Abstract
In a causally complex world, two (or more) factors may simultaneously be potential causes of an effect. To evaluate the causal efficacy of a factor, the alternative factors must be controlled for (orconditionalized on). Subjects judged the causal strength of two potential causes of an effect that covaried with each other, thereby setting up a Simpson's paradox—a situation in which causal judgments should vary widely depending on whether or not they are conditionalized on the alternative potential cause. In Experiments 1 (table format) and 2 (trial-by-trial format), the subjects did conditionalize their judgments for one causal factor on a known alternative cause. The subjects also demonstrated that they knew what information was needed to properly make causal judgments when two potential causes are available. In Experiment 3 (trial-by-trial), those subjects who were not told about the causal mechanism by which the alternative cause operated were less likely to conditionalize on it. However, the more a subject recognized the covariation between the alternative cause and the effect, the more the subject conditionalized on it. Such behavior may arise from the interaction between bottom-up and top-down processing.
Article PDF
Similar content being viewed by others
References
Ahn, W., Kalish, C. W., Medin, D. L., &Gelman, S. A. (1995). The role of covariation versus mechanism information in causal attribution.Cognition,54, 299–352.
Baker, A. G., Mercier, P., Vallée-Tourangeau, F., Frank, R., &Pan, M. (1993). Selective associations and causality judgments: Presence of a strong causal factor may reduce judgments of a weaker one.Journal of Experimental Psychology: Learning, Memory, & Cognition,19, 414–432.
Bullock, M., Gelman, R., &Baillargeon, R. (1982). The development of causal reasoning. In W. J. Friedman (Ed.),The developmental psychology of time (pp. 209–254). San Diego: Academic Press.
Cartwright, N. (1979).How the laws of physics lie. Oxford: Oxford University Press, Clarendon Press.
Chapman, G. B. (1991). Trial order affects cue interaction in contingency judgment.Journal of Experimental Psychology: Learning, Memory, & Cognition,17, 837–854.
Chapman, G. B., &Robbins, S. J. (1990). Cue interaction in human contingency judgment.Memory & Cognition,18, 537–545.
Cheng, P. W. (1993). Separating causal laws from casual facts: Pressing the limits of statistical relevance. In D. L. Medin (Ed.),The psychology of learning & motivation: Advances in research and theory (Vol. 30, pp. 215–264). San Diego: Academic Press.
Cheng, P. W. (1997). From covariation to causation: A causal power theory.Psychological Review,104, 367–405.
Flexser, A. J. (1981). Homogenizing the 2 3 2 contingency table: A method for removing dependencies due to subject and item differences.Psychological Review,88, 327–339.
Gigerenzer, G., Hell, W., &Blank, H. (1988). Presentation and content: The use of base rates as a continuous variable.Journal of Experimental Psychology: Human Perception & Performance, 14, 513–525.
Goedert, K. M., & Spellman, B. A. (2000).Controlling for alternative causes may require attention; discounting does not. Unpublished manuscript, University of Virginia.
Hasher, L., &Zacks, R. T. (1984). Automatic processing of fundamental information: The case of frequency of occurrence.American Psychologist,39, 1372–1388.
Hintzman, D. L. (1980). Simpson's paradox and the analysis of memory retrieval.Psychological Review,87, 398–410.
Kao, S., &Wasserman, E.A. (1993). Assessment of an information integration account of contingency judgment with examination of subjective cell importance and method of information presentation.Journal of Experimental Psychology: Learning, Memory, & Cognition,19, 1363–1386.
Koehler, J. J. (1996). The base rate fallacy reconsidered: Descriptive, normative and methodological challenges.Behavioral & Brain Sciences,19, 1–53.
Martin, E. (1981). Simpson's paradox resolved: A reply to Hintzman.Psychological Review,88, 372–374.
Medin, D. L., &Schaffer, M. M. (1978). Context theory of classification learning.Psychological Review,85, 207–238.
Melz, E. R., Cheng, P. W., Holyoak, K. J., &Waldmann, M. R. (1993). Cue competition in human categorization: Contingency or the Rescorla-Wagner learning rule? Comment on Shanks (1991).Journal of Experimental Psychology: Learning, Memory, & Cognition,19, 1398–1410.
Paulos, J. A. (1988).Innumeracy: Mathematical illiteracy and its consequences. New York: Vintage Books.
Pearl, J. (2000).Causality: Models, reasoning, and inference. New York: Cambridge University Press.
Price, P. C., &Yates, J. F. (1993). Judgmental overshadowing: Further evidence of cue interaction in contingency judgment.Memory & Cognition,21, 561–572.
Price, P. C., &Yates, J. F. (1995). Associative and rule-based accounts of cue interaction in contingency judgment.Journal of Experimental Psychology: Learning, Memory, & Cognition,21, 1639–1655.
Salmon, W. C. (1984).Scientific explanation and the causal structure of the world. Princeton, NJ: Princeton University Press.
Schaller, M. (1992a). In-group favoritism and statistical reasoning in social inference: Implications for formation and maintenance of group stereotypes.Journal of Personality & Social Psychology,63, 61–74.
Schaller, M. (1992b). Sample size, aggregation, and statistical reasoning in social inference.Journal of Experimental Social Psychology,28, 65–85.
Schaller, M., &O'Brien, M. (1992). “Intuitive analysis of covariance” and group stereotype formation.Personality & Social Psychology Bulletin,18, 776–785.
Shaklee, H., &Mims, M. (1982). Sources of error in judging event covariations: Effects of memory demands.Journal of Experimental Psychology: Learning, Memory, & Cognition,8, 208–224.
Shanks, D. R. (1993). Human instrumental learning: A critical review of data and theory.British Journal of Psychology,84, 319–354.
Shanks, D. R. (1995). Is human learning rational?Quarterly Journal of Experimental Psychology,48A, 257–279.
Simpson, E. H. (1951). The interpretation of interaction in contingency tables.Journal of the Royal Statistical Society: Series B,13, 238–241.
Spellman, B. A. (1993).The construction of causal explanations. Unpublished doctoral dissertation, University of California, Los Angeles.
Spellman, B. A. (1996a). Acting as intuitive scientists: Contingency judgments are made while controlling for alternative potential causes.Psychological Science,7, 337–342.
Spellman, B. A. (1996b).Conditionalizing causality. InD. R. Shanks, K. J. Holyoak, &D. L. Medin (Eds.),The psychology of learning and motivation: Vol. 34. Causal learning (pp. 167–206). San Diego: Academic Press.
Spellman, B.A. (1996c). The implicit use of base rates in experiential and ecologically valid tasks.Behavioral & Brain Sciences,19, 38.
Tversky, A., &Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases.Science,185, 1124–1131. [Reprinted in D. Kahneman, P. Slovic, & A. Tversky (Eds.) (1982).Judgment under uncertainty: Heuristics and biases (pp. 3-20). New York: Cambridge University Press.]
Tversky, A., &Kahneman, D. (1982). Evidential impact of base rates. In D. Kahneman, P. Slovic, & A. Tversky (Eds.),Judgment under uncertainty: Heuristics and biases (pp. 153–162). New York: Cambridge University Press.
Wainer, H. (1986). Minority contributions to the SAT score turnaround: An example of Simpson's paradox.Journal of Educational Statistics,11, 239–244.
Waldmann, M. R. (1996). Knowledge-based causal induction. In D. R. Shanks, K. J. Holyoak, & D. L. Medin (Eds.),The psychology of learning and motivation: Vol. 34. Causal learning (pp. 47–88). San Diego: Academic Press.
Waldmann, M. R., &Hagmayer, Y. (1995). When a cause simultaneously produces and prevents an effect. In J. D. Moore & J. F. Lehman (Eds.),Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society (pp. 425–430). Hillsdale, NJ: Erlbaum.
Ward, W.C., &Jenkins, H.M. (1965). The display of information and the judgment of contingency.Canadian Journal of Psychology,19, 231–241.
Wasserman, E. A., Elek, S. M., Chatlosh, D. L., &Baker, A. G. (1993). Rating causal relations: Role of probability in response-outcome contingency.Journal of Experimental Psychology: Learning, Memory, & Cognition,19, 174–188.
White, P. A. (1995). Use of prior beliefs in the assignment of causal roles: Causal powers versus regularity-based accounts.Memory & Cognition,23, 243–254.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Spellman, B.A., Price, C.M. & Logan, J.M. How two causes are different from one: The use of (un)conditional information in Simpson's paradox. Memory & Cognition 29, 193–208 (2001). https://doi.org/10.3758/BF03194913
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03194913