The Impact of Statistical Training on Children's Inductive Reasoning

The Impact of Statistical Training on Children’s Inductive Reasoning Susan L. Stanley (shlocke@uwm.edu) Chris A. Lawson (lawson2@uwm.edu) University of Wisconsin – Milwaukee Department of Educational Psychology Milwaukee, WI USA Abstract Regardless of age there are mixed findings concerning the extent to which individuals utilize statistical features of input to make inductive inferences. Direct instruction seems to be one important factor in linking one’s understanding of statistical properties with their reasoning. In the present study we examined the extent to which explicit training on some statistical principles would influence preschoolers’ inductive reasoning. The results indicate that a short training about random selection and the match between samples and populations increased children’s use of these principles to make inductive generalizations. Critically, the training effects were observed in a different domain than was presented in the training and for statistical principles not presented in the training. Thus, the present results suggest that the training had a broad impact on children’s reasoning. These results have important implications for understanding the nature of the statistical principles employed during induction. Keywords: statistical training; sample size; inductive reasoning; cognitive development; generalization Introduction Most decisions involve inductive generalizations, the use of specific information to draw general conclusions. Induction is interesting to cognitive scientists because, despite the apparent uncertainty of predictions, people are quite good inductivists. Among other things, our inductive reasoning is anchored by careful attention to statistical features of evidence. For example, recent advances in Bayesian models of induction suggest the inductive inferences of even the youngest learners are closely aligned with the most (statistically) optimal predictions (e.g., Xu & Kushnir, 2013). However, there are many cases in which children (Lopez, Gelman, Gutheil, & Smith, 1992) and adults (Kahneman, Slovis, & Tversky, 1982) fail to adhere to statistical properties of evidence and instead rely on other sources of information to make predictions. The present study focused on conditions in which children have yet to acquire the statistical principle that will support induction. We were particularly interested in understanding whether children could acquire such skills with minimal instruction, and whether learning about specific statistical principles (e.g., random sampling) would have a narrow effect on induction (e.g., to inferences regarding random selection) or a broader effect (e.g., to inferences concerning other statistical principles such as sample size). There is mixed evidence regarding the extent to which young children incorporate statistical evidence into their inductive inferences. On the one hand, recent studies indicate that prior to their first birthday infants exhibit an intuitive set of skills that enable them to generate expectations in-line with the statistical features of evidence (Xu & Garcia, 2008; Teglas, Girotto, Gonzalez, & Bonatti, 2007). For example, 8-month-olds expect a randomly selected sample will have the same distribution of white and red balls as the population from which it was chosen. In addition to exhibiting the intuition that samples match the distributions of the populations from which they were chosen, young infants also appear to be aware of the likely outcomes of the procedures used to yield samples. For example, infants expect the distribution of a sample to be similar to that of the population from which it was drawn when an actor randomly selected items from the sample, but not when the actor engaged in deliberate sampling (Xu & Tenenbaum, 2007; Denison, Reed, & Xu, 2011; Gweon & Schulz, 2011). Overall, by the end of the first year infants appear to exhibit some powerful expectations about the statistical properties of evidence. However, children appear limited in their ability to effectively use statistical properties to evaluate which samples provide the best support for induction. Some studies have shown that children are insensitive to the sample size principle of induction until after age 8 or 9 years of age (Gutheil & Gelman, 1997; Li, Cao, Li, Li, & Deak, 2009; Lopez et al., 1992; cf. Lawson, 2014; Lawson & Fisher, 2011). For example, Gutheil and Gelman (1997) presented children evidence about a single exemplar (e.g., “This butterfly has blue eyes”) and a sample of five exemplars (e.g., “These five butterflies have gray eyes.”) and asked them to generalize a property from one of the samples to an evidence target (e.g., “Do you think this butterfly has blue eyes like this butterfly, or gray eyes like these butterflies? ”). Children younger than 8 years of age responded randomly, indicating they failed to recognize that the larger sample provided better evidence to support induction. In contrast, children older than 8 consistently prefer to generalize from large, rather than small samples of evidence (see also Li et al., 2009; Lopez et al., 1992).