November 2009
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


Benchmark Scale (% pass point)

Test Form #1
(% to pass)

Test Form #2
(% to pass)

Test Form #3
(% to pass)


5.00 (65%)

5.39 (harder, 62%)

4.87 (easier, 67%)

5.35 (harder, 63%)


5.00 (60%)

5.12 (harder, 57%)

4.99 (easier, 61%)

5.17 (harder, 56%)


5.00 (65%)

4.98 (easier, 66%)

4.83 (easier,  67%)

4.82 (easier, 68%)


5.00 (55%)

5.39 (harder, 53%)

4.99 (easier, 56%)

5.20 (harder, 52%)


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

Please help with Standard Dataset 4: Andrich Rating Scale Model

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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