IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-05384180.html

Ecient Scoring of Multiple-Choice tests
[Notation efficace des questions à choix multiples]

Author

Listed:
  • Alexis Direr

    (LEO - Laboratoire d'Économie d'Orleans [2022-...] - UO - Université d'Orléans - UT - Université de Tours - UCA - Université Clermont Auvergne)

Abstract

This paper studies the optimal scoring of multiple choice tests in which the marks for wrong selections and omissions jointly minimize the mean square dierence between score and examinees' abilities. Examinees are loss averse and, as a result, reluctant to risk answers on the basis of their knowledge. I nd that it is ecient to incentivize the lowest able to omit, except when the test has a very large number of items. The mark for omission is positive when the test size is limited and negative when it is large. Loss aversion generally improves estimators eciency by spontaneously inducing more omission and thereby reducing the need to bias the mark upward to encourage omission.The model sheds light on the statistical properties of two widely used scoring methods, Number right scoring and Formula scoring.

Suggested Citation

  • Alexis Direr, 2025. "Ecient Scoring of Multiple-Choice tests [Notation efficace des questions à choix multiples]," Post-Print hal-05384180, HAL.
    • Handle: RePEc:hal:journl:hal-05384180
    DOI: 10.3917/reco.763.0417
    Note: View the original document on HAL open archive server: https://hal.science/hal-05384180v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-05384180v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.3917/reco.763.0417?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Pelin Akyol & James Key & Kala Krishna, 2022. "Hit or Miss? Test Taking Behavior in Multiple Choice Exams," Annals of Economics and Statistics, GENES, issue 147, pages 3-50.
    2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Nicholas Barberis & Ming Huang & Richard H. Thaler, 2006. "Individual Preferences, Monetary Gambles, and Stock Market Participation: A Case for Narrow Framing," American Economic Review, American Economic Association, vol. 96(4), pages 1069-1090, September.
    5. Pekkarinen, Tuomas, 2015. "Gender differences in behaviour under competitive pressure: Evidence on omission patterns in university entrance examinations," Journal of Economic Behavior & Organization, Elsevier, vol. 115(C), pages 94-110.
    6. David Budescu & Yuanchao Bo, 2015. "Analyzing Test-Taking Behavior: Decision Theory Meets Psychometric Theory," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1105-1122, December.
    7. Heath, Chip & Tversky, Amos, 1991. "Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexis DIRER, 2020. "Efficient scoring of multiple-choice tests," LEO Working Papers / DR LEO 2752, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    2. Qian Wu & Monique Vanerum & Anouk Agten & Andrés Christiansen & Frank Vandenabeele & Jean-Michel Rigo & Rianne Janssen, 2021. "Certainty-Based Marking on Multiple-Choice Items: Psychometrics Meets Decision Theory," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 518-543, June.
    3. Pau Balart & Lara Ezquerra & Iñigo Hernandez-Arenaz, 2022. "Framing effects on risk-taking behavior: evidence from a field experiment in multiple-choice tests," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1268-1297, September.
    4. Stefano DellaVigna, 2009. "Psychology and Economics: Evidence from the Field," Journal of Economic Literature, American Economic Association, vol. 47(2), pages 315-372, June.
    5. Chen Lian & Yueran Ma & Carmen Wang, 2019. "Low Interest Rates and Risk-Taking: Evidence from Individual Investment Decisions," The Review of Financial Studies, Society for Financial Studies, vol. 32(6), pages 2107-2148.
    6. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    7. Barberis, Nicholas & Huang, Ming, 2009. "Preferences with frames: A new utility specification that allows for the framing of risks," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1555-1576, August.
    8. Gul, Faruk & Pesendorfer, Wolfgang, 2015. "Hurwicz expected utility and subjective sources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 465-488.
    9. Fox, Craig R. & Weber, Martin, 2002. "Ambiguity Aversion, Comparative Ignorance, and Decision Context," Organizational Behavior and Human Decision Processes, Elsevier, vol. 88(1), pages 476-498, May.
    10. Aurélien Baillon & Zhenxing Huang & Asli Selim & Peter P. Wakker, 2018. "Measuring Ambiguity Attitudes for All (Natural) Events," Econometrica, Econometric Society, vol. 86(5), pages 1839-1858, September.
    11. Richard J. Arend, 2020. "Strategic decision-making under ambiguity: a new problem space and a proposed optimization approach," Business Research, Springer;German Academic Association for Business Research, vol. 13(3), pages 1231-1251, November.
    12. Francisco Gomes & Michael Haliassos & Tarun Ramadorai, 2021. "Household Finance," Journal of Economic Literature, American Economic Association, vol. 59(3), pages 919-1000, September.
    13. Greg Barron & Eldad Yechiam, 2009. "The coexistence of overestimation and underweighting of rare events and the contingent recency effect," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 4(6), pages 447-460, October.
    14. Marianne Andries, 2012. "Consumption-based Asset Pricing Loss Aversion," 2012 Meeting Papers 571, Society for Economic Dynamics.
    15. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality within Three Dimensions," Research in the History of Economic Thought and Methodology, in: Including a Symposium on Latin American Monetary Thought: Two Centuries in Search of Originality, volume 36, pages 119-155, Emerald Group Publishing Limited.
    16. Divya Aggarwal & Pitabas Mohanty, 2022. "Influence of imprecise information on risk and ambiguity preferences: Experimental evidence," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(4), pages 1025-1038, June.
    17. Mercè Roca & Robin Hogarth & A. Maule, 2006. "Ambiguity seeking as a result of the status quo bias," Journal of Risk and Uncertainty, Springer, vol. 32(3), pages 175-194, May.
    18. Balbontin, Camila & Hensher, David A. & Collins, Andrew T., 2017. "Do familiarity and awareness influence voting intention: The case of road pricing reform?," Journal of choice modelling, Elsevier, vol. 25(C), pages 11-27.
    19. Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
    20. Laure Cabantous & Denis Hilton, 2006. "De l'aversion à l'ambiguïté aux attitudes face à l'ambiguïté. Les apports d'une perspective psychologique en économie," Revue économique, Presses de Sciences-Po, vol. 57(2), pages 259-280.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-05384180. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.