classical test theory (CTT)

the theory that an observed score (e.g., a test result) that is held to represent an underlying attribute (e.g., intelligence) may be divided into two quantities—the true value of the underlying attribute and the error inherent to the process of obtaining the observed score. CTT may be represented mathematically as Xp = Tp + ep, where Xp is the observed score for respondent p, Tp is the respondent’s true score for the construct or characteristic being measured, and ep is random error that dilutes the expression of respondent p’s true score. The theory serves as the basis for models of test reliability and assumes that individuals possess stable characteristics or traits that persist through time. See also generalizability theory. Compare item response theory.