How Much Does Test Difficulty Change Across Years?

MEASUREMENT RESEARCH ASSOCIATES

TEST INSIGHTS

February 2008

Greetings!

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.

Exam	Difficulty year 1	Difficulty year 2	Difficulty year 3	Difficulty year 4	Average difficulty
Exam 1	5.00	4.96	5.01	5.02	5.00
Exam 2	5.00	5.02	5.15	5.16	5.08
Exam 3	5.00	5.28	5.20	5.42	5.23
Exam 4	5.00	5.12	5.29	5.37	5.20
Exam 5	5.00	4.60	4.55	4.70	4.71

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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 2nd. 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

Coming Rasch-related Events
May 15-17, 2013, Wed.-Fri.	In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
May 20-22, 2013, Mon.-Wed.	In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
May 31 - June 28, 2013, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 7, 2013, Fri.	SPHERE workshop: Response-Shift and subjective measures in health science, Nantes, France, www.sphere-nantes.fr/
June 19-21, 2013, Wed.-Fri.	SIS 2013 Conference on Advances in Latent Variables: Methods, Models and Applications, Brescia, Italy, meetings.sis-statistica.org/index.php/sis2013/ALV
July 1 - Nov. 30, 2013, Mon.-Sun.	Online Course: Introduction to Rasch Measurement Theory (D. Andrich, RUMM), uwa.edu.au
July 5 - Aug. 2, 2013, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug.1-5, 2013, Thur.-Mon.	TERA-PROMS Annual Meeting, Kaohsiung, Taiwan, tera.education.nsysu.edu.tw
Aug. 9 - Sept. 6, 2013, Fri.-Fri.	On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 22, 2013, Thursday.	Symposium in honor of Svend Kreiner, Copenhagen, Denmark, biostat.ku.dk/kreinersymposium
Sept. 4-6, 2013, Wed.-Fri.	IMEKO TC1-TC7-TC13 Symposium: Measurement Across Physical and Behavioural Sciences, Genoa, Italy, www.imeko-genoa-2013.it
Sept. 13 - Oct. 11, 2013, Fri.-Fri.	On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com
Sept. 18-20, 2013, Wed.-Fri.	In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 23-25, 2013, Mon.-Wed.	In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 26-27, 2013, Thurs.-Fri.	In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Oct. 18 - Nov. 15, 2013, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 20 - Oct. 25, 2013, Sun.-Fri.	International Association for Educational Assessment (IAEA) 39th Annual Conference, Tel Aviv, Israel, www.iaea-2013.com
Dec. 11-13, 2013, Wed.-Fri.	In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
March 12-14, 2014, Wed.-Fri.	In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
May 14-16, 2014, Wed.-Fri.	In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
May 19-21, 2013, Mon.-Wed.	In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
July 4 - Aug. 1, 2014, Fri.-Fri.	On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 8 - Sept. 5, 2014, Fri.-Fri.	On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Sept. 10-12, 2014, Wed.-Fri.	In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 12 - Oct. 10, 2014, Fri.-Fri.	On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com
Sept. 15-17, 2014, Mon.-Wed.	In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 18-19, 2014, Thurs.-Fri.	In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
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