Beyond existence: inferences about mental processes from reversed associations.

One of the aims of cognitive (neuro)psychology is to characterize the nature of, and the relationships between, mental processes underlying human behavior (c.f. Dunn & Kirsner, this issue). In this context, the double dissociation (DD) paradigm has played an important albeit debated role. In our efforts to come up with a clear and positive contribution to this discussion, which sometimes appears to be a muddle of terms and arguments, we turned to the framework of Dunn and Kirsner (1988). Their framework and analysis is a satisfyingly clear, logical elucidation of the possible meanings of “double dissociation.” These authors have shown that a data pattern called the reversed association (RA) (a stronger version of double dissociation) is sufficient to logically infer the existence of at least two processes underlying task behavior. However, some open questions remain. Here we tackle the specific question “What can be inferred from a reversed association beyond the mere existence of two processes?” We will show that the answer to this question depends heavily on assumptions about monotonicity of functional relationships. In the Dunn-Kirsner (DK) framework, the relationship between variables, processes and tasks can be understood as two nested transformations. First, levels of experimental variables, denoted v1, v2, ..., vn, are mapped onto levels of process efficiency, p1, p2, ..., pm. Second, pi are mapped onto levels of task performance, t1, t2, ... tk. Here vi denotes the level of the i variable, pi denotes the efficiency of the i process, and ti denotes the performance on the i task. Functions fi , with pi = fi(v1, v2, ..., vn), for i = 1, 2, ..., m, transform variables onto processes, and functions gi, with ti = gi(p1, p2, ..., pm), i = 1, ..., k, transform processes onto task performance levels.