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 Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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Coming Rasch-related Events
July 31 - Aug. 3, 2017, Mon.-Thurs. Joint IMEKO TC1-TC7-TC13 Symposium 2017: Measurement Science challenges in Natural and Social Sciences, Rio de Janeiro, Brazil,
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Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
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May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
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Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),
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