Making, 3, 140–152.
  • Over, D. E. (2007). Content-independent conditional inference. In M. J. Roberts (Ed.), Integrating the mind: Domain general vs domain specific processes in higher cognition (pp. 83–103). New York, NY: Psychology Press.
  • Paling, J. (2003). Strategies to help patients understand risks. British Medical Journal, 327, 745–748. doi:10.1136/bmj.327.7417.745
  • Pashler, H., & Wagenmakers, E.-J. (2012). Editor's introduction to the special section on replicability in psychology science: A crisis of confidence? Perspectives on Psychological Science, 7, 528–530. doi:10.1177/1745691612465253
  • Peters, E. (2012). Beyond comprehension: The role of numeracy in judgment and decisions. Current Directions in Psychological Science, 21(1), 31–35. doi:10.1177/0963721411429960
  • Ruscio, J. (2003). Comparing Bayes's theorem to frequency-based approaches to teaching Bayesian reasoning. Teaching of Psychology, 30, 325–328.
  • Sedlmeier, P. (1999). Improving statistical reasoning: Theoretical models and practical implications. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Sloman, S. A., Over, D., Slovak, L., & Stibel, J. M. (2003). Frequency illusions and other fallacies. Organizational Behavior & Human Decision Processes, 91, 296–309. doi:10.1016/S0749-5978(03)00021-9
  • Sperber, D. (1994). The modularity of thought and the epidemiology of representations. In L. A. Hirschfeld & S. A. Gelman (Eds.), Mapping the mind: Domain specificity in cognition and culture (pp. 39–67). New York, NY: Cambridge University Press.
  • Spiegelhalter, D., Pearson, M., & Short, I. (2011). Visualizing uncertainty about the future. Science, 333, 1393–1400. doi:10.1126/science.1191181
  • Stone, E. R., Yates, J. F., & Parker, A. M. (1997). Effects of numerical and graphical displays on professed risk-taking behavior. Journal of Experimental Psychology: Applied, 3, 243–256. doi:10.1037/1076-898X.3.4.243
  • Téglás, E., Girotto, V., Gonzalez, M., & Bonatti, L. L. (2007). Intuitions of probabilities shape expectations about the future at 12 months and beyond. Proceedings of the National Academy of Sciences, 104, 19156–19159. doi:10.1073/pnas.0700271104
  • Téglás, E., Vul, E., Girotto, V., Gonzalez, M., Tenenbaum, J. B., & Bonatti, L. L. (2011). Pure reasoning in 12-month-old infants as probabilistic inference. Science, 332, 1054–1059. doi:10.1126/science.1196404
  • Wolfe, C. R., & Reyna, V. F. (2010). Semantic coherence and fallacies in estimating joint probabilities. Journal of Behavioral Decision Making, 23, 203–223. doi:10.1002/bdm.650
  • Yamagishi, K. (2003). Facilitating normative judgments of conditional probability: frequency or nested sets? Experimental Psychology, 50, 97–106. doi:10.1026//1618-3169.50.2.97
  • Zacks, R. T., Hasher, L., & Sanft, H. (1982). Automatic encoding of event frequency: Further findings. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8, 106–116. doi:10.1037/0278-7393.8.2.106
  • Zacks, J. M., Speer, N., & Reynolds, J. R. (2009). Segmentation in reading and film comprehension. Journal of Experimental Psychology: General, 138, 307–327. doi:10.1037/a0015305
  • Zhu, L., & Gigerenzer, G. (2006). Children can solve Bayesian problems: The role of representation in mental computation. Cognition, 98, 287–308. doi:10.1016/j.cognition.2004.12.003

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