On measuring (in)dependence of cognitive processes

The authors provide a critical evaluation of the use of stochastic independence in psychological research. Specifically, they consider problems of confirming the null hypothesis, power of the statistical test, Simpson's paradox, and between-subjects and within-subject correlations. These problems are discussed in the context of research on theories of memory and cognitive development and illustrated with data on reasoning-remembering relationships. The authors conclude that demonstrations of response independence do not, by themselves, provide sufficient grounds for deciding whether a single process or multiple processes are necessary to account for performance. Instead, they argue that formal models are necessary if findings of (in)dependence are to be interpreted meaningfully in terms of underlying theoretical processes.