MCQ - Oust the Incorrect

An obvious criticism of the multiple-choice question (MCQ) format is susceptibility to lucky guessing. A subtle criticism is its all or nothing scoring. MCQ makes no attempt to discover what unsuccessful candidates do know about an item. An alternative method for MCQs is to ask each examinee to mark all options that are definitely incorrect.

Scoring for "eliminate the incorrect" is simple. When an examinee marks the "correct" option as incorrect, the score is 0. Otherwise the score is the number of "incorrect" options marked as incorrect. For a 5 option item, possible scores are 0 (no options marked or "correct" option marked) to 4 (all "incorrect" options marked). This partial credit approach discourages guessing, and enables the examinee to gain credit for whatever partially correct solution is obtained. Here is an example with a score of 3:

Which cities are definitely not the capital of Peru?
  [x] A.  Bogota
  [x] B.  Caracas
  [ ] C.  Colon
  [ ] D.  Lima
  [x] E.  Montevideo

In a 60 item verbal comprehension test the average point-biserial correlation for conventional scoring was .41. For revised scoring, the average item score-total score correlation was .51. Person separation reliability improved from .91 to .95 and separation from 3.3 to 4.5. This improvement is equivalent to adding 50 more items to the test.

The next stage is to construct a measurement model for this response structure and to explore alternative scoring strategies. I welcome comments.

MCQ - Oust the Incorrect, Y-Y Wu … Rasch Measurement Transactions, 1991, 5:2 p. 143

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

To be emailed about new material on
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from welcomes your comments:

Your email address (if you want us to reply):


ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website,

Coming Rasch-related Events
June 23 - July 21, 2023, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),
Aug. 11 - Sept. 8, 2023, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),


The URL of this page is