Intuitive statistics by 8-month-old infants

doi:10.1073/pnas.0704450105

Intuitive statistics by 8-month-old infants

Fei Xu* and
Vashti Garcia

Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, BC, Canada V6T 1Z4

Edited by Susan E. Carey, Harvard University, Cambridge, MA, and approved February 6, 2008 (received for review May 11, 2007)

Abstract

Human learners make inductive inferences based on small amounts of data: we generalize from samples to populations and vice versa. The academic discipline of statistics formalizes these intuitive statistical inferences. What is the origin of this ability? We report six experiments investigating whether 8-month-old infants are “intuitive statisticians.” Our results showed that, given a sample, the infants were able to make inferences about the population from which the sample had been drawn. Conversely, given information about the entire population of relatively small size, the infants were able to make predictions about the sample. Our findings provide evidence that infants possess a powerful mechanism for inductive learning, either using heuristics or basic principles of probability. This ability to make inferences based on samples or information about the population develops early and in the absence of schooling or explicit teaching. Human infants may be rational learners from very early in development.

Footnotes

*To whom correspondence should be addressed. E-mail: fei{at}psych.ubc.ca
Author contributions: F.X. designed research; V.G. performed research; F.X. analyzed data; and F.X. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
↵ † The box contained 70 red balls and five white ones (or five red balls and 70 white ones). The probability of drawing a random sample of four red and one white balls in a particular order is 70/75 × 69/74 × 68/73 × 67/72 × 5/71 = 0.0531. The probability of drawing a random sample of one red and four white balls in a particular order is 70/75 × 5/74 × 4/73 × 3/72 × 2/71 = 0.000004056. Alternatively, the probability of drawing a sample of four red and one white balls irrespective of order is 0.0531 × 5 = 0.2655, and the probability of drawing a sample of one red and four white balls irrespective of order is 0.000004056 × 5 = 0.0000228. We do not know which of these two calculations (if either) underpin the infant's performance in our tasks, although the latter may seem more plausible.