Final answer:
A nurse determines a positive Romberg's sign when the client has a significant sway while standing with feet together and eyes closed, which indicates proprioceptive deficits.
Step-by-step explanation:
During a neurological assessment, a positive Romberg's sign is determined by the nurse based on the observation of significant sway when the client stands erect with feet together, arms at the side, and eyes closed. This indicates deficits in proprioception, which refers to the sense of body positioning and movement, and may suggest issues with the proprioceptive projections to the cerebellum or a problem in the dorsal column pathway. The Romberg's test is an important component of the neurological exam as it helps assess the coordination and balance which rely on both proprioceptive and vestibular inputs to maintain posture without visual feedback.