Classical (Psychometric) Test Theory

Abstract

Classical test theory (CTT) has been developed to quantify measurement error and to solve related problems such as correcting observed dependencies between variables (e.g., correlations) for attenuation due to measurement errors. Basic concepts of CTT are true score and measurement error variables. These concepts are defined as specific conditional expectations and their residuals, respectively. The definitions of these concepts already imply a number of properties that were considered axioms in early presentations of CTT. Models of CTT consist of assumptions about the true score and error variables allowing to identify the theoretical parameters (such as true score variance and error variance) from the variances and covariances of the observable measurements (test score variables). A number of implications of the assumptions defining models of CTT may be tested empirically via structural equation modeling. Hinting at more recent theories and their goals such as item response theory, generalizability theory, and latent state-trait theory concludes this article.