A method for judging measures of stochastic dependence: further comments on the current controversy

A large number of reports have been published on stochastic independence between implicit and explicit measures of memory. This is often taken to imply that different memory systems mediate implicit and explicit memory performance. In these cases, stochastic independence is inferred from contingency analysis of overall success rates in two memory tasks when performance in one or both of the tasks is, to a large extent, mediated by factors other than memory. Typically, the difference between performance with studied and nonstudied items is not large in implicit memory tasks. It is argued that this must be taken into account when evaluating the contingency analysis. A method is presented for estimating the relevant joint and conditional probabilities, assuming that the aspects of performance in the two tasks that are related to memory are dependent to the maximum possible extent. The method is applied to a number of published studies, and it is shown that the difference between these estimated probabilities and those given by stochastic independence is too small to allow any conclusion to be drawn about memory systems from contingency analysis of data reported in these studies.