What theory suggests that the shape of the skull can determine mental abilities or character traits?

The theory that suggests the shape of the skull can determine mental abilities or character traits is known as phrenology. This concept, which emerged in the early 19th century, posits that the brain is the organ of the mind and that specific areas of the brain are responsible for various personality traits and intellectual capabilities. Phrenologists believed that by examining the bumps and contours of an individual's skull, they could infer characteristics associated with intelligence, emotions, and behaviors.

This concept has been largely discredited in modern psychology and neuroscience, but it played a significant role in the early attempts to understand the relationship between physical attributes and psychological traits. The other options do not pertain to the study of skull shape in relation to mental abilities or character. Neuroscience focuses on the brain and nervous system's biological functions, psychotherapy involves therapeutic techniques to address mental health issues, and psychometrics is the field dedicated to measurement theories and techniques in psychology, particularly relating to tests and assessments of psychological constructs.