Probability in the Measure of Achievement

Book Review

George Ingebo's 148 page book (MESA Press, 1997) is a strong resource for Rasch proponents aiming to promote clear thinking about measurement. There has long been a need for a short book to explain the basic concepts and specifications for successful Rasch measurement to those who have not had latent-trait model training. Dr. Ingebo's book does just that with a special emphasis on demonstrating the usefulness of Rasch measurement to educators, administrators, and parents. He also shows that Rasch measurement is far more useful than traditional population-based approaches to performance evaluation.

The book is easy to read and makes one wonder why traditional measurement approaches have lasted so long. The book will also whet the reader's research appetite with its succinct summaries of studies that demonstrate Rasch's superiority over traditional approaches.

There are four chapters and a glossary. Each chapter is divided into topics, which permit the reader to focus on topics of greatest interest. Though the presentation of theory is aimed at those without a latent-trait measurement background, this book does address advanced topics such as empirical methods to demonstrate the properties of the model and the methodology used to link different test forms to a common scale.

In Chapter 1, Dr. Ingebo explains what is wrong with the traditional way tests are assembled. He provides a clear explanation of what happens when student ability and test difficulty are not matched. He points out that it is not necessary for all students to take the same test to receive ability estimates that are expressed on the same ability continuum. Though this chapter may fail to clarify the distinction between chance and probability, that won't impede the reader's understanding of Rasch. The difference between item difficulty calibrations and p-values is clearly explained.

Chapter 2 is a workshop on how to create large-scale item banks that have all the items within a general content domain (math, language arts, etc.) calibrated onto a single continuum of difficulty. Dr. Ingebo accomplishes this by using a common item equating procedure. He describes in complete detail how the different forms of an exam can be linked together and how the common items that linked the exam forms together are selected.

In Chapter 3, Dr. Ingebo explains the theory behind the Rasch model. He also provides the reader with empirical designs to test whether several Rasch-calibrated examinations are really measuring the difficulty of the items in an unvarying way. Not only does he provide a brief summary of his findings, but, more important, he asks the right questions. He shows that because the Rasch model can provide stable calibrations across student populations, across grades, and across time, it becomes possible to measure a student at different points in time and so to measure the student's progress.

Chapter 4 compares the use of conventional population-based raw-score statistics with the use of Rasch ability estimates. The advantages of Rasch are clear. There is also a brief discussion about reporting information. But I would like to see more examples that graphically report results to parents, teachers, and administrators (RMT 4:1 pp. 98,100).

This work is a sturdy introduction to the Rasch model. The important ideas behind the model are presented in layman's terms. The application of the model is shown to be useful to everyone. The reader can see that the Rasch model is not an esoteric idea understood by only a few mathematicians. Rather it can be understood by almost anyone and, further, that it is used successfully right now in real school districts to produce real student benefits.

Thomas R. O'Neill
American Society of Clinical Pathologists

O'Neill T. (1998) Review of Probability in the Measure of Achievement by George S. Ingebo. Rasch Measurement Transactions 11:4 p. 597-8.

Review of Probability in the Measure of Achievement. O'Neill T. by George S. Ingebo. … Rasch Measurement Transactions, 1998, 11:4 p. 597-8.


Please help with Standard Dataset 4: Andrich Rating Scale Model



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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