Scores and Measures

"Obviously, most psychometricians would favor a less straightforward sense of representation, one in which sameness or difference of test scores only indicated sameness or difference of the attribute represented with a specific probability. For example, Rasch's theory of test scores, mentioned in Chapter 1, allows people of the same ability to obtain different scores and people of different levels of ability to get the same score on particular occasions."

Joel Michell (1999) Measurement in Psychology: Critical History of a Methodological Concept. Cambridge: Cambridge University Press. p. 166-7 n.

Can anyone illuminate what he might be after here?

Trevor Bond

Michell is contrasting Rasch models with "error-free" models. In these strictly deterministic models, a latent measure is always observed as a particular score, and a particular score always indicates the same latent measure. Under Rasch model conditions, in contrast, the relationship between measures and scores is probabilistic. Any score can be observed for a particular measure, and any measure can generate a particular score. Figures 1 and 2 illustrate this for a test of 5 uniformly distributed items.

Michell, however, errs when he perceives the Rasch model to be a model of psychological processes, rather than the necessary and sufficient expression of measurement. "If Rasch's hypothesis is correct, the estimates can be regarded as measures of the ability involved. Some psychologists claim to be able in this way to measure intellectual abilities." (p. 12)

Scores and measures. Michell J, Bond T. … Rasch Measurement Transactions, 2000, 14:1 p.731

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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