Quality & Quantity

, Volume 48, Issue 1, pp 173–187 | Cite as

The use of imagery in statistical reasoning by university undergraduate students: a preliminary study

  • Maria Pietronilla Penna
  • Mirian Agus
  • Maribel Peró-Cebollero
  • Joan Guàrdia-Olmos
  • Eliano Pessa


Many students have difficulty in grasping several concepts that are related to the solution of statistical problems. The bibliography reports how the ability of students to solve problems can be affected by the mode of the statistical problem presentation: verbal–numerical and pictorial–graphical. The dual-coding theory predicts that the graphical representation mode should enhance students’ statistical reasoning. Solving these problems requires the building, by the subjects, of a mental model, which in turn relies on visuo-spatial processing. To test this hypothesis we analysed how the ability to solve problems of 473 undergraduate students is affected by the mode of the statistical problem presentation. The study used a quasi-experimental mixed design to explore how the student’s performance is related to visuo-spatial and numerical abilities, statistical expertise, time pressure and problem representation mode (verbal/pictorial). Data analysis, based on the Hierarchical Loglinear Model and then the Logit Model, highlighted that the effect of facilitation, induced by the graphical presentation mode, would seem more likely to occur in inexperienced subjects with high visuo-spatial competence.


Statistical reasoning Imagery Individual differences Visuo-spatial ability Numerical ability Statistical expertise 


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  1. Abedi J.A., Lord C.: The language factor in mathematics tests. Appl. Meas. Educ. (2010). doi: 10.1207/S15324818AME1403_2
  2. Agresti A.: An Introduction to Categorical Data Analysis. Wiley–Blackwell, New York (2007)CrossRefGoogle Scholar
  3. Aickin M.: Graphics for the minimal sufficient cause model. Qual. Quant. 35, 49–60 (2001)CrossRefGoogle Scholar
  4. Beilock S.L., DeCaro M.S.: From poor performance to success under stress: working memory, strategy selection, and mathematical problem solving under pressure. J. Exp. Psychol. Learn. Mem. Cogn. 33, 983 (2007)CrossRefGoogle Scholar
  5. Bennett R.E., Morley M., Quardt D., Rock D.A.: Graphical modeling: a new response type for measuring the qualitative component of mathematical reasoning. Appl. Meas. Educ. 13, 303–322 (2000)CrossRefGoogle Scholar
  6. Bezerra R.F., Jalloh S., Stevenson J.: Formulating hypotheses graphically in social research. Qual. Quant. 32, 327–353 (1998)CrossRefGoogle Scholar
  7. Blajenkova O., Kozhevnikov M.: The new object-spatial-verbal cognitive style model: theory and measurement. Appl. Cogn. Psychol. 23, 638–663 (2009). doi: 10.1002/acp.1473 CrossRefGoogle Scholar
  8. Borooah V.K.: Logit and Probit: Ordered and Multinomial Models. Sage Publications, Inc., Thousand Oaks (2001)Google Scholar
  9. Brase G.L.: Pictorial representations in statistical reasoning. Appl. Cogn. Psychol. 23, 369–381 (2009). doi: 10.1002/acp.1460 CrossRefGoogle Scholar
  10. Britt, D.W., Chen, Y.C.: Increasing the capacity of conceptual diagrams to embrace contextual complexity. Qual. Quant. 1–10 (2011). doi: 10.1007/s11135-011-9479-0
  11. Cinanni V., Marucci F.S., Penna M.P., Pascalis V.De : Dimensioni dell’immaginazione: validazione di uno strumento di misura delle capacità immaginative. G. Ital. Psicol. 20, 109–138 (1993)Google Scholar
  12. Cook D.: Incorporating exploratory methods using dynamic graphics into multivariate statistics classes: curriculum development. In: Shelley, M.C., Yore, L.D., Hand, B. (eds.) Quality Research in Literacy and Science Education, pp. 337–355. Springer, Dordrecht (2009)CrossRefGoogle Scholar
  13. Cook A.R., Teo S.W.L.: The communicability of graphical alternatives to tabular displays of statistical simulation studies. PLoS ONE 6, e27974 (2011). doi: 10.1371/journal.pone.0027974 CrossRefGoogle Scholar
  14. Cosmides L., Tooby J.: Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition 58, 1–73 (1996)CrossRefGoogle Scholar
  15. Evans J.S.B.T., Handley S.J., Neilens H., Over D.: The influence of cognitive ability and instructional set on causal conditional inference. Q. J. Exp. Psychol. 63, 892–909 (2010)CrossRefGoogle Scholar
  16. Friedman J.H., Tukey J.W.: A projection pursuit algorithm for exploratory data analysis. IEEE Trans Comput 100, 881–890 (1974)CrossRefGoogle Scholar
  17. Galesic M., Garcia-Retamero R.: Graph Literacy. Med. Decis. Mak. 31, 444 (2011)CrossRefGoogle Scholar
  18. Garcia-Retamero R., Galesic M., Gigerenzer G.: Cómo favorecer la comprensión y la comunicación de los riesgos sobre la salud. Psicothema 23, 599–605 (2011)Google Scholar
  19. Garfield J.: The challenge of developing statistical reasoning. J. Stat. Educ. 10, 58–69 (2002)Google Scholar
  20. Garfield J.: Assessing statistical reasoning. Stat. Educ. Res. J. 2, 22–38 (2003)Google Scholar
  21. Garfield J., Ben-Zvi D.: Developing students’ statistical reasoning: connecting research and teaching practice. Springer, New York (2008)Google Scholar
  22. Gigerenzer G., Goldstein D.G.: Reasoning the fast and frugal way: models of bounded rationality. Psychol. Rev. 103, 650 (1996)CrossRefGoogle Scholar
  23. Gigerenzer G., Hoffrage U.: How to improve Bayesian reasoning without instruction: frequency formats. Psychol. Rev. 102, 684 (1995)CrossRefGoogle Scholar
  24. Gigerenzer G., Hug K.: Domain-specific reasoning: social contracts, cheating, and perspective change. Cognition 43, 127–171 (1992)CrossRefGoogle Scholar
  25. Girotto V., Gonzalez M.: Solving probabilistic and statistical problems: a matter of information structure and question form. Cognition 78, 247–276 (2001)CrossRefGoogle Scholar
  26. Green J.A.: Loglinear analysis of cross-classified ordinal data: applications in developmental research. Child Dev. 59, 1–25 (1988)CrossRefGoogle Scholar
  27. Hoffrage U., Gigerenzer G., Krauss S., Martignon L.: Representation facilitates reasoning: what natural frequencies are and what they are not. Cognition 84, 343–352 (2002)CrossRefGoogle Scholar
  28. Hofstetter C.H.: Contextual and mathematics accommodation test effects for English-language learners. Appl. Meas. Educ. 16, 159–188 (2003)CrossRefGoogle Scholar
  29. Johnson-Laird P.N.: Mental Models: Toward a Cognitive Science of Language, Inference and Consciousness. Harvard University Press, Cambridge (1983)Google Scholar
  30. Keeley J., Zayac R., Correia C.: Curvilinear relationships between statistics anxiety and performance among undergraduate students: evidence for optimal anxiety. Stat. Educ. Res. J. 7, 4–15 (2008)Google Scholar
  31. Kellen V., Chan S., Fang X.: Facilitating conditional probability problems with visuals. In: Jacko, J. (ed.) Human–Computer Interaction. Interaction Platforms and Techniques, pp. 63–71. Springer, Berlin (2007)CrossRefGoogle Scholar
  32. Konold C.: Informal conceptions of probability. Cogn. Instr. 6, 59–98 (1989). doi: 10.1207/s1532690xci0601_3 CrossRefGoogle Scholar
  33. Lunsford, M.L., Poplin, P.: From research to practice: basic mathematics skills and success in introductory statistics. J. Stat. Educ. 19. (2011). Accessed 26 Feb 2012
  34. Marradi A.: Metodologia delle scienze sociali. Il Mulino, Bologna (2007)Google Scholar
  35. Maule A.J., Hockey G.R.J., Bdzola L.: Effects of time-pressure on decision-making under uncertainty: changes in affective state and information processing strategy. Acta Psychol. 104, 283–301 (2000)CrossRefGoogle Scholar
  36. Moro R., Bodanza G.A.: El debate acerca del efecto facilitador en problemas de probabilidad condicional:?‘ Un caso de experimentación crucial?. Interdisciplinaria 27, 163–174 (2010)Google Scholar
  37. Moro R., Bodanza G.A., Freidin E.: Sets or frequencies? How to help people solve conditional probability problems. J. Cogn. Psychol. 23, 843–857 (2011)CrossRefGoogle Scholar
  38. Onwuegbuzie A.J., Wilson V.A.: Anxiety: nature, etiology, antecedents, effects, and treatments—a comprehensive review of the literature. Teach. High. Educ. 8, 195–209 (2003)CrossRefGoogle Scholar
  39. Paivio A.: Imagery and Verbal Processes. Holt, Rinehart and Winston, New York (1971)Google Scholar
  40. Perepiczka M., Chandler N., Becerra M.: Relationship between graduate students’ statistics self-efficacy, statistics anxiety, attitude toward statistics, and social support. Prof. Couns. Res. Pract. 1, 99–108 (2011)Google Scholar
  41. Pessa, E., Penna, M.P.: Manuale di scienza cognitiva. Intelligenza artificiale classica e psicologia cognitiva. Editori Laterza, Roma (2000)Google Scholar
  42. Rieskamp J., Hoffrage U.: Inferences under time pressure: how opportunity costs affect strategy selection. Acta Psychol. 127, 258–276 (2008)CrossRefGoogle Scholar
  43. Rumsey D.J.: Statistical literacy as a goal for introductory statistics courses. J. Stat. Educ. 10, 6–13 (2002)Google Scholar
  44. Sedlmeier P.: Improving Statistical Reasoning by Using the Right Representational Format. Erlbaum, Mahwah (2002)Google Scholar
  45. Sloman S.A., Over D., Slovak L., Stibel J.M.: Frequency illusions and other fallacies. Organ. Behav. Hum. Decis. Process. 91, 296–309 (2003)CrossRefGoogle Scholar
  46. Tempelaar, D.T.: Statistical reasoning assessment: an analysis of the SRA instrument. Paper presented at the ARTIST conference on assessment in statistics, Lawrence University, 2004Google Scholar
  47. Tempelaar D.T., Gijselaers W.H., Van der Loeff S.S., Nijhuis J.F.H.: A structural equation model analyzing the relationship of student achievement motivations and personality factors in a range of academic subject-matter areas. Contemp. Educ. Psychol. 32, 105–131 (2007)CrossRefGoogle Scholar
  48. Thurstone, L.L., Thurstone, T.G.: PMA: Abilità mentali primarie: Manuale di istruzioni livello intermedio [Primary mental abilities (1963)] Organizzazioni Speciali, Firenze (1981)Google Scholar
  49. Tubau E.: Enhancing probabilistic reasoning: the role of causal graphs, statistical format and numerical skills. Learn. Individ. Differ. 18, 187–196 (2008)CrossRefGoogle Scholar
  50. Tufte E.R.: The Visual Display of Quantitative Information. Graphics Press, Cheshire (2001)Google Scholar
  51. Tversky A., Kahneman D.: Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychol. Rev. 90, 293 (1983)CrossRefGoogle Scholar
  52. Valero-Mora, P.M., Ledesma, R.D.: Using interactive graphics to teach multivariate data analysis to psychology students. J. Stat. Educ. 19. (2011). Accessed 10 Jan 2012
  53. Wild C., Pfannkuch M.: Statistical thinking in empirical enquiry. Int. Stat. Rev. 67, 223–248 (1999)Google Scholar
  54. Yamagishi K.: Facilitating normative judgments of conditional probability: frequency or nested sets?. Exp. Psychol. 50, 97–106 (2003)CrossRefGoogle Scholar
  55. Zhu L., Gigerenzer G.: Children can solve Bayesian problems: the role of representation in mental computation. Cognition 98, 287–308 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Maria Pietronilla Penna
    • 1
  • Mirian Agus
    • 1
    • 2
  • Maribel Peró-Cebollero
    • 3
  • Joan Guàrdia-Olmos
    • 3
  • Eliano Pessa
    • 4
  1. 1.Department of Pedagogy, Psychology and Philosophy, Faculty of Educational SciencesUniversity of Cagliari, ItalyCagliariItaly
  2. 2.Department of Methodology of the Behavioural Sciences, Faculty of PsychologyUniversity of BarcelonaBarcelonaSpain
  3. 3.Department of Methodology of the Behavioral Sciences, Faculty of PsychologyUniversity of Barcelona, SpainBarcelonaSpain
  4. 4.Department of Psychology, Faculty of Letters and PhilosophyUniversity of Pavia, ItalyPaviaItaly

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