MEASUREMENT RESEARCH ASSOCIATES TEST INSIGHTSJanuary 2010
 Greetings and Happy New Year,   One of the most useful outputs from the Rasch Winsteps program is the Wright Map.  The Wright Map can be helpful for any organization that uses multiple choice examinations, as it provides a picture of how well their exam is measuring. Mary E. Lunz, Ph.D. Executive Director
Using The Very Useful Wright Map
The Wright Map provides a picture of a multiple choice exam by placing the difficulty of the exam items on the same measurement scale as the ability of the candidates.  This provides the user with a comparison of candidates and items, to better understand how appropriately the test measured.  A sample Wright Map is shown below.

The Wright Map is organized as two vertical histograms. The left side shows candidates and the right side shows items. The left side of the map shows the distribution of the measured ability of the candidates from most able at the top to least able at the bottom.  The items on the right side of the map are distributed from the most difficult at the top to the least difficult at the bottom.

On the left side, the Wright Map shows the mean (M) and two standard deviation points (S = one SD and T = two SD) for measured candidate ability.  On the right side of the map, the mean difficulty of the items (M) and two standard deviation points (S = one SD and T = two SD) for the items are shown.  The sample map below shows that the mean (M) ability of the candidates is approximately one standard deviation (S) above the mean (M) difficulty of the items.

Each "x" represents a candidate on the left side or an item on the right side of the map.  The candidates at the top of the map had the highest scores, while the items at the top of the map are the most difficult. The candidates at the bottom of the map earned the lowest scores, and the items at the bottom of the map are easiest. Theoretically, when candidates and items are opposite each other on the map, the difficulty of the item and the ability of the candidate are comparable, so the candidate has approximately a 50% probability of answering the item correctly.

The items at the top of the map were probably answered correctly by about 30% of the candidates who are the most able. The items at the bottom of the map are the very easy items and were probably answered correctly by over 90% of the candidates.  Those items are well below the ability of the least able candidate indicating that all candidates have a greater than 50% probability of answering the items correctly.  However, tests discriminate best between marginally acceptable and marginally unacceptable candidates when a large group of items have difficulty estimates close to the pass point. The ability of the candidates close to the pass point is the most essential differentiation to make, and having a large number of items at this critical point gives the most accurate information for those candidates.

The pass point is marked on the map.  The map shows that over half of the items were within plus or minus one standard deviation of the pass point.  There were also many candidates aligned within one standard deviation of the pass point.  Therefore, this sample exam includes a sufficient number of items in the center of the item distribution, close to the pass point to differentiate between candidates who should pass or fail as accurately as possible.

The Wright Map

### MEASURE                                 |                               MEASURE  <more> --------------------- PERSONS -+- ITEMS   --------------------- <rare>    3                                   +                                   3                                        |                                        |                                        |         More able candidates           |           More difficult items                                        |                                        |                                        |                                        |                                     X  |    2                                X  +                                   2                                     X  |  X                                    XX T|                                   XXX  |                                   XXX  |  X                               XXXXXXX  |                                XXXXXX  |T                               XXXXXXX  |  XX                      XXXXXXXXXXXXXXXX S|  XXX                         XXXXXXXXXXXXX  |  XX    1                 XXXXXXXXXXXXXXXX  +  XX                               1                        XXXXXXXXXXXXXX  |  XXXX                           XXXXXXXXXXX  |  XXXXXX                 XXXXXXXXXXXXXXXXXXXXX M|S XXXXX                             XXXXXXXXX  |  XXXXX                            XXXXXXXXXX  |  XXXXXX                     XXXXXXXXXXXXXXXXX  |  XXXXXXXX    Pass point         XXXXXXXXXXXXXXX  |  XXXXXXXXX____________________                                XXXXXXX S|  XXXXXX                             XXXXXXXXX  |  XXXXXXXXX    0                          XXXXXXX  +M XXXXXXX                          0                          XXXXXXXXXXXX  |  XXXXXXX                                   XXX  |  XXXXXXXXXXX                                    XX  |  XXXXXXX                                     X T|  XXXXX                                        |  XXXXX                                     X  |  XXXXXXXXXX                                        |S XXX        Less able candidates         X  |  XXXX                                        |  XX   -1                                   +  XXX                             -1                                        |  XX                                        |  XXX                                        |                                        |T                                        |                                        |                                        |                                        |  X                                        |  X   -2                                   +                                  -2                                        |                                        |  X                                        |                                        |  X                                        |                                        |                                        |             Less difficult items                                        |                                        |   -3                                   +                                  -3  <less> --------------------- PERSONS -+- ITEMS   ------------------<frequent>

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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
June 30 - July 29, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
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, imeko-tc7-rio.org.br
Aug. 7-9, 2017, Mon-Wed. In-person workshop and research coloquium: Effect size of family and school indexes in writing competence using TERCE data (C. Pardo, A. Atorressi, Winsteps), Bariloche Argentina. Carlos Pardo, Universidad Catòlica de Colombia
Aug. 7-9, 2017, Mon-Wed. PROMS 2017: Pacific Rim Objective Measurement Symposium, Sabah, Borneo, Malaysia, proms.promsociety.org/2017/
Aug. 10, 2017, Thurs. In-person Winsteps Training Workshop (M. Linacre, Winsteps), Sydney, Australia. www.winsteps.com/sydneyws.htm
Aug. 11 - Sept. 8, 2017, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 18-21, 2017, Fri.-Mon. IACAT 2017: International Association for Computerized Adaptive Testing, Niigata, Japan, iacat.org
Sept. 15-16, 2017, Fri.-Sat. IOMC 2017: International Outcome Measurement Conference, Chicago, jampress.org/iomc2017.htm
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
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