title: Shapley weights of test items
metadata.name: dc.contributor.author
metadata.value: Lutsenko, Mikhail M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Shadrinceva, Natalia V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-10-12T09:54:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-10-12T09:54:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lutsenko M. M., Shadrinceva N. V. Shapley weights of test items. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 3, pp. 300–312.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.307
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8515
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: One of the problems of the theory of testing is the problem of determining the weights of the
  test item. For most tests, the weights of assignments are considered to be equal, but as the
  complexity of test design and increasing the number of test items, the need for determining the
  complexity of the test increases. This is especially important when comparing students to solve
  different tests or in cases when the time for the solution to all the test items is not enough. In
  addition, the resolution of the test increases significantly if different test items are attributed to
  different weights. In the work for a course that has a hierarchical structure and is known for the
  duration of the development of its sections, we built a “sum of attainments” cooperative game
  in which players are the parts of the course, and the value of the characteristic function on a
  coalition is the time necessary for a student to study the coalition of the parts. We have found
  simple formulas for the calculation of the Shapley value as constructed in the game and so expanded the class of cooperative games for which the Shapley value is calculated analytically.
  The basis of the proof lies in the decomposition of the characteristic function in a sum of the
  dual unanimity games and using the properties of a cone in the set of partially ordered elements
  (parts of course). The component of the Shapley value is the average time of learning the part
  of the course and it may be used as the weight of the item for a final test. The theory of duality
  (complementarity), developed for cooperative games permits us to link “the sum of attainments
  game”, “the airport game” and “the peer group game”. Examples of the calculation of weights
  for test items has been prepared by the use of a particular model term course. Refs 16. Figs 2.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: TU game
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Shapley value
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: analytical game solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: teaching test
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: weight of item
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: partial ordered set of players
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Shapley weights of test items
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Lutsenko.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8515/1/07-Lutsenko.pdf
resources.format: Adobe PDF
resources.size: 291,99 kB