Social Science Statistics Blog

In Simple heuristics that make us smart Gigerenzer et. al. argue that, contrary to popular belief, many of the cognitive heuristics people use are actually very rational given the constraints on memory and time that we have to face. One strand of their research suggests that people are far better at reasoning about probabilities when they are presented as natural frequencies rather than numbers (as most studies do). Thus, for instance, if people see pictures of, say, 100 cars, 90 of which are blue, they are more likely not to "forget" this base rate than if they are just told that 90% of cars are blue.

A recent paper in the journal Cognition (vol 98, 287-308) expands on this theme. Zhu & Gigerenzer found that children steadily gain in the ability to reason about probabilities, as long as the information is presented using natural frequencies. Children were told a story such as the following:

Pingping goes to a small village to ask for directions. In this village, the probability that the person he meets will lie is 10%. If a person lies, the probability that he/she has a red nose is 80%. If a person doesn't like, the probability that he/she also has a red nose is 10%. Imagine that Pingping meets someone in the village with a red nose. What is the probability that the person will lie?

Another version of the story gave natural frequencies instead of conditional probabilities, for instance "of the 10 people who lie, 8 have a red nose." None of the fourth-grade through sixth-grade children could answer the conditional probability question correctly, but sixth graders approached the performance of adult controls for the equivalent natural frequency question: 53% of them matched the correct Bayesian posterior probability. The fact that none of the kids could handle the probability question is not surprising -- they had not yet been taught the mathematical concepts of probability and percentage. What is interesting is that, even without being taught, they were capable of reasoning "the Bayesian way" about as well as adults do.

The most interesting part of this research, for me, is less about the question of whether people "are Bayesian" (whatever that means), but rather that it highlights a very important message: representation matters. When information is presented using a representation that is natural, we find it a lot easier to reason about it correctly. I wonder how many of our apparent limitations reveal less about problems with our reasoning, and more about the choice or representation or the nature of the task.