Concepts of potency and resistance in causal prediction

This study examined the development of causal prediction using physical systems with effects of continuous magnitude. Accurately predicting the magnitude of an effect (ME) requires integration of information about the potency (P) of the causal agent and the resistance (R) of the effect. 10 5-year-olds, 10 9-year-olds, and 10 adults each viewed 36 instances of each of 2 causal mechanisms in which 6 levels of P were crossed with 6 levels of R. For every (P, R) pair, subjects were asked to predict ME. For one mechanism (the balance), an accurate combination of P and R would correspond to a subtraction model (ME = P-R), whereas for the other mechanism (the ramp), a division model (ME = P/R) would yield accurate predictions. Subjects' theoretical models of the roles of P and R were inferred from (a) correlations of their predictions with ideal answers, (b) multiple regression analyses, and (c) analysis of the number of categories P and R that each subject employed. Relative to older subjects, 5-year-olds treated P and R as having fewer categories of intensity. Although 5-year-olds did not generally achieve high correlations with ideal answers, many systematically used P and/or R to influence their predictions. Subjects used P and R more systematically on the balance problem than on the ramp problem. 9-year-olds employed the correct model (subtraction) on the balance problem but applied the subtraction model to the ramp problem as well. Adults converged on the correct models for each mechanism. The results are interpreted in terms of the progressive refinement of a rough, qualitative theory.