MEASUREMENT RESEARCH ASSOCIATES
TEST INSIGHTS
October 2008
Greetings! 
 
A multiple-choice certification exam may have acceptable reliability, but it's likely that it can be improved in the most important area - the precision of candidate ability estimates near the cut score. The article below describes how.
 
Ross Brown
Manager Computer Based Testing and Analysis
Targeting Multiple Choice Examinations for Accurate Outcomes
The purpose of certification examinations is to make accurate pass or fail decisions about candidates. The more information available about the candidates who are close to the cut score, the more accurate the pass/fail decisions are. The Rasch perspective suggests that including more items with difficulties close to the cut score yields the most information about those candidates close to the cut score. This is often called test targeting.
 
On most tests, the item difficulties range from very easy to very difficulty. For test targeting, the items that are too easy and too difficult are replaced with items that have difficulties close to the pass point. These items are those that are answered correctly by between 30% and 80% of candidates. The Wright Map in Figure 1 created by the Winsteps Program (Linacre, 1989), is ideal for tracking item difficulty distribution relative to the pass point. Both candidate measures and item difficulties are on the same scale, so the distribution of candidate measures can be compared to the distribution of item difficulties. In the Wright Map below, the items within the bracket on the right are the targeted items.
 
There are costs to targeting tests. Item writers often find it difficult to write items that perform at this level. As tests become more targeted, they appear more difficult to candidates. But common-item test equating allows more difficult test forms to be developed while maintaining the pass point as an absolute standard. The table shows two examples of tests that were made more targeted. The equating difficulty is the average item difficulty of the test expressed in scaled scores.  When more items are in the target range of .30 to .80, the test becomes more difficult, but the difference in difficulty is accounted for in the analysis. The passing standard is maintained on the more difficult exam forms, but the percent correct necessary to pass decreases as the test becomes more difficult.  Thus, the test is better psychometrically, and does not penalize the candidates.
 

Exam

Percent of exam items with difficulties from 0.30 to 0.80

Equating Difficulty

Passing Standard

Percent Correct Necessary to Pass

Exam 1, Year 1

26%

5.00

5.63

61%

Exam 1, Year 2

47%

5.74

5.63

48%

Exam 2, Year 1

49%

5.00

5.73

65%

Exam 2, Year 2

74%

5.76

5.73

49%

 
Figure 1 Wright Map of Candidates and Items
 

MEASURE                                 |                               MEASURE

  <more> -------------------- Candidate-+- ITEMS   --------------------- <rare>

    2                               .# T+                                   2

                                     #  |T

          More Able Candidates   #####  |  X      Difficult Items

                              .#######  |  XXXX

                              .#######  |  XXXXXX

                              ########  |  XX

                         .############ S|  X

                     .################  |  XXXXXXXXX

                    ##################  |  XXXXX

                       .##############  |  XX

    1      .##########################  +  XXXXXXX                          1

                .#####################  |S XXXXX                |

                .##################### M|  XXXXXX               |

                     .################  |  XXXXXXX              |

                       .##############  |  XXXXXXXXXX           |   Targeted

                      ################  |  XXXXXXXXXX           |    Items

                    .#################  |  XXXXXXXXXXXXXXXX     |

      Cut Score  ­                 .### S|  XXXXXXXXXXXXX        |           

                        .#############  |  XXXXXXXXXXXXXX       |

                               .######  |  XXXXXXXXXXXXXX       |

    0                       ##########  +M XXXXXXXXXX           |            0

                                 .####  |  XXXXXXXXXXX          |

                                   ###  |  XXXXXXXXXX           |

                                  .### T|  XXXXXXXXXXXXX        |

                                   .##  |  XXXXXXXXXXX          |

                                     #  |  XXXXXX

         Less Able Candidates           |  XXXXXXXXXXXX

                                     .  |  XXXXXXXX

                                     .  |  XXXXXXXXX

                                     .  |S XXXXX

   -1                                   +  XXXX                            -1

                                        |  XXXXXXXX

                                        |  XX

                                        |  XXXX

                                        |  XXXXXX

                                        |  XXXX           Easy Items

                                        |  XX

                                        |  X

                                        |  X

                                        |T XXXX

                                        +  XXX                            

                                        |

   -2                                   +                                  -2

  <less> -------------------- Candidate-+- ITEMS   ------------------<frequent>

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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