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.

Graduates and professionals are likely to encounter classical test theory. Therefore, introductory chapters review the elements of this theory. The perspective on the relationship between Rasch measurement theory and classical test theory is that the former is an elaboration of the ideals of the latter, not that they are entirely in conflict. However, because the centrality of invariance as a requirement for measurement had been articulated by two giants of social measurement, L. L. Thurstone and L. Guttman, reference is made to their work. In particular, Thurstone had articulated the requirements of invariance in almost identical terms as G. Rasch, but did not express it in terms of a mathematical equation, and the elementary Guttman design which is introduced in the early chapters, is shown to be a deterministic form of the Rasch model. The distinctive contribution of Rasch compared to that of Thurstone and Guttman is that the model studied in this book has built into it the principle of invariance and is immediately probabilistic. Therefore, the deviation of data from the model implies some kind of deviation from invariance and measurement. Together with the relationships shown with classical test theory, the book provides a unified theme for approaches to social measurement, rather than as a compendium of techniques.

Finally, the book stresses that the requirement of invariance, and its expression in the Rasch model, is necessary, but not sufficient to ensure sound measurement. All the principles of measurement, of experimental design and of statistical inference must be applied in the process of constructing instruments that provide invariance of comparisons and reliable and valid measurement. Indeed, the explicit requirements of invariance in the Rasch model can at times appear more demanding of the data than do other theories and approaches.