Psychometrically relevant population differences may limit the transferability of research instruments between migrants and their source population and may contribute to a low performance of quantitative questionnaires. Based on a review of existing taxonomies, this book develops a comprehensive analytical framework of equivalence that can serve multiple purposes. It allows to examine psychometrically relevant population differences, it can assist in the re-adaptation of questionnaires and it is a valuable tool for cross-group comparative research. The application of the framework is illustrated through the examination of equivalence of the Revised Illness Perception Questionnaire (IPQ-R) between chronically ill Turks residing in Turkey and Turkish migrants residing in Germany.