February 2008

Welcome to Test Insights published by Measurement Research Associates.  Test Insights comes from 30 years of experience working with certification, in-service, and oral examinations.  The purpose is to provide information and insights into common issues and problems encountered by certification boards and related associations, colleges, and societies.  This is meant to be a "quick" read which we hope you will find useful.


                       Mary E. Lunz, Ph.D.

How Much Does Test Difficulty Change Across Years?

The test equating process is designed to calculate differences in the difficulty of examinations among administrations.  In this example common item Rasch-model test equating techniques are used for multiple choice examinations.  By accounting for differences in difficulty across years, all candidates have a comparable opportunity to pass the examination, regardless of when they take the test.  Test equating also insures that the established criterion referenced pass point is maintained across test administrations.  It is expected that different test forms, given for different administrations, will have different levels of difficulty. 


The question is how different in difficulty are the test forms across annual administrations. The data reported are from five different certification examinations that were constructed to meet the established content guidelines of that field.  All of the examinations were analyzed using the Rasch model.  The scaled scores range from 1 to approximately 10.  Higher scaled scores indicate a more difficult test form, while lower scaled scores indicate an easier test form.  The year 1 test difficulty is set at 5.00.  Rasch common item horizontal test equating was used for each of the certification examinations.  The average test difficulty is reported for each of four years, counting the first year.  The last column shows the average change in difficulty during the four year period. 


For these examinations there is some change in test difficulty that needs to be accounted for across years to maintain the criterion referenced standard.  However, for most years, there is not a dramatic change in test difficulty.  Three of the five examinations became more difficult during the four-year period.  However, Exam 5 became easier on average as the years progressed.  For all examinations, except, Exam 1, the changes in the examination were substantial enough to affect the passing and failing candidates if the differences in the difficulty of the test had not been taken into account through the test equating process.



year 1


year 2


year 3


year 4

Average difficulty

Exam 1






Exam 2






Exam 3






Exam 4






Exam 5






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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 Journal of Applied Measurement
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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