When right-handed males categorize faces presented in the right and left visual fields as male or female, a right visual-field advantage results. Subjects in the present study were divided on the basis of Annett's model according to sex and handedness, males and females, right-handers, nonfamilial left-handers, and familial left-handers. It was predicted that males would show a field advantage consistent with the cerebral hemisphere specialized for speech production (the left hemisphere in the case of right-handers and nonfamilial left-handers, and the right hemisphere in the case of familial left-handers). It was also predicted that females would be either weakly or inconsistently lateralized. A signal-detection paradigm in general confirmed these predictions. It was also shown that a subject's ability to change decisional criteria appropriately over trials was a function of visual field for both males and females. Decision making over time may therefore reveal a fundamental duality distinguishing the cerebral hemispheres in both sexes. Some of the implications of these results are discussed.