8-month-old infants use intuitive statistics..

Here is a fascinating result from Xu and Garcia, a demonstration that our brains begin to employ statistics at a very young age. Here are some (slightly edited) clips from their paper:

One hallmark of human learning is that human learners are able to make inductive inferences given a small amount of data. Our hunter–gatherer ancestors may have tasted a few berries on a tree and then decided that all berries from the same kind of tree are edible. They may have encountered a few friendly people from a neighboring tribe and made the inference that people in that tribe are likely to be friendly in general. Once such generalizations are made, the inferences may go in the other direction as well. This type of statistical inference (going from samples to populations, and from populations to samples) is present in virtually every domain of learning, be it foraging, social interaction, visual perception, word learning, or causal reasoning . Inductive learning in general requires some understanding of intuitive statistics, perhaps a simpler version of what scientists do in laboratory experiments or field studies.

Xu and Garcia performed six experiments investigating whether 8-month-old infants are "intuitive statisticians." Their results show that, given a sample, the infants are 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 are able to make predictions about the sample...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.

Here is one of the experiments, which asked whether 8-month-old infants could use the information in a sample to make inferences about a larger population:

...8-month-old infants watched some events unfold on a puppet stage. Each infant was first given a set of six ping-pong balls in a small container to play with for a few seconds; half of the ping-pong balls were red, half were white. Then the infant was shown four familiarization trials. On each trial, a large box was brought onto the stage. The experimenter opened the front panel of the box and drew the infant's attention to the box. The box contained either mostly red ping-pong balls and a few white ping-pong balls or mostly white ping-pong balls and a few red ping-pong balls. The experimenter showed the infants these two displays alternately; thus the infants were equally familiarized with each display. Then the test trials began (see Fig. 1 for a schematic representation of the test events). On each test trial, the same box was brought onto the stage, its content not known to the infants. The experimenter shook the box for a few seconds, closed her eyes, reached into the top opening, and pulled out a ping-pong ball. She then placed it into a transparent sample display container next to the large box. A total of five ping-pong balls were drawn from the box, one at a time. In half of the test trials, a sample of four red and one white ping-pong balls were drawn. In the other half of the test trials, a sample of one red and four white ping-pong balls were drawn. After the five ping-pong balls were placed in the sample display container, the experimenter opened the front panel of the box to reveal its content. The infant's looking time was recorded. The experimenter then cleared the stage and started the next test trial until a total of eight test trials were completed. Only one outcome display was shown for each infant, either the mostly white or the mostly red one. On alternate test trials, the infants were shown the two samples (four red and one white or one red and four white). For an infant who saw the mostly red outcome display when the box was opened, the four red and one white sample was more probable and therefore expected, whereas the four white and one red ball sample was much less probable and therefore unexpected,{dagger} assuming each set was a random sample from the box. For an infant who saw the mostly white outcome display, the converse was true.


Figure - Schematic representation of the test events (Images 1, 3, and 5) The experimenter shook the box for a few seconds, closed her eyes, reached into the top opening, and pulled out a ping-pong ball. (Images 2, 4, and 6) She then placed the ball into a transparent sample display container next to the large box. Test outcomes are shown at the bottom.

The infants looked reliably longer at the unexpected outcome (M = 9.9s) than the expected outcome (M = 7.5 s). It appears that infants were able to predict the content of the box from which the samples had been drawn.