Improving User Performance in Conditional Probability Problems with Computer-Generated Diagrams

  • Vince Kellen
  • Susy Chan
  • Xiaowen Fang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8006)


Many disciplines in everyday life depend on improved performance in probability problems. Most adults struggle with conditional probability problems and prior studies have shown user accuracy is less than 50%. This study examined user performance when aided with computer-generated Venn and Euler-type diagrams in a non-learning context. Following relational complexity, working memory and mental model theories, this study manipulated problem complexity in diagrams and text-only displays. Partially consistent with the study hypotheses, complex visuals outperformed complex text-only displays and simple text-only displays outperformed complex text only displays. However, a significant interaction between users’ spatial ability and the use of diagram displays led to a reversal of performance for low-spatial users in one of the diagram displays. Participants with less spatial ability were significantly impaired in their ability to solve problems with less relational complexity when aided by a diagram.


Human-computer interaction diagrams Bayesian reasoning relational complexity spatial ability working memory individual differences mental models 


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  1. 1.
    Gigerenzer, G., Hoffrage, U.: How to improve Bayesian reasoning without instruction: frequency formats. Psychological Review 102, 684–701 (1995)CrossRefGoogle Scholar
  2. 2.
    Kahnamen, D., Lovallo, D.: Timid choices and bold forecasts: a cognitive perspective on risk taking. Management Science 39(1), 17–31 (1993)CrossRefGoogle Scholar
  3. 3.
    Sedlmeier, P.: How to improve statistical thinking: Choose the task wisely and learn by doing. Instructional Science 28, 227–262 (2000)CrossRefGoogle Scholar
  4. 4.
    Baddeley, A.: Working memory. Clarendon Press, Oxford (1986)Google Scholar
  5. 5.
    Miyake, A., Shah, P.: An Introduction. In: Miyake, A., Shah, P. (eds.) Models of Working Memory. Cambridge University Press (1999)Google Scholar
  6. 6.
    Johnson-Laird, P.N., Legrenzi, P., Girotto, V., Legrenzi, M.S.: Naive probability: A mental model theory of extensional reasoning. Psychological Review 106, 62–88 (1999)CrossRefGoogle Scholar
  7. 7.
    Fangmeier, T., Knauff, M., Ruff, C., Sloutsky, V.: fMRI evidence for a three-stage model of deductive reasoning. Journal of Cognitive Neuroscience 18(3), 320–334 (2006)CrossRefGoogle Scholar
  8. 8.
    Knauff, M., Jola, C., Strube, G.: Spatial reasoning: No need for visual information. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 447–457. Springer, Heidelberg (2001)Google Scholar
  9. 9.
    Ruff, C.C., Knauff, M., Fangmeier, T., Spreer, J.: Reasoning and working memory: Common and distinct neuronal processes. Neuropsychologia 41, 1241–1253 (2003)CrossRefGoogle Scholar
  10. 10.
    Eddy, D.M.: Probabilistic reasoning in clinical medicine: Problems and opportunities. In: Kahneman, D., Slovic, P., Tversky, A. (eds.) Judgment under Uncertainty: Heuristics and Biases, pp. 249–267. Cambridge University Press, Cambridge (1982)CrossRefGoogle Scholar
  11. 11.
    Gigerenzer, G., Hoffrage, U.: Overcoming difficulties in Bayesian Reasoning: A reply to Lewis & Keren and Mellers & McGraw. Psychological Review 106, 425–430 (1999)CrossRefGoogle Scholar
  12. 12.
    Sloman, S.A., Over, D., Slovak, L., Stibel, J.M.: Frequency illusions and other fallacies. Organizational Behavior and Human Decision Processes 91, 296–301 (2003)CrossRefGoogle Scholar
  13. 13.
    Brase, G.L.: Pictorial representations in statistical reasoning. Applied Cognitive Psychology (2008), doi:10.1002/acp.1460Google Scholar
  14. 14.
    Calvillo, D.P., DeLeeuw, K.E., Revlin, R.: Deduction with Euler Circles: Diagrams That Hurt. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds.) Diagrams 2006. LNCS (LNAI), vol. 4045, pp. 199–203. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Halford, G.S., Wilson, W.H., Phillips, S.: Processing capacity defined by relational complexity: Implications for comparative, developmental, and cognitive psychology. Behavioral and Brain Sciences (21), 803–865 (1998)Google Scholar
  16. 16.
    Cowan, N.: The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences 24, 87–185 (2000)CrossRefGoogle Scholar
  17. 17.
    Cowan, N., Elliott, E.M., Saults, J.S., Morey, C.C., Mattox, S., Hismjatullina, A., Conway, A.R.: On the capacity of attention: Its estimation and its role in working memory and cognitive aptitudes. Cognitive Psychology 51, 42–100 (2005)CrossRefGoogle Scholar
  18. 18.
    Brase, G.L., Cosmides, L., Tooby, J.: Individuation, counting, and statistical inference: the role of frequency and whole-object representations in judgment under uncertainty. Journal of Experimental Psychology: General 127(1), 3–21 (1998)CrossRefGoogle Scholar
  19. 19.
    Klauer, K.C., Stegmaier, R., Meiser, T.: Working memory involvement in propositional and spatial reasoning. Thinking and Reasoning 3(1), 9–47 (1997)CrossRefGoogle Scholar
  20. 20.
    Cowan, N.: What are the differences between long-term, short-term, and working memory? In: Sossin, W.S., Lacaille, J.-C., Castellucci, V.F., Belleville, S. (eds.) Progress in Brain Research, vol. 169. Elsevier B.V. (2008)Google Scholar
  21. 21.
    Miller, G.A.: The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review 63, 81–97 (1956)CrossRefGoogle Scholar
  22. 22.
    Halford, G.S., Wilson, W.H., Phillips, S.: Relational knowledge: The foundation of higher cognition. Trends in Cognitive Sciences 14(11), 497–505 (2010)CrossRefGoogle Scholar
  23. 23.
    Kroger, J.K., Sabb, F.W., Fales, C.I., Bookheimer, S.Y., Cohen, M.S., Holyoak, K.J.: Recruitment of anterior dorsolateral prefrontal cortex in human reasoning: a parametric study of relational complexity. Cerebral Cortex 12, 477–485 (2002)CrossRefGoogle Scholar
  24. 24.
    Halford, G.S., Cowan, N., Andrews, G.: Separating cognitive capacity from knowledge: A new hypothesis. Trends in Cognitive Science 11(6), 236–242 (2007)CrossRefGoogle Scholar
  25. 25.
    Hegarty, M.: Individual differences in use of diagrams as memory in mechanical reasoning. Learning and Individual Differences 9(1), 19–42 (1997)CrossRefGoogle Scholar
  26. 26.
    Ekstrom, R.B., French, J.W., Harman, H.H.: Manual for kit of factor-referenced cognitive tests. Educational Testing Service, Princeton (1976)Google Scholar
  27. 27.
    Hegarty, M., Waller, D.: Individual differences in spatial ability. In: Shah, P., Miyake, A. (eds.) The Cambridge Handbook of Visuospatial Thinking, pp. 121–169. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  28. 28.
    Miyake, A., Friedman, N.P., Rettinger, D.A., Shah, P., Hegarty, M.: How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. Journal of Experimental Psychology: General 130(4), 621–640 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vince Kellen
    • 1
  • Susy Chan
    • 1
  • Xiaowen Fang
    • 1
  1. 1.College of Computing and Digital MediaDePaul UniversityChicagoUSA

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