A Course in Rasch Measurement Theory

Abstract

This book has arisen from two postgraduate level courses in Rasch measurement theory that have been taught both online and in intensive mode for over two decades at Murdoch University and The University of Western Australia. The theory is generally applied in the fields of education, psychology, sociology, marketing and health outcomes to create measures of social constructs. Social measurement often begins with assessments in ordered categories, with two categories being a special case. To increase their reliability and validity, instruments are composed of multiple, distinct items which assess the same variable. Rasch measurement theory is used to assess the degree to which the design and administration of the instrument are successful and to diagnose problems which need correcting. Following confirmation that an instrument is working as required, persons may be measured on a linear scale with an arbitrary unit and arbitrary origin. The main audiences for the book are graduate students and professionals who are engaged in social measurement. Therefore, the emphasis of course is on first principles of both the theory and its applications. Because software is available to carry out analyses of real data, small hand-worked examples are presented in the book. The software used in the analysed examples, which is helpful in working through the text, is RUMM2030 (Rasch unidimensional models for measurement). Although the first principles are emphasized, much of the course is based on research by the two authors and their colleagues. The distinctive feature of Rasch measurement theory is that the model studied in this book arises independently of any data—it is based on the requirement of invariant comparisons of objects with respect to instruments within a specified frame of reference and vice versa. This is a feature of all measurement. Deviations of the data from the model are taken as anomalies to be explained and the instrument improved. The approach taken is to provide the researcher with confidence to be in control of the analysis and interpretation of data, and to make professional rather than primarily statistical decisions. Because statistical principles are necessarily involved, reviews of the necessary statistics are provided in Appendix D.