The law of large numbers in children's diversity-based reasoning

Adults increase the certainty of their inductive inferences by observing more diverse instances. However, most young children fail to do so. The present study tested the hypothesis that children's sensitivity to instance diversity is determined by three variables: ability to discriminate among instances (Discrimination); an intuition that large numbers of instances increase the strength of conclusion (Monotonicity); ability to detect subcategories and evaluate numerical differences between the subcategories, or Extraction. A total of 219 Chinese children aged 6 to 11 were tested for sensitivity to diversity by means of Discrimination, Monotonicity, and Extraction. The results indicated that children at all ages were able to discriminate instances and attend to set size. However, only 9- and 11-year-olds demonstrated Extraction and sensitivity to diversity. Furthermore, among all children diversity scores increased linearly with the level of Extraction. These results suggest that the law of large numbers plays a role in children's diversity-based reasoning.