On variability, Simpson's paradox, and the relation between recognition and recall: reply to Tulving and Flexser.

Tulving and Flexser's (1992) defense of the Tulving-Wiseman law rests on the partitioning of data points into 2 sets, which they call constrained and unconstrained. This dichotomy depends crucially on the implicit assumption that within-condition variance is 0. Simulations are done to show the effects of variability on the maximum contingency that can be displayed by an average 2 x 2 table. The results help explain the form of the regularity known as the Tulving-Wiseman law, as well as the conditions under which exceptions are found. This analysis reinforces the conclusion that the law is an artifact and serves as a reminder of the dangers posed by variability and Simpson's paradox when contingency analyses are done.