Final answer:
The research method designed by Fantz is known as the visual preference method, used to study infants' cognitive and perceptual preferences by observing their gaze on various stimuli.
Step-by-step explanation:
The research method designed by Fantz to study whether infants can distinguish one stimulus from another by measuring the length of time they attend to different stimuli is called the visual preference method. This method is used to gain insights into an infant's cognitive and perceptual development. Infants are shown various stimuli, and their gaze is monitored to see which ones they prefer or pay attention to the longest. This can reveal innate preferences, such as a preference for human faces, which is significant for newborns as this facilitates interaction with caregivers. This method is a form of structured observation, similar to experiments where children's cognitive abilities are tested by observing their reactions to specific tasks or changes in their environment.