The Eternal Question about Raw Score: Is Right worth more than Wrong?

Question: Suppose that there are two examinees: A and B. Both have a score of 25 out of 50 on an ability test. But A answered the 25 most difficult items correctly, and B answered 25 easiest correctly. Is it logical that they have the same Rasch ability estimates? Does a right answer to a hard item more than cancel out a wrong answer to an easy item?

Reply: This isn't merely a "Rasch" problem, but a fundamental conceptual problem in understanding person performance. What is the ability of examinee A, regardless of the analytical model? On the easy items, very incompetent, or very careless, or .... On the hard items, very competent, or very lucky, or ....

If this was a driving test, or a test of surgical skills, we hope examinee A fails. But if this is Albert Einstein on an arithmetic test, we hope he passes.

Under Rasch model conditions, every way of making a raw score has some probability of being observed. It just so happens that A responded in the most unlikely way, and B in the most likely, but, from the Rasch perspective, both manifested the same ability. In effect, the Rasch model takes the position that the penalty for failing an easy item is the same as the credit for succeeding on a hard one, so that all ways of making 25 on 50 items have the same measure. But definitely not the same quality-control fit statistics.

Of course, if you don't believe an examinee's answers to the easy (or hard) items correspond to that examinee's ability, you can make them missing data - if you dare!

The Eternal Question: Is Right worth more than Wrong? Linacre J.M. … Rasch Measurement Transactions, 2002, 15:4 p. 855

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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