Calculate or wait: Is man an eager or a lazy intuitive statistician?

REFERENCES

• Aha, D. W. (Ed.). (1997). Lazy learning. Dordrecht: Kluwer Academic.
   Google Scholar
• Ashby, F. G., & Maddox, W. T. (2005). Human category learning. Annual Review of Psychology, 56(1), 149–178. doi:10.1146/annurev.psych.56.091103.070217
   PubMed Web of Science ®Google Scholar
• Brown, N. R., & Siegler, R. S. (1993). Metrics and mappings: A framework for understanding real-world quantitative estimation. Psychological Review, 100, 511–534. doi:10.1037/0033-295X.100.3.511
   PubMed Web of Science ®Google Scholar
• Brunswik, E. (1955). Representative design and probabilistic theory in functional psychology. Psychological Review, 62, 193–217. doi:10.1037/h0047470
   PubMed Web of Science ®Google Scholar
• Busemeyer, J. R., & Townsend, J. T. (1993). Decision field-theory: A dynamic cognitive approach to decision making in an uncertain environment. Psychological Review, 100, 432–459. doi:10.1037/0033-295X.100.3.432
   PubMed Web of Science ®Google Scholar
• Chater, N., Tenenbaum, J. B., & Yuille, A. (2006). Probabilistic models of cognition: Conceptual foundations. Trends in Cognitive Sciences, 10, 287–291. doi:10.1016/j.tics.2006.05.007
   PubMed Web of Science ®Google Scholar
• Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114. doi:10.1017/S0140525X01003922
   PubMed Web of Science ®Google Scholar
• DeLosh, E. L., Busemeyer, J. R., & McDaniel, M. A. (1997). Extrapolation: The sine qua non for abstraction in function learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 23, 968–986. doi:10.1037/0278-7393.23.4.968
   PubMed Web of Science ®Google Scholar
• Denrell, J. (2005). Why most people disapprove of me: Experience sampling in impression formation. Psychological Review, 112, 951–978. doi:10.1037/0033-295X.112.4.951
   PubMed Web of Science ®Google Scholar
• Dougherty, M. R., & Hunter, J. E. (2003). Hypothesis generation, probability judgment, and individual differences in working memory capacity. Acta Psychologica, 113, 263–282. doi:10.1016/S0001-6918(03)00033-7
   PubMed Web of Science ®Google Scholar
• Engelberg, J., Manski, C. F., & Williams, J. (2009). Comparing the point predictions and subjective probability distributions of professional forecasters. Journal of Business and Economic Statistics, 27, 30–41. doi:10.1198/jbes.2009.0003
   Web of Science ®Google Scholar
• Fiedler, K. (2000). Beware of samples! A cognitive-ecological sampling approach to judgment biases. Psychological Review, 107, 659–676. doi:10.1037/0033-295X.107.4.659
   PubMed Web of Science ®Google Scholar
• Fiedler, K., & Juslin, P. (2006). Information sampling and adaptive cognition. New York, NY: Cambridge University Press.
   Google Scholar
• Flannagan, M. J., Fried, L. S., & Holyoak, K. J. (1986). Distributional expectations and the induction of category structure. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 241–256. doi:10.1037/0278-7393.12.2.241
   PubMed Web of Science ®Google Scholar
• Fox, S., & Thornton, G. C. (1993). Implicit distribution-theory – The influence of cognitive representation of differentiation on actual ratings. Perceptual and Motor Skills, 76, 259–276. doi:10.2466/pms.1993.76.1.259
   Google Scholar
• Fried, L. S., & Holyoak, K. J. (1984). Induction of category distributions – A framework for classification learning. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10, 234–257. doi:10.1037/0278-7393.10.2.234
   PubMed Web of Science ®Google Scholar
• Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124–158. doi:10.2307/749671
   Web of Science ®Google Scholar
• Gaissmaier, W., Schooler, L. J., & Rieskamp, J. (2006). Simple predictions fueled by capacity limitations: When are they successful? Journal of Experimental Psychology: Learning, Memory, and Cognition, 32, 966–982. doi:10.1037/0278-7393.32.5.966
   PubMed Web of Science ®Google Scholar
• Galesic, M., & Garcia-Retamero, R. (2011). Graph literacy: A cross-cultural comparison. Medical Decision Making, 31, 444–457. doi:10.1177/0272989X10373805
   PubMed Web of Science ®Google Scholar
• Gigerenzer, G., & Murray, D. J. (1987). Cognition as intuitive statistics. Hillsdale, NJ: Erlbaum.
   Google Scholar
• Gilovich, T., Griffin, D. W., & Kahneman, D. (Eds.). (2002). Heuristics and biases: The psychology of intuitive judgment. New York, NY: Cambridge University Press.
   Google Scholar
• Goodwin, P. (1996). Statistical correction of judgmental point forecasts and decisions. Omega, 24, 551–559. doi:10.1016/0305-0483(96)00028-X
   Web of Science ®Google Scholar
• Greene, R. L. (1986). Effects of intentionality and strategy on memory for frequency. Journal of Experimental Psychology: Learning, Memory, and Cognition, 12, 489–495. doi:10.1037/0278-7393.12.4.489
   Web of Science ®Google Scholar
• Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday cognition. Psychological Science, 17, 767–773. doi:10.1111/j.1467-9280.2006.01780.x
   PubMed Web of Science ®Google Scholar
• Griffiths, T. L., & Tenenbaum, J. B. (2011). Predicting the future as Bayesian inference: People combine prior knowledge with observations when estimating duration and extent. Journal of Experimental Psychology: General, 140, 725–743. doi:10.1037/a0024899
   PubMed Web of Science ®Google Scholar
• Hansson, P., Juslin, P., & Winman, A. (2008). The role of short-term memory capacity and task experience for overconfidence in judgment under uncertainty. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34, 1027–1042. doi:10.1037/a0012638
   PubMed Web of Science ®Google Scholar
• Hendrick, C., & Constantini, A. F. (1970). Number averaging behavior – Primacy effect. Psychonomic Science, 19, 121–122.
   Google Scholar
• Hertwig, R., Barron, G., Weber, E. U., & Erev, I. (2004). Decisions from experience and the effect of rare events in risky choice. Psychological Science, 15, 534–539. doi:10.1111/j.0956-7976.2004.00715.x
   PubMed Web of Science ®Google Scholar
• Hora, S. C., Hora, J. A., & Dodd, N. G. (1992). Assessment of probability-distributions for continuous random-variables – A comparison of the bisection and fixed value methods. Organizational Behavior and Human Decision Processes, 51, 133–155. doi:10.1016/0749-5978(92)90008-U
   Web of Science ®Google Scholar
• Jako, R. A., & Murphy, K. R. (1990). Distributional ratings, judgment decomposition, and their impact on interrater agreement and rating accuracy. Journal of Applied Psychology, 75, 500–505. doi:10.1037/0021-9010.75.5.500
   Web of Science ®Google Scholar
• Juslin, P., Karlsson, L., & Olsson, H. (2008). Information integration in multiple cue judgment: A division of labor hypothesis. Cognition, 106, 259–298. doi:10.1016/j.cognition.2007.02.003
   PubMed Web of Science ®Google Scholar
• Juslin, P., & Persson, M. (2002). PROBabilities from EXemplars (PROBEX): A ‘lazy’ algorithm for probabilistic inference from generic knowledge. Cognitive Science, 26, 563–607. doi:10.1207/s15516709cog2605_2
   Web of Science ®Google Scholar
• Juslin, P., Winman, A., & Hansson, P. (2007). The naive intuitive statistician: A naive sampling model of intuitive confidence intervals. Psychological Review, 114, 678–703. doi:10.1037/0033-295X.114.3.678
   PubMed Web of Science ®Google Scholar
• Kahneman, D., & Miller, D. T. (1986). Norm theory: Comparing reality to its alternatives. Psychological Review, 93(2), 136–153. doi:10.1037/0033-295X.93.2.136
   Web of Science ®Google Scholar
• Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291. doi:10.2307/1914185
   Web of Science ®Google Scholar
• Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and Biases. New York, NY: Cambridge University Press. doi:10.1017/CBO9780511809477
   Google Scholar
• Kalish, M. L., Lewandowsky, S., & Kruschke, J. K. (2004). Population of linear experts: Knowledge partitioning and function learning. Psychological Review, 111, 1072–1099. doi:10.1037/0033-295X.111.4.1072
   PubMed Web of Science ®Google Scholar
• Kareev, Y., Arnon, S., & Horwitz-Zeliger, R. (2002). On the misperception of variability. Journal of Experimental Psychology: General, 131, 287–297. doi:10.1037/0096-3445.131.2.287
   PubMed Web of Science ®Google Scholar
• Lichtenstein, S., Slovic, P., Fischhoff, B., Layman, M., & Combs, B. (1978). Judged frequency of lethal events. Journal of Experimental Psychology: Human Learning and Memory, 4, 551–578. doi:10.1037/0278-7393.4.6.551
   Google Scholar
• Lindskog, M., Winman, A., & Juslin, P. (2013). Naïve point estimation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 39, 782–800. doi:10.1037/a0029670
   PubMed Web of Science ®Google Scholar
• 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(2), 165–188. doi:10.1037/0022-3514.57.2.165
   PubMed Web of Science ®Google Scholar
• Lipkus, I. M., & Peters, E. (2009). Understanding the role of numeracy in health: Proposed theoretical framework and practical insights. Health Education & Behavior, 36, 1065–1081. doi:10.1177/1090198109341533
   PubMed Web of Science ®Google Scholar
• Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). General performance on a numeracy scale among highly educated samples. Medical Decision Making, 21(1), 37–44. doi:10.1177/0272989X0102100105
   PubMed Web of Science ®Google Scholar
• Ludke, R. L., Stauss, F. F., & Gustafson, D. H. (1977). Comparison of five methods for estimating subjective-probability distributions. Organizational Behavior and Human Decision Processes, 19, 162–179. doi:10.1016/0030-5073(77)90060-5
   PubMed Web of Science ®Google Scholar
• Malmi, R. A., & Samson, D. J. (1983). Intuitive averaging of categorized numerical stimuli. Journal of Verbal Learning and Verbal Behavior, 22, 547–559. doi:10.1016/S0022-5371(83)90337-7
   Google Scholar
• Mozer, M., Pashler, H., & Homaei, H. (2008). Optimal predictions in everyday cognition: The wisdom of individuals or crowds? Cognitive Science, 32, 1133–1147. doi:10.1080/03640210802353016
   PubMed Web of Science ®Google Scholar
• Nisbett, R. E., Krantz, D. H., Jepson, C., & Kunda, Z. (1983). The use of statistical heuristics in everyday inductive reasoning. Psychological Review, 90, 339–363. doi:10.1037/0033-295X.90.4.339
   Web of Science ®Google Scholar
• Nisbett, R. E., & Kunda, Z. (1985). Perception of social distributions. Journal of Personality and Social Psychology, 48, 297–311. doi:10.1037/0022-3514.48.2.297
   PubMed Web of Science ®Google Scholar
• Nosofsky, R. M., & Johansen, M. K. (2000). Exemplar-based accounts of ‘multiple-system’ phenomena in perceptual categorization. Psychonomic Bulletin & Review, 7, 375–402.
   PubMed Web of Science ®Google Scholar
• Oaksford, M., & Chater, N. (2006). Bayesian rationality. Oxford: Oxford University Press.
   Google Scholar
• O'Hagan, A., Buck, C. E., Daneshkhah, A., Eiser, J. R., Garthwaite, P. H., Jenkinson, D. J., … Rakow, T. (2006). Uncertain judgements: Eliciting expert probabilities. Chichester: Wiley.
   Google Scholar
• Peters, E., Vastfjall, D., Slovic, P., Mertz, C. K., Mazzocco, K., & Dickert, S. (2006). Numeracy and decision making. Psychological Science, 17, 407–413. doi:10.1111/j.1467-9280.2006.01720.x
   PubMed Web of Science ®Google Scholar
• Peterson, C.R., & Beach, L. R. (1967). Man as an intuitive statistician. Psychological Bulletin, 68(1), 29–46. doi:10.1037/h0024722
   PubMed Web of Science ®Google Scholar
• Pitz, G. F., Leung, L. S., Hamilos, C., & Terpening, W. (1976). The use of probabilistic information in making predictions. Organizational Behavior and Human Performance, 17(1), 1–18. doi:10.1016/0030-5073(76)90050-7
   Web of Science ®Google Scholar
• Pollard, P. (1984). Intuitive judgments of proportions, means, and variances: A review. Current Psychology, 3(1), 5–18. doi:10.1007/BF02686528
   Google Scholar
• Reyna, F. V., Nelson, L. W., Han, K. P., & Dieckmann, F. N. (2009). How numeracy influences risk comprehension and medical decision making. Psychological Bulletin, 135, 943–973. doi:10.1037/a0017327
   PubMed Web of Science ®Google Scholar
• Slovic, P., Fischhoff, B., & Lichtenstein, S. (1977). Behavioral decision theory. Annual Review of Psychology, 28(1), 1–39. doi:10.1146/annurev.ps.28.020177.000245
   Web of Science ®Google Scholar
• Spencer, J. (1961). Estimating averages. Ergonomics, 4, 317–328. doi:10.1080/00140136108930533
   Web of Science ®Google Scholar
• Spencer, J. (1963). A further study of estimating averages. Ergonomics, 6, 255–265. doi:10.1080/00140136308930705
   Web of Science ®Google Scholar
• Stewart, N., Chater, N., & Brown, G. D. A. (2006). Decision by sampling. Cognitive Psychology, 53(1), 1–26. doi:10.1016/j.cogpsych.2005.10.003
   PubMed Web of Science ®Google Scholar
• Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011). How to grow a mind: Statistics, structure, and abstraction. Science, 331, 1279–1285. doi:10.1126/science.1192788
   PubMed Web of Science ®Google Scholar
• Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty – Heuristics and biases. Science, 185, 1124–1131. doi:10.1126/science.185.4157.1124
   PubMed Web of Science ®Google Scholar
• Tversky, A., & Koehler, D. J. (1994). Support theory: A nonextensional representation of subjective probability. Psychological Review, 101, 547–567. doi:10.1037/0033-295X.101.4.547
   Web of Science ®Google Scholar
• von Helversen, B., & Rieskamp, J. (2008). The mapping model: A cognitive theory of quantitative estimation. Journal of Experimental Psychology: General, 137, 73–96. doi:10.1037/0096-3445.137.1.73
   PubMed Web of Science ®Google Scholar
• Vul, W., Goodman, N. D., Griffiths, T. L., & Tenenbaum, J. B. (2009). One and done? Optimal decisions from very few samples. In Proceedings of the 31st Annual Conference of the Cognitive Science Society (pp. 66–72). Presented at the 31st annual conference of the cognitive science society.
   Google Scholar
• Winkler, R. L. (1967). Assessment of prior distributions in bayesian analysis. Journal of the American Statistical Association, 62(319), 776–800. doi:10.1080/01621459.1967.10500894
   Web of Science ®Google Scholar
• Zacks, R. T., Hasher, L., & Sanft, H. (1982). Automatic enconding of event frequency: Further findings. Journal of Experimental Psychology: Learning, Memory and Cognition, 8(2), 106–116. doi:10.1037/0278-7393.8.2.106
   Web of Science ®Google Scholar