The Psychometrics of JRR Tolkien

Few people realize that deep in the heart of The Hobbit, Tolkien placed an allegory that deftly demonstrates the psychometric concepts of Difficulty and Discrimination. For those not familiar with the story, Bilbo and his companions attempt to liberate treasure from an evil dragon. On the way, they are captured and imprisoned deep underground, then Bilbo is separated from his companions as they attempt to escape. Lost and alone in the dark, Bilbo stumbles upon the lair of Gollum. In the ensuing dialog, Gollum and Bilbo quickly reach an impasse — Gollum wants to eat Bilbo, but Bilbo’s sword prevents this while Bilbo wants to escape the cave but doesn’t know the way out.


To break the impasse, they agree to a game of riddles where, if Gollum wins, he gets to eat Bilbo and, if Bilbo wins, Gollum must guide him to the exit. This is where things get interesting, psychometrically speaking.


Tolkien first introduces the concept of Difficulty. Some riddles are harder and some easier. Then, at contest’s conclusion, Tolkien unleashes the topic of Discrimination. Under pressure to come up with another riddle, Bilbo blurts “What have I got in my pocket?” when his hand brushes the ring he’d found earlier in the story. Gollum takes this for a riddle and is furious because he knows he can’t answer correctly but is unable to explain why.


Had Gollum understood the concept of Discrimination, he could have effectively argued the unfairness of this riddle: Knowing what Bilbo had in his pocket has nothing to do with the answerer’s ability to solve riddles (i.e. his Theta) so it is a bad question and should be removed from the exam/contest.


In short, had Gollum understood basic Psychometrics he might have successfully removed the question, eaten Bilbo, regained the ring, fallen into the clutches of Sauron and ultimately caused the destruction of Middle Earth. In a single episode, Tolkien demonstrates the importance of properly understanding Difficulty and Discrimination and in so doing shows his disdain for those who don’t care about exam validity.

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Andrew Lunstad

Andrew has a wide range of expertise, from education to software development to startup leadership. He currently focuses on developing strong partnerships for ASC in the educational assessment space. Previously, he designed a number of modules in FastTest, including a reporting engine and a test scheduling system. Before joining ASC, Andrew worked on core software for Cisco routers, a mobile app development platform, and founded a video game startup in the 1990s.

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