The psychological part of the Starfleet Academy entrance examination, a staged crisis built around each candidate's deepest fear, which Wesley Crusher faces on Relva VII.
The psych test is the most dreaded part of the Starfleet Academy entrance examination. Candidates are not told when it will begin or what form it will take, because it is a staged emergency designed around each applicant's greatest fear.
It appears in Coming of Age, in which Wesley Crusher sits the examination on Relva VII alongside the Benzite Mordock and two other candidates. While he waits to be called, an explosion in a nearby laboratory traps two men, and Wesley can save only one of them before the room is sealed. The scene mirrors the death of his father, who was lost on a mission under Picard's command.
Wesley makes the choice and is told that this was the test. He passes it but loses the single Academy place to Mordock on overall score, and Picard consoles him by admitting that he failed the examination himself the first time.