Cryptic crossword clue
Those who believe in it should have their heads examined 10

The most common and most likely answer to this crossword clue is the 10 letter word PHRENOLOGY

I've seen this crossword clue in The Daily Telegraph
P
H
R
E
N
O
L
O
G
Y

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The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does PHRENOLOGY mean?

PHRENOLOGY noun
  1. The science, now generally discredited, which studies the relationships between a person's character and the morphology (structure) of the skull.

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