January 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


                             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






                                        |  X

                                        |  X

   -2                                   +                                  -2


                                        |  X


                                        |  X



                                        |             Less difficult items



   -3                                   +                                  -3

  <less> --------------------- PERSONS -+- ITEMS   ------------------<frequent>

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

Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou Journal of Applied Measurement
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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