A minimax procedure in the context of sequential mastery testing

Hendrik J. Vos

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Abstract

The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master or a nonmaster, or to continue sampling and administering another random test item. The framework of minimax sequential decision theory (minimum information approach) is used; that is, optimal rules are obtained by minimizing the maximum expected losses associated with all possible decision rules at each stage of sampling. The binomial model is assumed for the probability of a correct response given the true level of functioning, whereas threshold loss is adopted for the loss function involved. Monotonicity conditions are derived, that is, conditions sufficient for optimal rules to be in the form of sequential cutting scores. The paper concludes with a simulation study in which the minimax sequential strategy is compared with other procedures that exist for similar classification decisions in the literature.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages29
Publication statusPublished - 1999

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.99-04

Keywords

  • Classification
  • Mastery Tests
  • Models
  • METIS-136391
  • Sampling
  • IR-104140
  • Foreign Countries

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    Vos, H. J. (1999). A minimax procedure in the context of sequential mastery testing. (OMD research report; No. 99-04). Enschede: University of Twente, Faculty Educational Science and Technology.