Final answer:
The psychologist in question is likely a Developmental Psychologist, focusing on cognitive changes and learning disabilities such as dyslexia, which involves letter reversals.
Step-by-step explanation:
A psychologist observed administering a battery of tests to determine why a child is reversing letters like "b" and "d" would most likely be a Developmental Psychologist. Developmental psychologists study physical and cognitive changes that occur throughout one's lifespan, including how children learn language and develop literacy skills. In particular, the difficulty with letter reversal can be a sign of dyslexia, which is a learning disability described as a neurological disorder affecting reading and language processing abilities.