Abstract
The idea that naturally sampled frequencies facilitate performance in statistical reasoning tasks because they are a cognitively privileged representational format has been challenged by findings that similarly structured numbers presented as chances similarly facilitate performance, on the basis of the claim that these are technically single-event probabilities. A crucial opinion, however, is that of the research participants, who possibly interpret chances as de facto frequencies. A series of experiments here indicate that not only is performance improved by clearly presented natural frequencies, rather than chances phrasing, but also that participants who interpreted chances as frequencies, rather than as probabilities, were consistently better at statistical reasoning. This result was found across different variations of information presentation and across different populations.
This is a preview of subscription content, log in via an institution to check access.
References
Atkinson, D., & Peijnenburg, J. (1999). Probability as a theory dependent concept. Synthese, 118, 307–328.
Brase, G. L., & Barbey, A. K. (2006). Mental representations of statistical information. In A. Columbus (Ed.), Advances in psychology research (Vol. 41, pp. 91–113). New York: Nova.
Brase, G. L., Fiddick, L., & Harries, C. (2006). Participant recruitment methods and statistical reasoning performance. Quarterly Journal of Experimental Psychology, 59, 965–976.
Cosmides, L., & Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty. Cognition, 58, 1–73.
Evans, J. S. B. T., Handley, S. J., Perham, N., Over, D. E., & Thompson, V. A. (2000). Frequency versus probability formats in statistical word problems. Cognition, 77, 197–213.
Gigerenzer, G. (1994). Why the distinction between single-event probabilities and frequencies is important for psychology (and vice versa). In G. Wright & P. Ayton (Eds.), Subjective probability (pp. 129–161). Chichester, U.K.: Wiley.
Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102, 684–704.
Gigerenzer, G., Todd, P. M., & the ABC Research Group (1999). Simple heuristics that make us smart. Oxford: Oxford University Press.
Girotto, V., & Gonzalez, M. (2000). Strategies and models in statistical reasoning. In W. Schaeken & G. De Vooght (Eds.), Deductive reasoning and strategies (pp. 267–285). Mahwah, NJ: Erlbaum.
Girotto, V., & Gonzalez, M. (2001). Solving probabilistic and statistical problems: A matter of information structure and question form. Cognition, 78, 247–276.
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.
Howson, C., & Urbach, P. (1993). Scientific reasoning: The Bayesian approach (2nd ed.). Chicago: La Salle.
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: Springer.
Sloman, S. A., Over, D., Slovak, L., & Stibel, J. M. (2003). Frequency illusions and other fallacies. Organizational Behavior & Human Decision Processes, 91, 296–309.
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. 38–67). Cambridge: Cambridge University Press.
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.
Von Mises, R. (1957). Probability, statistics, and truth (2nd rev. English ed.). New York: Macmillan.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brase, G.L. Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning. Psychonomic Bulletin & Review 15, 284–289 (2008). https://doi.org/10.3758/PBR.15.2.284
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3758/PBR.15.2.284