Theories and Applications in Social Measurement

A Unit of Coursework in January 2000 in Perth, Western Australia

Australian Institute of Education - Murdoch University - The University of Western Australia

This unit provides a theory of social measurement that unifies major approaches used in education, psychology and sociology for the construction of scales for performance assessment, questionnaires for measuring attitude and preference and choice. The history, philosophy and mathematics of the theory are integrated in the process of considering the designs for data collection, the models for analysis, and the software for implementing the analyses. Basic principles will be emphasized throughout, and it will be shown how the study of bias, implementation of item banking, the study of profiles, and the like, arise from the same theory. This theory is based on the simple logistic model of Rasch for dichotomous responses, and it is extended into ordered category responses and into paired comparison response formats including those for preference and choice data.

Summary of content

Fundamental questions of the designs of observational frameworks and mathematical response models for the translation of observations into measurements, are examined. The course will commence with a study of the principles of psychological measurement outlined by Thurstone in the 1920's. The fundamental observational framework of Thurstone is the "paired comparison" design where a person responds to a pair of items at the same time. Within this design, two basic kinds of response processes are possible.

(i) The judge can decide which of two items, objects, etc, have more of the property, irrespective of their own location on the scale. This is done, for example, when expert judges might look at two pieces of writing, or two items, and decide which is the better or which is the more difficult, respectively. Here, the judges' own positions are expected to be so high, that their own ability, location, etc., plays no role. The response process of this kind is said to be cumulative. This design is becoming more commonly used as organizations use judges to compare items, in part to triangulate data from the direct responses of respondents to the items, and in part to form larger item banks. It is expected that some results from a major Australian study in the use of a paired comparison will be discussed.

(ii) The person responding makes a choice, and this in turn involves the person's own location. For example, in comparing two cups of coffee which differ only in the amount of sugar that they have, persons will choose the one they like best, and will reject cups of coffee with too much sugar or too little sugar, according to their own personal taste. This design has not been used as much as it can be for the evaluation of programs, and the like, where ideal levels of some property might be most appropriate, rather than more and more of some property. For example, in supporting rehabilitation, it might be that an ideal amount of support is appropriate, not too much and not too little. Because of the recent developments in the theory, item construction, and software which makes this response process readily manageable, the topic is covered in the course.

Although the paired comparison design itself does not play a central role in Rasch models, the paired comparison concept is central. Thus, the case for the Rasch models is that a comparison of two objects of measurement, or two instruments used for measurement, can be made independently of the locations of other persons or other instruments respectively, within a conformable class of persons and instruments. Rasch models will be applied to the pair comparison design. Following a study of the paired comparison design, the unit will deal with the direct response design where each person responds to each item, as in standard achievement assessment and attitude assessment. In this stage, it will be shown that the use of Rasch models can integrate the Guttman and popular Likert approach to attitude measurement.

Throughout the unit, it is intended to emphasize basic issues in using models for measurement. Therefore, a few examples and models will be studied in depth. The unit will not provide a compendium of many different approaches associated with many different standard types of measurement problems. Nevertheless, by focusing on basic principles, all of the most common types of questionnaires and models for their analysis are covered.

Basic principles of tests of fit of models and the use of degrees of freedom will be reviewed.

Topics Covered

Cumulative models. More is better.

The requirements of measurement, the pair comparison design and Thurstone's law of comparative judgement.

The Rasch model for paired comparisons, estimation and model fit.

The Rasch model for dichotomous and ordered response data, applications to the construction of performance assessments, studies in the tests of fit including item bias.

Principles for construction and application of item banks.

The theme of item banking, which is concerned with the possible use of different items for different persons at different times while obtaining measurements on the same scale, is integrated throughout the unit, as well as having specific discussions on designing and using item banks.

Unfolding models. An ideal, not too much and not too little, is the best.

Response functions for preference and choice data.

Construction of response formats and data analysis.

Methods of questionnaire and test construction for analysis of responses according to both the cumulative and unfolding models.

Reconciling the Thurstone, Likert, Guttman models using Rasch models.

Use of specialized software.

Use of Windows-based software for the analysis of data according to cumulative response models (RUMM for direct responses and RUMMcc for pair comparisons) and unfolding models (RUMMFOLDss for direct responses and RUMMFOLDpp for pairwise preferences) will be shown. Students will obtain student versions of the programs.

Course Arrangements

A set of reading materials, written lecture notes and exercises forms an integral part of the unit. The unit can be attended for formal assessment in a doctoral or masters program, or can be studied as a professional development unit. The essential difference is that for the former, the enrolment has to be made formally with the University, and a major assignment has to be presented for assessment.

The lectures, demonstrations and presentations will involve meeting for three hours each day for 10 days, from a Wednesday to a Tuesday, which therefore includes two weekends in January 2000.


A range of accommodation at Murdoch University, The University of Western Australia, in Fremantle and in Perth will be available.

The Pre-requisite Course Unit

If you are familiar with the basics of measurement and statistics and have had experience in Rasch measurement or other test theory, then you have the prerequisites. The immediate prerequisite unit is the one that was offered in the Australian Summer in 1998. This pre-requisite unit is available externally in the second semester of 1999 - that is from July to November 1999. A Study Guide and Assignments will be available on-line. There should also be a discussion group available on-line for students who enrol in this mode. If you would like to enrol in this unit, let me know at my email address.


Students at Australian universities, please contact me directly about costs and registration requirements. Other students can enrol on a direct fee-paying basis. The fee for the unit is $US960.00. Check with your own university about transferability of course credits. Anyone can enrol in the unit as a professional development unit for which no formal assessment and grading is carried out. If participants submit assignments, they will be marked. Those enrolled are given a certificate of participation. The cost of this form of enrolment is $US700.00.

Workshop on Health Outcome Issues

Following the course, a workshop will focus on the application of Rasch analyses to health outcome issues. This will be jointly organized by Alan Tennant, Charterhouse Principal Research Fellow in the Rheumatology & Rehabilitation Research Unit at the University of Leeds, UK, and Annette Mercer, Director of the Survey Research Centre, Department of Public Health, The University of Western Australia, whose department will host the workshop. The workshop will offer an introduction to the application of these methods in health outcome studies, and provide practical illustrations of the lessons learnt in the course in that context.

David Andrich

Professor, School of Education

Murdoch University


Western Australia 6150

Phone: 011+61+8 9360 2245

Fax: 011+61+8 9360 6280

Course on Social Measurement, Australia Andrich D.A. … Rasch Measurement Transactions, 1999, 12:4 p.

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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