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Multiple-Answer Multiple-Choice Test Items: Responding and Scoring Through Bayes and Minimax Strategies

Published online by Cambridge University Press:  01 January 2025

George T. Duncan  and
E. O. Milton
George T. Duncan*
Affiliation:
Carnegie-Mellon Univérsity
E. O. Milton
Affiliation:
University of California, Davis
*
Requests for reprints should be sent to George T. Duncan, Department of Statistics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213.
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Abstract

A multiple-answer multiple-choice test item has a certain number of alternatives, any number of which might be keyed. The examinee is also allowed to mark any number of alternatives. This increased flexibility over the one keyed alternative case is useful in practice but raises questions about appropriate scoring rules. In this article a certain class of item scoring rules called the binary class is considered. The concepts of standard scoring rules and equivalence among these scoring rules are introduced in the “misinformation” model for which the traditional “knowledge” model is a special case. The examinee’s strategy with respect to a scoring rule is examined. The critical role of a quantity called the scoring ratio is emphasized. In the case of examinee uncertainty about the number of correct alternatives on an item, a Bayes and a minimax strategy for the examinee are developed. Also an appropriate response for the examiner to the minimax strategy is outlined.

Keywords

multiple-choice testtest scoringBayesminimaxmultiple-answer test items
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 43 - 57
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

Research partially supported under Grants N00014-67-A-0314-0022 from the Office of Naval Research and GS-32514 and MPS 75-07539 from the National Science Foundation.

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