Blind Guides to "Measurement"

Measuring Health: A Guide to Rating Scales and Questionnaires. Ian McDowell & Claire Newell (M&N). 2nd ed. Oxford: Oxford University Press, 1996.

Health Measurement Scales: A Practical Guide to their Development and Use, 2nd ed. David L. Streiner & Geoffrey R. Norman (S&N). New York: Oxford University Press, 1995.

M&N painstakingly summarize many health status surveys. They fail, however, in their attempt to describe the application of Rasch measurement to health research. They imbed Rasch measurement in descriptive Item Response Theory, rather than prescriptive fundamental measurement theory. As a result, they label the lack of a discrimination parameter in Rasch's models as a "limitation" (p. 22). They do not mention mathematical invariance or statistical sufficiency, which, because they are always assumed by all users, ought to be core issues in a book on any kind of measurement.

S&N Chapter 12 is on IRT. They too describe Rasch measurement as a special case of IRT that "assumes" equal discrimination among the items. But equal or pre-assigned discrimination is essential to the parameter separation that is the hallmark of mathematical thinking and successful measurement. Thus, far from being an inconvenient assumption, equal discrimination is a fundamental requirement for measurement. Furthermore, this requirement is assumed to be met whenever ratings are summed into a total score (Andersen 1977), as is standard practice in the health field.

Ironically, after presenting Rasch measurement in the context of IRT, S&N exclaim that "the major potential advantage of ICC [Item Characteristic Curve] scaling is that it allows test-free measurement; that is, people can be compared to one another on the trait even if they took different items!" -- a property produced only by pre-specifying discriminations. In fact, all three of S&N's supporting examples (Jastak & Wilkinson 1984, Connolly, et al. 1976; Woodcock, 1973) were explicitly developed on the basis of Rasch measurement and not descriptive IRT. S&N also impose IRT's need for large sample sizes on Rasch measurement, even though IRT theoreticians (Lord 1983; Hambleton & Cook 1977) admit that Rasch works well on small samples [see also RMT 7:4 p. 382].

Further, S&N mistakenly take the difference between error-free mathematical ideals and error-prone observations as counting against Rasch measurement, citing Bruce Choppin's (1976 p. 238) comment that "no item fits the model exactly." It is sad that a book that purports to be about measurement, mathematical thinking, and scientific generalization, misunderstands the difference between the abstract and the concrete. Here is another example of psychosocial scientists taking "refuge in quantitative methods that, because they assume more, demand less foundational research as the basis for their application. Methods that always yield a scaling solution, like the method of summated ratings [or IRT], are almost universally preferred to methods which, like Coombs' [or Rasch's], do not produce a [meaningful] scaling solution when they are falsified by the data. Surprisingly, vulnerability to falsification is commonly deemed by psychologists to be a fault rather than a virtue" (Michell, 1990: 130).

M&N lamented, in their first edition, that "the development of [Activity of Daily Living] scales has been so uncoordinated. More recent scales have not been planned explicitly on a careful review of the strengths and weaknesses of previous instruments, and the definition of disability itself seems usually to be taken for granted rather than clearly stated. There is no evidence for an accumulation of a body of scientific knowledge... We know relatively little about the overlap among the various measurement methods" [emphasis mine]. According to these books, little has changed since that statement was written, but the growing body of Rasch research, easily accessible via MEDLINE, indicates that these blatant flaws in health measurement methods are already being corrected. Perhaps Oxford University, or at least its Press, is still fulfilling its destiny as "the home of lost causes and forsaken beliefs" (Matthew Arnold).

William P. Fisher, Jr.
Louisiana State University Medical Center
New Orleans

Andersen EB. Sufficient statistics and latent trait models. Psychometrika 1977: 42(1):69-81.

Choppin B. Recent developments in item banking. In: De Gruitjer DNM, van der Kamp LJ, editors. Advances in Psychological and Educational Measurement. New York: Wiley, 1976: 233-45.

Connolly AJ, Nachtman W, Pritchett EM. Keymath: Diagnostic Arithmetic Test. Circle Pines, MN: American Guidance Service, 1976.

Hambleton RK, Cook LL. Latent trait models and their use in the analysis of educational test data. Journal of Educational Measurement 1977; 14(2):75-96.

Jastak S, Wilkinson GS. The Wide Range Achievement Test - Revised: Administration manual. Wilmington, DE: Jastak Associates, 1984.

Lord FM. Small N justifies Rasch model. In: Weiss DJ, editor. New horizons in testing: latent trait test theory and computerized adaptive testing. New York, NY: Academic Press, Inc., 1983: 51-61.

Michell J. An introduction to the logic of psychological measurement. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1990.

Woodcock RW. Woodcock Reading Mastery Tests. Circle Pines, MN: American Guidance Service, Inc., 1973.

Blind Guides to "Measurement". Fisher W. P. Jr. … Rasch Measurement Transactions, 1997, 11:2 p. 566-7.

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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