Educational achievement is a very important issue for parents, teachers, and the government. An accurate measurement plays a very important role in evaluating achievement fairly, and, therefore, analysis methods have been developed considerably in recent years. Education based on long-time learning processes forms a fruitful base for item tests,…

When comparing data derived from tests or questionnaires in cross-national studies, researchers commonly assume measurement invariance in their underlying scaling models. However, different cultural contexts, languages, and curricula can have powerful effects on how students respond in different countries. This article illustrates how the…