MEASUREMENT RESEARCH ASSOCIATES
TEST INSIGHTS
November 2009
Greetings
 
Test equating is a method of insuring that candidates are measured against the same criterion-referenced standard regardless of the test administration they challenge.  An exam meant to test the same area may vary in difficulty from administration to administration. Test equating accounts for these differences so that the same criterion-referenced standard can be used.

Mary E. Lunz, Ph.D.
                      Executive Director

Test Equating For Comparable Passing Standards
The purpose of test equating is to place examination administrations on the same Benchmark Scale. The differences in the difficulty of the two administrations are accounted for so the same criterion-referenced standard can be used from administration to administration.

For certification testing, Rasch common item test equating is frequently used in conjunction with a criterion-referenced standard. First a criterion-referenced standard is established on a Benchmark Scale. The data from an exam is used to calibrate the Benchmark scale. The exam should match the test blueprint to assure content validity, and it should include a sufficient number of items that have been field-tested or previously used, to insure that the exam is a satisfactory measure of the construct. A criterion-referenced standard can be established using any of the accepted methods, such as a modified Angoff, objective standard setting, bookmark (if item calibrations are available), or other. After the Benchmark Scale is established, the criterion-referenced standard is established as a score on that scale.

Equating to that Benchmark Scale and criterion standard requires that subsequent test administrations include a number of items that are calibrated to the Benchmark Scale (commonly called equators). The group of items chosen to be equators should represent all content areas, and should include items with a range of difficulty calibrations. The purpose of the equators is to statistically identify differences in difficulty between the Benchmark Scale and the current test administration. The current test administration may be more difficult or easier than the Benchmark Scale. Test equating allows these differences to be taken into account, so that the criterion-referenced standard can be used.

Using the Rasch model, the initial mean difficulty of the Benchmark Scale is set at a scaled score of 5.00. The mean difficulty represents the average difficulty of all items on the test. Therefore, if a subsequent test form is more difficult, the mean difficulty will be more than 5.00, but if the test is easier, the mean difficulty will be less than 5.00.

The pass point that is determined by the standard setting is set as a scaled score on the Benchmark Scale. However, if we translate the scaled score back to a percent correct, it is easier to understand how test equating works. For example, if a test administration is more difficult, the percent correct necessary to pass would be lowered to be equivalent to the criterion standard. On the other hand, if a test administration is easier, the percent correct necessary to pass would be higher to be equivalent to the criterion standard. Test equating is the statistical process that accounts for the differences in test difficulty and then adjusts the scale of the current test administration so that the same criterion standard can be used.

The table below shows how the test equating process works. Five different exams are represented. The test forms are different administrations of the each exam, each of which includes equator items and is calibrated to the Benchmark Scale.  Some test administrations of a particular exam are more difficult while others are easier. The results are simulated from samples of real data and the percent to pass is an approximation for demonstration purposes.


Mean Item Difficulty and Percent Correct Equivalent of the Criterion Standard

Exam

Benchmark Scale (% pass point)

Test Form #1
(% to pass)

Test Form #2
(% to pass)

Test Form #3
(% to pass)

1

5.00 (65%)

5.39 (harder, 62%)

4.87 (easier, 67%)

5.35 (harder, 63%)

2

5.00 (60%)

5.12 (harder, 57%)

4.99 (easier, 61%)

5.17 (harder, 56%)

3

5.00 (65%)

4.98 (easier, 66%)

4.83 (easier,  67%)

4.82 (easier, 68%)

4

5.00 (55%)

5.39 (harder, 53%)

4.99 (easier, 56%)

5.20 (harder, 52%)

5

5.00 (65%)

5.28 (harder, 63%)

5.20 (harder, 64%)

5.42 (harder, 61%)


Measurement Research Associates, Inc.
505 North Lake Shore Dr., Suite 1304
Chicago, IL  60611
Phone: (312) 822-9648     Fax: (312) 822-9650


Coming Rasch-related Events
March 21, 2019, Thur. 13th annual meeting of the UK Rasch user group, Cambridge, UK, http://www.cambridgeassessment.org.uk/events/uk-rasch-user-group-2019
April 4 - 8, 2019, Thur.-Mon. NCME annual meeting, Toronto, Canada,https://ncme.connectedcommunity.org/meetings/annual
April 5 - 9, 2019, Fri.-Tue. AERA annual meeting, Toronto, Canada,www.aera.net/Events-Meetings/Annual-Meeting
April 12, 2019, Fri. On-line course: Understanding Rasch Measurement Theory - Master's Level (G. Masters), https://www.acer.org/au/professional-learning/postgraduate/rasch
July 2-5, 2019, Tue.-Fri. 2019 International Measurement Confederation (IMEKO) Joint Symposium, St. Petersburg, Russia,https://imeko19-spb.org
July 11-12 & 15-19, 2019, Thu.-Fri. A Course in Rasch Measurement Theory (D.Andrich), University of Western Australia, Perth, Australia, flyer - http://www.education.uwa.edu.au/ppl/courses
Aug 5 - 10, 2019, Mon.-Sat. 6th International Summer School "Applied Psychometrics in Psychology and Education", Institute of Education at HSE University Moscow, Russia.https://ioe.hse.ru/en/announcements/248134963.html
Aug. 9 - Sept. 6, 2019, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 14 - 16, 2019. Wed.-Fri. An Introduction to Rasch Measurement: Theory and Applications (workshop led by Richard M. Smith) https://www.hkr.se/pmhealth2019rs
August 25-30, 2019, Sun.-Fri. Pacific Rim Objective Measurement Society (PROMS) 2019, Surabaya, Indonesia https://proms.promsociety.org/2019/
Oct. 11 - Nov. 8, 2019, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Nov. 3 - Nov. 4, 2019, Sun.-Mon. International Outcome Measurement Conference, Chicago, IL,http://jampress.org/iomc2019.htm
Jan. 24 - Feb. 21, 2020, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
May 22 - June 19, 2020, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 26 - July 24, 2020, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 7 - Sept. 4, 2020, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 9 - Nov. 6, 2020, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 25 - July 23, 2021, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com