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

Measurement Research Associates, Inc.
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Coming Rasch-related Events
Sept. 27-29, 2017, Wed.-Fri. In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 25-27, 2017, Wed.-Fri. In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement
Dec. 6-8, 2017, Wed.-Fri. In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com