Mathematical constraints and the Tulving-Wiseman law: a rejoinder

Hintzman (1991; 1992) has claimed that the reason data points approximate the recognition failure function discovered by Tulving and Wiseman (1975) is that they are mathematically constrained to do so, and the reason that a few data points do not approximate the function, but are exceptions to it, is that these data points are less subject to mathematical constraints. He has additionally argued that such exceptions are more likely with low levels of recall and strong underlying sources of positive covariance. We provide empirical evidence relevant to this mathematical model using 301 observations from a database of all relevant experimental conditions published between 1973 and 1992 (Nilsson & Gardiner, 1993). We conclude that mathematical constraints have only a minor influence on the function, not the causal role assigned to them in Hintzman's (1992) model. By our account, both the function and exceptions to it reflect a single psychological principle, the functional effectiveness of contextual cues.