Classical test theory
Separate observed scores into true score and error
Classical test theory represents an observed score as a true score plus measurement error under a defined replication process. The true score is an expected score over hypothetical replications, not an independently known psychological truth. Reliability is a population variance ratio, and item statistics and reliability estimates can change across populations and test forms. CTT often supports familiar total-score analyses.
Use when evaluating a fixed test or composite through item statistics, reliability and standard errors, and a score-level measurement framework matches the intended application.
Strengths
- Provides an accessible framework for score error and reliability
- Supports practical evaluation of fixed tests
Limitations
- Item and reliability statistics depend on the sample and form
- Simple applications may obscure differing precision across trait levels
Know the boundary
A CTT true score is an expectation under replications, not proof of a person's essential ability.