Constructors of new test item formats must be wary, because test-wise examinees are looking for loopholes. Wu ("Oust the Incorrect" RMT 5,2 p.143) proposes a novel partial credit scoring method for multiple- choice questions (MCQs) based on asking each examinee to mark all options that are definitely incorrect. The score for an item is the number of incorrect options an examinee marks as incorrect, and is zero when the examinee marks the correct option as incorrect.
What happens when examinees use a guessing strategy? Then their expected score depends on how many options they decide to guess incorrect. The Table illustrates what expected scores occur when there is one correct answer. The rows are the number of options in the MCQ. The columns correspond to the number of options the examinee decides to guess incorrect in an MCQ. Then each cell gives the expected score for each row-column combination. For instance, when 2 options are guessed incorrect in a 5 option MCQ, then there will be a score of 0 if the correct option is marked incorrect, and a score of 2 otherwise. The probability of missing the correct option is 4/5 for the first mark, and 3/4 for the second mark, i.e. 4/5 * 3/4 = 3/5 for the two marks. The expected score is (the probability of missing the correct answer) * (the score for correctly selecting incorrect options) = 3/5 * 2 = 6/5 points. Only the two-option (True/False) and three-option MCQs are immune to guessing strategy abuse.
Conclusion: Use 3-option MCQs, or defeat guessing strategies by including MCQ items with none or several correct answers.
Number of MCQ Options: Number guessed incorrect: 0 1 2 3 4 5 2 0 1/2 0 - - - 3 0 2/3 2/3 0 - - 4 0 3/4 1 3/4 0 - 5 0 4/5 6/5 6/5 4/5 0 Expected Guessing Score
More "Oust The Incorrect", B Xiao Rasch Measurement Transactions, 1991, 5:3 p. 165
|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|
|Forum||Rasch 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, www.rasch.org.
|Coming Rasch-related Events|
|Jan. 30-31, 2020, Thu.-Fri.||A Course on Rasch Measurement Theory - Part 1, Sydney, Australia, course flyer|
|Feb. 3-7, 2020, Mon.-Fri.||A Course on Rasch Measurement Theory - Part 2, Sydney, Australia, course flyer|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Apr. 14-17, 2020, Tue.-Fri.||International Objective Measurement Workshop (IOMW), University of California, Berkeley, https://www.iomw.org/|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt53f.htm