Two general classes of theory have been proposed to handle data in signal detection and recognition memory. Previous research has considered that one might test such theories by considering the shape of the receiver operating characteristic (ROC) curve, but this has not proved to be helpful. Similarly, the question of the invariance of the ROC curve under different testing procedures is shown to be incidental to this task. It does not appear to be possible to generate empirical predictions peculiar to continuous theories, but various predictions have been extracted from discrete, or finite‐state, theories. Previous results favour a special case of discrete theory in both detection and recognition. However, results are presented which appear to offer a conclusive refutation of finite‐state theory as a model for recognition memory of unrelated wo