Recognition failure of recallable words: problems of mathematical constraint and dependence

The graph space of P ( RN | RL ) vs. P ( RN ), probabilities of recognition given recall and overall recognition, is the setting for the Tulving-Wiseman (TW) function of recognition failure research. According to Hintzman (1991, 1992), the moderate scatter of data points about the TW curve is an artefactual regularity caused by a mathematical constraint when P ( RN ) < P ( RL ). However, both constrained and unconstrained (when P ( RN ) ≥ P ( RL )) points conform equally well to the TW function, consistent with the unobserved fact that the location of both kinds of points is determined by the same mathematical rule. Hintzman's claim that there is no regularity in the data plot when P ( RN ) < P ( RL ) other than that produced by the constraint is not supported by this study. He based his claim on an incorrect use of the measure of dependence (association) called gamma. The graph space corresponding to gamma is that of P ( RN | RL ) vs. P ( RN | nRL ), as shown by using the Bayes function (Bayes' theorem). The margin-free measure gamma is a function of two thetas, theta being a margin-sensitive measure of dependence that is the parameter of the Bayes function. The variance of gamma reflects the fact that it is compounded of the theta variances, so a margin-free measure is obtained at the expense of greater variability.