Insight into the Law of Large Numbers: A Comparison of Piagetian and Judgement Theory

Abstract

Subjects were tested for their understanding of the law of large numbers in three ways: by means of a Piagetian task involving the distribution of balls between two compartments, by means of written tasks similar to those devised by Kahneman and Tversky (1972), and by means of a task involving comparisons of samples of counters drawn from a larger population. For the sample comparison task, subjects relied heavily on proportional information-ignoring sample size, thereby supporting the conclusions of Kahneman and Tversky (1972). However with regard to the other two tasks an order effect was found: subjects did significantly better with the Kahneman and Tversky tasks if they had first been tested on a Piagetian task. In Experiment II, the order effect was replicated, indicating that subjects may have a narrow insight into the law of large numbers which is not recruited in appropriate contexts unless primed by the task environment.

Get full access to this article

View all access options for this article.

References

Bar-Hillel

(1979). The role of sample size in sample evaluation. Organizational Behaviour and Human Performance 24, 245–57.

Bryant

P. E.

(1974). Perception and Understanding in Young Children London: Methuen.

Cohen

L. J.

(1979). On the psychology of prediction: Whose is the fallacy?. Cognition 7, 385–407.

Cohen

L. J.

(1981). Can human irrationality be experimentally demonstrated?. The Behavioral and Brain Sciences 4, 317–31.

Donaldson

(1978). Children's Minds Glasgow: Fontana.

Kahneman

Tversky

(1972). Subjective probability: A judgement of representativeness. Cognitive Psychology 3, 430–51.

Kahneman

Tversky

(1982). On the study of statistical intuitions. Cognition 11, 123–141.

Piaget

Inhelder

(1975). The Origin of the Idea of Chance in Children London: Routledge and Kegan Paul.

Shaklee

(1979). Bounded rationality and cognitive developments: Upper limits of growth?. Cognitive Psychology 11, 327–45.

10.

Tversky

Kahneman

(1971). Belief in the law of small numbers. Psychological Bulletin 76, 105–10.