# More "Oust The Incorrect"

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 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

 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
Aug. 11 - Sept. 8, 2023, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 29 - 30, 2023, Tue.-Wed. Pacific Rim Objective Measurement Society (PROMS), World Sports University, Macau, SAR, China https://thewsu.org/en/proms-2023
Oct. 6 - Nov. 3, 2023, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Facets), www.statistics.com
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024