How Much Bias in answer till 3 wrong?

"Terminating the test after answering three consecutive items incorrectly is a common practice with individually-administered intelligence tests. Obviously, treating the not reached items as incorrect (which is the typical interpretation - that the examinee would not have answered any of the remaining items correctly) is not a good idea. This practice results in Rasch ability estimates that are biased. On the other hand, if you treat the data as missing, the bias is not as extreme, but it is still there."

Edward W. Wolfe, Michigan State University

Is this bias a serious problem? Ed Wolfe mentions further that he is doing authoritative simulation studies based on real data. But let's imagine a simple scenario. We have a uniform item bank of Rasch-behaving items. Start by administering an item three logits below the examinee. Then advance up the item bank, administering items equally spaced in difficulty. Stop after three consecutive failures. What examinee measures would we expect to obtain for different items spacings?

Effective of 3 consecutive errors rule


The Figure shows the results of a simple simulation study according to these criteria. Values close to -4 logits correspond to no correct answers at all. Although the overall bias is negligible, the impact on individual examinees can be huge! Definitely do not use the "3 error" stopping rule with a test containing closely spaced items!

How Much Bias? Wolfe, E.W., Linacre, J.M. … Rasch Measurement Transactions, 2000, 14:2 p.750




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
Rasch Books and Publications: Winsteps and Facets
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 Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang 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
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

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