Psychometrics: Classical test theory · True Score and Measurement Error
How classical test theory splits every score into a true part and error, and what that means for reliability, the standard error of measurement and reading test results.
Try 3 questions
1. In classical test theory, how is a person's observed test score modeled?
- Ability minus item difficulty
- True score times a reliability factor
- True score plus random error
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Answer: True score plus random error
Classical test theory rests on the equation X = T + E: every observed score is a true score plus an error component.
2. In classical test theory, what exactly is a person's "true score"?
- Their innate, fixed level of ability
- Their score once guessing is removed
- Their average over endless independent retests
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Answer: Their average over endless independent retests
The true score is defined statistically as the expected value of observed scores across infinitely many independent administrations, not as some deeper real ability.
3. Classical test theory assumes random measurement error has what average across many testings of the same person?
- Zero
- A small positive value
- Equal to the standard error
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Answer: Zero
Errors are assumed to push scores up as often as down, so they average out to zero, which is why the long-run mean equals the true score.
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