Difficulties and Average Category Measures

"Why do the average category measures sometimes say an obviously easy lower rating scale category is more difficult than a much harder higher category?"

Tetsuhito Shizuka

This often perplexes us. First, a definition: "difficulty" is always a combination of "difficulty of observing" and "difficulty of doing". We hope that "difficulty of observing" is much less than "difficulty of doing" so that "doing" dominates the data.

For instance, imagine an observation protocol designed to assess speed. We can easily observe cars driving less than 50 km/hour: we can give them a rating of "1". It is more difficult to observe cars driving faster than 50 km/hour, because we have less time in which to observe each one: we can give them a rating of "3". It is almost impossible to observe cars driving exactly 50 km/hour, because they are rare, but we can give those cars (if we observe any) a rating of "2".

On the intended rating scale of "slow", "medium", "fast", the ratings are ordered 1,2,3. In difficulty of observing, however, the ratings are ordered 1,3,2. These two orderings will be confounded in our data set. Consequently we can expect that the step calibrations, the Rasch rating scale parameters, will be disordered.

If we note down all the cars observed in category 1, and then average their measures on our entire instrument, we obtain an average measure for category 1. This reports "what is the average measure of cars rated 1 in this sample?". Similarly, the average measure for category 2 reports on "what is the average measure of cars rated 2 in this sample?" These averages are measures on the underlying linear metric, but are descriptive of this sample and this use of the rating scale. Since observation of a higher category is supposed to be indicative of an object with more of the variable, we expect that the average measure for category 2 will be noticeably higher than that for category 1, and 3 higher than 2. If not, this use of the rating scale has produced a blurred or contradictory description of this sample, so that we have good reason to examine our measuring instrument for flaws. Do the items cooperate to form one variable? Do higher categories indicate more of the variable in a uniform way? Are raters using the instrument in the manner intended?

John Michael Linacre

Difficulties and Average Category Measures Shizuka T., Linacre J.M. … Rasch Measurement Transactions, 2000, 13:4 p. 717




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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