Children's and Adults' Interpretation of Covariation Data: Does Symmetry of Variables Matter?

In a series of 3 experiments, the authors investigated the influence of symmetry of variables on children's and adults' data interpretation. They hypothesized that symmetrical (i.e., present/present) variables would support correct interpretations more than asymmetrical (i.e., present/absent) variables. Participants were asked to judge covariation in a series of data sets presented in contingency tables and to justify their judgments. Participants in Experiments 1 and 2 were elementary school children (Experiment 1: n = 52 second graders, n = 44 fourth graders; Experiment 2: n = 50 second graders). Participants in Experiment 3 were adults (n = 62). In Experiment 1, children in the symmetrical variables condition performed better than those in the asymmetrical variables condition. Children in the symmetrical variables condition judged more data patterns correctly and they more frequently justified their choices by referring to the complete table. Experiment 2 ruled out the possibility that this effect was caused by differences in question format. Even when question format was held constant, second graders performed better with symmetrical variables. Experiment 3 showed that adults' data interpretation is also affected by symmetry of variables. Collectively, these results indicate that symmetry of variables affects interpretation of covariation data. The authors argue that symmetrical variables provide a context for meaningful comparison. With asymmetrical variables, the importance of the comparison is less salient. Thus, the symmetry of variables should be considered by researchers as well as educators.