Intuitive Statistics: Identifying Children’s Data Comparison Strategies using Eye Tracking

Intuitive Statistics: Identifying Children’s Data Comparison Strategies using Eye Tracking Bradley J. Morris (bmorri20@kent.edu), Patrick F. Cravalho (pcravalh@kent.edu), Angela Junglen (ajungle1@kent.edu), Christopher Was (cwas@kent.edu) Department of Educational Psychology, 405 White Hall Kent, OH 44242 USA Amy M. Masnick (Amy.M.Masnick@hofstra.edu) Department of Psychology, Hauser Hall Hempstead, NY 11549 USA Abstract People often compare sets of numbers informally, in considering prices or sports performance. Children who lack knowledge of formal comparison strategies (e.g., statistics) may use intuitive strategies like estimation that create summary values with approximations of means and variance. There were two goals for this experiment: (1) to classify data comparison strategies and (2) to evaluate whether children’s strategy discovery and selection is effective. Using eye tracking, we identified strategies used by 41 8-12-year-old children when comparing number sets, by examining how the properties of the data sets (e.g., mean ratios and variance) influenced accuracy and confidence in differences. We classified strategies from eye tracking patterns; these strategies were associated with different levels of accuracy, and strategy selection was adaptive in that selection was related to the statistical properties of the sets being compared. The results demonstrate that children are quite adept at informally comparing data sets and adaptively select strategies to match the properties of the sets themselves. Keywords: Intuitive statistics, cognitive development, eye tracking Introduction How does a shopper determine which store has the lowest prices? This could be achieved by comparing sets of prices using a formal statistical analysis like a t-test. However, when comparing numbers in context (data), outside of a research setting, such comparisons are more likely to occur informally. Surprisingly, there has been relatively little research investigating how people compare sets of numbers (e.g., Morris & Masnick, in press) despite the rapidly growing literature investigating comparisons between single numbers (e.g., Dehaene, 2009). In the current paper, we investigate the comparison of number sets in children using eye tracking in order to classify and evaluate naive strategies for performing data comparisons. Number representation and comparison Numbers are represented as both a verbal category (e.g. “twelve”, an exact value) and an activation function on an approximate number system (Dehaene, 2009; Feigenson, Dehaene, & Spelke, 2004; Opfer & Siegler, 2012). Differences between single-digit numbers are detected more quickly and accurately as the ratio of the numbers increases (Dehaene, 2009). For example, reaction times are slower and evaluations are less accurate when comparing 9 and 10 (9:10 ratio of numbers), than when comparing 3 and 9 (1:3 ratio of numbers). This distance effect is evidence that numerical quantities are compared using approximate representations. This effect is detected across species (Brannon, 2003), across age of participants (Feigenson et al., 2004), and across presentation formats (e.g., dots, Arabic numbers, fractions; Buckley & Gillman, 1974; Dehaene, 2001; Sprute & Temple, 2011). Multi-digit number comparisons (e.g., 63 vs. 72) demonstrate a unique distance effect in that two- and three- digit numbers produce distance effects for each place value unit (i.e., tens vs. ones; Korvorst & Damian, 2008; Nuerk, Weger, & Willmes, 2001). Eye tracking results demonstrate more fixations when there is incompatibility between places (e.g., 47 vs. 51), where one number has a larger value in the tens column, but the other one has a larger value in the ones column (Moeller, Fischer, Nuerk, & Willmes, 2009). The Approximate Number System (ANS) allows children, even infants, to discriminate quantities, although the threshold at which accurate discrimination occurs changes over development (Mou & vanMarle, in press). Specifically, infants can distinguish quantities at a ratio of 1:2; by early elementary school, children distinguish at a 4:5 ratio; and adults discriminate quantities at a 9:10 ratio (Halberda & Feigenson, 2008; Xu & Spelke, 2000). Children are also adept at using the ANS to estimate solutions to problems for which they lack formal solution strategies (Gilmore, McCarthy, & Spelke, 2007). One explanation for the increasing acuity is the strategies children (and adults) use to compare quantities (Hyde, 2011; Mu & van Marle, in press). That is, strategies are related to goals (e.g., accuracy) and constrained by processing limitations (e.g., working memory; Hyde, 2011). Comparing number sets There is evidence that when comparing number sets, adults create and compare approximate summaries of the