How well do classification images characterize human observers' strategies in perceptual tasks? We show mathematically that from the classification image of a noisy linear observer, it is possible to recover the observer's absolute efficiency. If we could similarly predict human observers' performance from their classification images, this would suggest that the linear model that underlies use of the classification image method is adequate over the small range of stimuli typically encountered in a classification image experiment, and that a classification image captures most important aspects of human observers' performance over this range. In a contrast discrimination task and in a shape discrimination task, we found that observers' absolute efficiencies were generally well predicted by their classification images, although consistently slightly (approximately 13%) higher than predicted. We consider whether a number of plausible nonlinearities can account for the slight under prediction, and of these we find that only a form of phase uncertainty can account for the discrepancy.