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Psychometrika

, Volume 31, Issue 2, pp 125–145 | Cite as

Admissible probability measurement procedures

  • Emir H. ShufordJr.
  • Arthur Albert
  • H. Edward Massengill
Article

Abstract

Admissible probability measurement procedures utilize scoring systems with a very special property that guarantees that any student, at whatever level of knowledge or skill, can maximize his expected score if and only if he honestly reflects his degree-of-belief probabilities. Section 1 introduces the notion of a scoring system with the reproducing property and derives the necessary and sufficient condition for the case of a test item with just two possible answers. A method is given for generating a virtually inexhaustible number of scoring systems, both symmetric and asymmetric, with the reproducing property. A negative result concerning the existence of a certain subclass of reproducing scoring systems for the case of more than two possible answers is obtained. Whereas Section 1 is concerned with those instances in which the possible answers to a query are stated in the test itself, Section 2 is concerned with those instances in which the student himself must provide the possible answer(s). In this case, it is shown that a certain minor modification of a scoring system with the reproducing property yields the desired admissible probability measurement procedure.

Keywords

Public Policy Probability Measurement Statistical Theory Special Property Test Item 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Psychometric Society 1966

Authors and Affiliations

  • Emir H. ShufordJr.
    • 1
  • Arthur Albert
    • 2
  • H. Edward Massengill
    • 1
  1. 1.Lexington
  2. 2.Arcon Inc.Lexington

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