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Theoretical evaluation of partial credit scoring of the multiple-choice test item

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  • Rasmus A. X. Persson

    (University of Gothenburg)

Abstract

In multiple-choice tests, guessing is a source of test error which can be suppressed if its expected score is made negative by either penalizing wrong answers or rewarding expressions of partial knowledge. Starting from the most general formulation of the necessary and sufficient scoring conditions for guessing to lead to an expected loss beyond the test-taker’s knowledge, we formulate a class of optimal scoring functions, including the proposal by Zapechelnyuk (Econ. Lett. 132, 24–27 (2015)) as a special case. We then consider an arbitrary multiple-choice test taken by a rational test-taker whose knowledge of a test item is defined by the fraction of the answer options which can be ruled out. For this model, we study the statistical properties of the obtained score for both standard marking (where guessing is not penalized), and marking where guessing is suppressed either by expensive score penalties for incorrect answers or by different marking schemes that reward partial knowledge.

Suggested Citation

  • Rasmus A. X. Persson, 2023. "Theoretical evaluation of partial credit scoring of the multiple-choice test item," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 143-161, August.
    • Handle: RePEc:spr:metron:v:81:y:2023:i:2:d:10.1007_s40300-022-00237-w
    DOI: 10.1007/s40300-022-00237-w
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    References listed on IDEAS

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    1. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    2. Jef Vanderoost & Rianne Janssen & Jan Eggermont & Riet Callens & Tinne De Laet, 2018. "Elimination testing with adapted scoring reduces guessing and anxiety in multiple-choice assessments, but does not increase grade average in comparison with negative marking," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-27, October.
    3. Zapechelnyuk, Andriy, 2015. "An axiomatization of multiple-choice test scoring," Economics Letters, Elsevier, vol. 132(C), pages 24-27.
    4. Jean Gibbons & Ingram Olkin & Milton Sobel, 1979. "A subset selection technique for scoring items on a multiple choice test," Psychometrika, Springer;The Psychometric Society, vol. 44(3), pages 259-270, September.
    5. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    6. James Ramsay & Marie Wiberg & Juan Li, 2020. "Full Information Optimal Scoring," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 297-315, June.
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