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  • Print publication year: 2005
  • Online publication date: February 2010

2 - Good Sampling, Distorted Views: The Perception of Variability


Time pressure, structural limitations of the cognitive system, or paucity of available data often force people to make do with but a sample, when they try to learn of the characteristics of their environment. In such cases, sample statistics must be relied upon to infer the parameter values in the population. Because sample data provide, by definition, only a partial view of reality, the degree to which that view is a veridical reflection of reality is of great importance. It is well known that, in the quest for accurate estimates of population parameters, larger samples are to be preferred over smaller ones. This is so since the variance of the sampling distribution of any statistic is inversely related to sample size (typically to the square root of it). Still, often the size of the sample available is quite small. Consider, for example, one important limiting factor, working-memory capacity – a structural characteristic of the human cognitive system that determines the number of items that can be considered simultaneously; it is about seven items for an average adult (Miller, 1956) and could even be considerably lower than that (see Cowan, 2001, for an estimate as low as four). Nonetheless, even if the samples used by people are typically quite small in size, some solace may be obtained if one could assume their statistics to provide unbiased estimates of the population parameters in question.

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Bacon, F. (1620/1905). Novum Organum (transl. R. L. Ellis & J. Spedding, edited by J. M. Robertson). London: George Routledge and Sons
Cowan, N. (2001). The magical number 4 in short-term memory: A consideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87–185
de-Jong, P. F., & Das-Smaal, E. A. (1995). Attention and intelligence: The validity of the Star Counting Test. Journal of Educational Psychology, 87, 80–92
Engle, R. W. (2002). Working memory capacity as executive attention. Current Directions in Psychological Science, 11, 19–23
Gilbert, D. T., & Malone, P. S. (1995). The correspondence bias. Psychological Bulletin, 117, 21–38
Gilbert, D. T., Pelham, B. W., & Krull, D. S. (1988). On cognitive busyness: When person perceivers meet persons perceived. Journal of Personality and Social Psychology, 54, 733–740
Hays, W. L. (1963). Statistics for psychologists. New York: Holt, Rinehart, & Winston
Hogarth, R. M., & Einhorn, H. J. (1992). Order effects in belief updating: The belief-adjustment model. Cognitive Psychology, 24, 1–55
Huttenlocher, J., & Burke, D. (1976). Why does memory span increase with age?Cognitive Psychology, 8, 1–31
Jurden, F. H. (1995). Individual differences in working memory and complex cognition. Journal of Educational Psychology, 87, 93–102
Kareev, Y. (1995). Through a narrow window: Working memory capacity and the detection of covariation. Cognition, 56, 263–269
Kareev, Y., Arnon, S., & Horwitz-Zeliger, R. (2002). On the misperception of variability. Journal of Experimental Psychology: General, 131, 287–297
Kareev, Y., Lieberman, I., & Lev, M. (1997). Through a narrow window: Sample size and the perception of correlation. Journal of Experimental Psychology: General, 126, 278–287
Linville, P. W., & Fischer, G. W. (1993). Exemplar and abstraction models of perceived group variability and stereotypicality. Social Cognition, 11, 92–125
Linville, P. W., & Fischer, G. W. (1998). Group variability and covariation: Effects of intergroup judgment and behavior. In Sedikides, C., Schopler, J., et al. (Eds.), Intergroup cognition and intergroup behavior (pp. 123–150). Mahwah, NJ: Lawrence Erlbaum
Linville, P. W., Fischer, G. W., & Salovey, P. (1989). Perceived distributions of the characteristics of in-group and out-group members: Empirical evidence and a computer simulation. Journal of Personality and Social Psychology, 57, 165–188
Linville, P. W., & Jones, E. E. (1980). Polarized appraisals of out-group members. Journal of Personality and Social Psychology, 38, 689–703
Mandler, G. (1967). Organization and Memory. In Spence, K. W. & Spence, J. T. (Eds.), The psychology of learning and motivation, (Vol. 1, pp. 328–372). New York: Academic Press
Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63, 81–97
Peterson, C. R., & Beach, L. F. (1967). Man as an intuitive statistician. Psychological Bulletin, 68, 29–46
Pollard, P. (1984). Intuitive judgments of proportions, means, and variances: A review. Current Psychological Research and Review, 3, 5–18
Ross, L. (1977). The intuitive psychologist and his shortcomings. In Berkowitz, L. (Ed.), Advances in experimental social psychology (Vol. 10, pp. 173–220). San Diego: Academic Press
Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105–110