Published online 31 March 2008 | Nature | doi:10.1038/news.2008.713

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Babies have an eye for statistics

Infants intuitively understand probability.

Even 8-month-old kids can tell if things don't add up.

Babies have many talents — such as the ability to charm a roomful of adults. But statistical reasoning? It's not the first skill that springs to mind regarding a gurgling 8-month-old.

Yet researchers have found that babies do possess an intuitive grasp of statistics. The work, published this week in the Proceedings of the National Academy of Sciences USA, is amongst the first to show that infants can predict the likelihood of a future event1.

The ability to do this without teaching or experience shows that we begin using probability to make predictions from a very young age. The authors suggest that an infant's statistical intuition resembles that of a scientist, supporting a proposition made by some cognitive scientists that "children are scientists".

Researchers have long appreciated that babies understand rudimentary mathematics. A baby is surprised if he sees two dolls being placed in a case, but only one doll when the case is opened2. Non-human primates can also grasp simple maths (see 'Monkeys add up like we do').

The new study tackles an infant’s grasp of probability. “We know nothing about infants’ logical abilities,” says psychologist Luca Bonatti of the University of Nantes in France, who was not involved in the study. “Most researchers thought that there was nothing to study in this field, because of course probabilistic prediction was beyond infants’ abilities.”

Baby logic

Fei Xu and Vashti Garcia of the University of British Columbia in Vancouver put a collection of red and white ping-pong balls in a box. Babies were shown examples of boxes containing mostly red or mostly white balls, to give them an idea of what the boxes might contain. Then an adult brought out a new box, shook it up, and drew out five balls: four of one colour, and one of the other.

Afterwards, they opened a panel, showing the babies the content of the box from which the balls were drawn, and recorded how long the infants gazed at its contents. Babies stare at unexpected events longer than expected outcomes.

If the adult drew mostly red balls from a box that was revealed to contain mostly white balls, for example, the infants stared at it for roughly two seconds longer than if the box and the withdrawn sample were both of mostly the same colour. “Given limited available evidence, they can infer how the whole population should look,” says Bonatti.

The babies weren't simply confused by a colour mismatch between any two sets of balls. If adults drew five ping pong balls out of their pocket, and showed babies that the sample didn't match a box of balls, the babies were unsurprised. That makes sense, given that there's no reason to expect an adult's pocket to contain the same mix of colours as the box.

Primary prediction

Bonatti and his colleagues also recently showed that one-year-olds have an intuitive grasp of probability, using a similar setup. They showed infants four balls bouncing around in a box, with one being a unique colour, and watched the infants' responses when one ball bounced out. The children were suprised when the extracted ball was the odd-one-out, they reported last November3.

Bonatti says his experiment showed that infants can do this even in a one-off situation, without any prior exposure to the experimental setup or any practice. Xu and Garcia's work, he says, additionally suggests that children might be able to build on past experience to help with their assessment of probabilistic events.

"We showed something about the ability to reason about future single events in the absence of experience. They showed something about the ability to reason about classes in the presence of the experience about these classes," he explains.

The question that remains, says Bonatti, is how these reasoning abilities develop from infancy to a adulthood: sometimes culminating in not-very-rational adults. "We, and Xu and Garcia, show that at the origin of human cognition, humans seem to be far more rational than what the literature about adult reasoning seems to suggest," he says. "How come we start so well and we end up so poorly? A whole new set of investigations can be opened now." 

  • References

    1. Xu, F. & Garcia, V. Proc. Natl Acad. Sci. USA 105, 5012-5015 (2008). | Article |
    2. Wynn, K. Nature 358, 749-750 (1992). | Article |
    3. Téglás, E., Girotto, V., Gonzalez, M., & Bonatti, L. L. Proc. Natl Acad. Sci. USA 104, 19156-19159 (2007).
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