Using Classical Test Theory in Combination with Item Response Theory

Abstract

This study is about relations between classical test theory (CTT) and item response theory (IRT). It is shown that CTT is based on the assumption that measures are exchangeable, whereas IRT is based on conditional independence. Thus, IRT is presented as an extension of CTT, and concepts from both theories are related to one another. Furthermore, it is demonstrated that IRT can be used to provide CTT statistics in situations where CTT fails. Reliability, for instance, can be determined even though a test was not administered to the intended population.