Reasoning from Samples to Populations: Can Children use Variability Information to Predict Future Outcomes?

• In Event: Categories and Concepts

Abstract

The ability to reason from specific instances to general characteristics of populations allows us to make inferences that go beyond our direct experience, and provides a critical guide for action. For example, from the items displayed in a shop’s window, we can infer the category, quality, and variety of the merchandise for sale. This inference supports future decisions about whether this shop is likely to carry the specific product we are looking for, regardless of whether that product is displayed in the window. Development of this ability has previously been explored in infants: Dewar and Xu (2010) presented 9-month-olds with samples from three concealed populations that suggested a second-order generalization (e.g., populations contain items of the same shape). They found that infants then looked longer when the samples drawn from a new, fourth population did not share this same general property, suggesting the infants formed abstract expectations about the populations based on the samples observed. However, it remains unclear whether young learners are able to utilize their inferences of higher-order regularities to guide subsequent actions. Here, we go beyond previous work by asking first, whether 2- to 3-year-olds’ inferences about unknown populations from samples are sensitive to variability information, and whether these higher-order inferences inform their search for novel outcomes.

To investigate this, we presented children with two identical opaque containers (Figure 1). An experimenter told children that she was going to show them some of the balls from inside each one. She then randomly drew four balls from each container in turn, placing each ball into a clear tray next to its container. One container had a uniform-sample of four yellow balls. The other had a varied-sample of one red, one blue, one purple, and one yellow ball (fixed order). After drawing both samples, the experimenter held up a picture of a novel colored ball (green) and said: “One of these two boxes has a green ball, like this, inside. Can you point to the box you think has the green ball inside?” As neither sample included this object, first-order information does not indicate either population as more likely. However, if children are sensitive to the variability of the samples they observe, and can use this information to form a general hypothesis about the sameness or difference of the objects in each population, we would expect them to select the varied sample.

Out of a total of 40 children (M = 40.1 mos., range: 25.3 – 47.8 mos.), a significant majority chose the varied-sample container (72.5%, p = 0.006, two-tailed binomial). Bayes Factor analysis indicates strong evidence in favor of our hypothesis: BF10 = 11.6, 95% credible intervals: [0.57, 0.84]. This finding suggests that young children can reason from samples for abstract hypotheses about populations, and can use these hypotheses to guide their subsequent inferences about novel outcomes. Future work will investigate whether children perform similarly when this task is presented in a variety of real-world domains, including the variability or uniformity of choices made by two different social agents.

Authors

• Elizabeth Lapidow, University of California - San Diego
  Presenting Author

• Mariel Kathryn Goddu, Harvard University
  Non-Presenting Author

• Caren M. Walker, University of California - San Diego
  Non-Presenting Author