ABSTRACT

Classical test theory (CTT) is a model of measurement error, meaning that CTT assumes that observed measurement values such as test scores contain a component caused by random measurement error. Measurement models from a later date also incorporate measurement error but are different from CTT in that they explicitly assume that the items have one or more latent variables in common, reflecting one or more shared attributes. Latent variables simplify the covariance structure of the items. CTT does not have latent variables and thus does not restrict the inter-item covariances; hence it takes the observed item scores as face values except for measurement error. The primary goal of CTT is to estimate the degree to which test scores are reliable and hence, error-free. We discuss CTT and define test-score reliability. We explain traditional methods for estimating reliability and methods based on a single test administration, and for the latter methods, we discuss statistical topics. Next, we discuss the measurement precision of individual test scores. We continue with methods for scale construction based on principal component analysis and factor analysis. Finally, we discuss reliability based on the factor model, hence based on latent variables.