Intuitions about sample size: The empirical law of large numbers

Journal of Behavioral Decision Making

Volumn 10, Issue 1, 1997, Pages 33-51

  Sedlmeier, Peter ^a   Gigerenzer, Gerd ^b  

^a UNIVERSITY OF PADERBORN   (Germany)

^b MAX PLANCK INSTITUTE FOR HUMAN COGNITIVE AND BRAIN SCIENCES   (Germany)

Author keywords

Frequency distribution; Law of large numbers; Sample size; Sampling distribution

Indexed keywords

EID: 21444448147     PISSN: 08943257     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1099-0771(199703)10:1<33::aid-bdm244>3.0.co;2-6     Document Type: Article

References (57)

1. Bar-Hillel, M. The role of sample size in sample evaluation', Organizational Behavior and Human Performance, 24 (1979), 245-257.
2. Bar-Hillel, M. 'Studies of representativeness', in Kahneman, D., Slovic, P., and Tversky, A. (eds), Judgment under Uncertainty: Heuristics and biases. Cambridge MA: Cambridge University Press, 1982.
3. Beach, L. R., Beach, B. H., Carter, W. B., and Barclay, S. 'Five studies of subjective equivalence', Organizational Behavior and Human Performance, 12 (1974), 351-371.
4. Bernoulli, J. Ars conjectandi, Basilea: Thurnisius, 1713.
5. Cohen, J. Statistical Power Analysis for the Behavioral Sciences (2nd edn) Hillsdale, NJ: Erlbaum, 1988.
6. Daston, L. Classical Probability in the Enlightenment, Princeton, NJ: Princeton University Press, 1988.
7. DuCharme, W. M. and Peterson, C. R. 'Proportion estimation as a function of proportion and sample size', Journal of Experimental Psychology, 81 (1969), 536-541.
8. Evans, J. St B. T. and Bradshaw, H. 'Estimating sample-size requirements in research design: A study of intuitive statistical judgment', Current Psychological Research & Reviews, 5 (1986), 10-19.
9. Evans, J. St B. T. and Dusoir, A. E. 'Proportionality and sample size as factors in intuitive statistical judgement', Acta Psychologies 41 (1977), 129-137.
10. Evans, J. St B. T. and Pollard, P. 'Statistical judgement: A further test of the representatives construct', Acta Psychologica, 51 (1982), 91-103.
11. Evans, J. St B. T. and Pollard, P. 'Intuitive statistical inferences about normally distributed data', Acta Psychologica, 60 (1985), 57-71.
12. Feller, W. An Introduction to Probability Theory and its Applications. Vol I (2nd edn), New York: Wiley, 1957
13. Fine, T. L. Theories of Probability: An examination of foundations, New York: Academic Press, 1973.
14. Fischhoff, B., Slovic, P. and Lichtenstein, S. 'Subjective sensitivity analysis', Organizational Behavior and Human Performance, 23 (1979), 339-359.
15. Fisher, R. A. Statistical Methods and Scientific Inference, Edinburgh: Oliver and Boyd, 1956.
16. Freedman, D., Pisani, R., Purves, R. and Adhikari, A. Statistics (2nd edn), New York: Norton, 1991.
17. Freudenthal, H. 'The "empirical law of large numbers" or "the stability of frequencies"', Educational Studies in Mathematics, 4 (1972), 484-490.
18. Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L., Beatty, J. and Krüger, L. The Empire of Chance: How probability changed science and everyday life, Cambridge: Cambridge University Press, 1989.
19. Huntsberger, D. V. and Billingsley, P. Elements of Statistical Inference (3rd edn), Boston: Allyn and Bacon, 1973.
20. Irwin, F. W., Smith, W. A. S. and Mayfield, J. F. 'Tests of two theories of decision in an "expanded judgments" situation', Journal of Experimental Psychology 51 (1956), 261-268.
21. Jepson, C., Krantz, D. H. and Nisbett, R. E. 'Inductive reasoning: Competence or skill?' The Behavioral and Brain Sciences, 3 (1983), 494-501.
22. Jones, C. J. and Harris, P. L. 'Insight into the law of large numbers: A comparison of Piagetian and judgment theory', Quarterly Journal of Experimental Psychology, 34A (1982), 479-488.
23. Kahneman, D. and Tversky, A. 'Subjective probability: a judgment of representativeness', Cognitive Psychology, 3 (1972), 430-454.
24. Kahneman, D. and Tversky, A. 'On the study of statistical intuitions', Cognition, 11 (1982), 123-141.
25. Koslowski, B., Okagaki, L., Lorenz, C and Umbach, D. 'When covariation is not enough: The role of causal mechanism, sampling method, and sample size in causal reasoning', Child Development, 60 (1989), 1316-1327.
26. Kunda, Z. and Nisbett, R. E. The psychometrics of everyday life', Cognitive Psychology, 18 (1986a), 195-224.
27. Kunda, Z. and Nisbett, R. E. 'Prediction and the partial understanding of the law of large numbers', Journal of Experimental Social Psychology, 22 (1986b), 339-354.
28. Levin, I. P. 'Averaging processes and intuitive statistical judgments', Organizational Behaviour and Human Performance, 12 (1974a), 83-91.
29. Levin, I. P. 'Averaging processes in ratings and choices based on numerical information', Memory & Cognition, 2 (1974b), 786-790.
30. Levin. I. P. 'Information integration in numerical judgments and decision processes', Journal of Experimental Psychology: General, 104 (1975), 39-53.
31. Maistrov, L. E. Probability Theory: a historical sketch. New York: Academic Press, 1974.
32. Murray, J., Iding, M., Farris, H. and Revlin, R. 'Sample-size salience and statistical inference', Bulletin of the Psychonomic Society, 25 (1987), 367-369.
33. Nisbett, R. E. (ed.) Rules for Reasoning, Hillsdale, NJ: Erlbaum, 1993.
34. Nisbett, R. E., Krantz, D. H., Jepson, C. and Kunda Z. 'The use of statistical heuristics in everyday inductive reasoning', Psychological Review, 90 (1983), 339-363.
35. Oakes, M. Statistical Inference: A commentary for the social and behavioral sciences, New York: Wiley, 1986.
36. Olson, C. L. 'Some apparent violations of the representativeness heuristic in human judgment', Journal of Experimental Psychology: Human Perception and Performance, 2 (1976), 599-608.
37. Pearson, K. 'James Bernoulli's theorem', Biometrika, 17 (1925), 14-210.
38. Peterson, C. R. and Beach, L. R. 'Man as an intuitive statistician', Psychological Bulletin, 68 (1967), 29-46.
39. Peterson, C. R., DuCharme, W. M. and Edwards, W. 'Sampling distributions and probability revisions', Journal of Experimental Psychology, 76 (1968), 236-243.
40. Piaget, J. and Inhelder, B. The Origin of the Idea of Chance in Children (L. Leake, Jr, P. Burrel and H. D. Fishbein, trans.), New York: Norton, 1975 (original work published 1951).
41. Poisson, S. D. Recherches sur la probabilité des jugements en matière criminelle et en matière civile, précédé des règles générales du calcul des probabilités, Paris: Bachelier, 1837.
42. Reagan, R. T. 'Variations on a seminal demonstration of people's insensitivity to sample size', Organizational Behavior and Human Decision Processes, 43 (1989), 52-57.
43. Real, L. A. 'Animal choice behavior and the evolution of cognitive architecture', Science, 253 (1991), 980-986.
44. Real, L. and Caraco, T. 'Risk and foraging in stochastic environments', Annual Review of Ecology and Sy-stematics, 17 (1986), 371-390.
45. Révész, P. The Laws of Large Numbers, New York: Academic Press, 1968.
46. Rosenthal, R. and Rosnow, R. L. Essentials of Behavioral Research: Methods and data analysis (2nd edn), New York: McGraw-Hill, 1991.
47. Sanitioso, R. and Kunda, Z. 'Ducking the collection of costly evidence: Motivated use of statistical heuristics', Journal of Behavioral Decision Making, 4 (1991), 161-178.
48. Scheafler, R. L. Introduction to Probability and its Applications, Belmont, CA: Duxbury Press, 1990.
49. Sedlmeier, P. 'People's appreciation of sample size in frequency distributions and sampling distributions', unpublished manuscript. University of Chicago, 1994.
50. Sedlmeier, P. and Gigerenzer, G. 'Do studies of statistical power have an effect on the power of studies?' Psychological Bulletin, 105 (1989), 309-316.
51. Stigler, S. M. 'An Edgeworth curiosum', The Annals of Statistics, 8 (1980), 931-934.
52. Stigler, S. M. The History of Statistics: The measurements of uncertainty before 1900, Cambridge, MA: Belknap/Harvard University Press, 1986.
53. Swieringa, R., Gibbins, M., Larsson, L. and Sweeney, J. L. 'Experiments in the heuristics of human information processing', Journal of Accounting Research, 4 (Suppl.) (1976), 159-187.
54. Teigen, K. H. 'Subjective sampling distributions and the additivity of estimates', Scandinavian Journal of Psychology, 15 (1974a), 50-55.
55. Teigen, K. H. 'Overestimation of subjective probabilities', Scandinavian Journal of Psychology, 15 (1974b), 56-62.
56. Tversky, A. and Kahneman, D. 'Belief in the law of small numbers', Psychological Bulletin, 73 (1971), 105-110.
57. Well, A. D., Pollatsek, A. and Boyce, S. J. 'Understanding the effects of sample size on the variability of the mean', Organizational Behavior and Human Decision Processes, 47 (1990), 289-312.