Calculation of values of the complexities of the test tasks for adaptive intelligence test


Development of assessment tests of intelligence and abilities, as well as the selection of appropriate to the objectives of the study and to the research sample and/or to the target population diagnostic tools require estimating and measuring of the complexity of test tasks. In this work we propose a method (algorithm) of mathematical computation of the values of task complexity of the adaptive Bertling-Holling test, on the basis of which were also carried out calculations of the values of abilities of a group of subjects. The test requires the generation of a large number of different tasks, the essence of which consists in identifying regularities in the structure of geometrical figures with additional elements. Testing of 30 subjects by 30 tests tasks was organized and conducted at the Faculty of Information Technology of MCUPE. Tasks complexity was calculated on the basis of the test results. Selection of tasks was carried out with regard to the condition of uniform coverage of all possible combinations of used in the test tasks. The IRT (Item Response Theory) technology was used in the calculation of the difficulties of tasks and in the assessment of abilities. The developed method for estimating difficulty of test items can be used in the designing and carrying out similar tests of intelligence and educational tests.

General Information

Keywords: test of intelligence, adaptive test, test designing, Rush model, Item Response Theory (IRT), Newton-Raphson method

Journal rubric: Mathematical Psychology

Article type: scientific article

For citation: Voitov V.K. Calculation of values of the complexities of the test tasks for adaptive intelligence test . Eksperimental'naâ psihologiâ = Experimental Psychology (Russia), 2013. Vol. 6, no. 2, pp. 120–128. (In Russ., аbstr. in Engl.)


  1. Chelyshkova M. B. Teorija i praktika konstruirovanija pedagogicheskih testov. Uchebnoe posobie. M.: «Logos», 2002.
  2. Nejman Ju. M., Hlebnikov V. A. Vvedenie v teoriju modelirovanija i parametrizacii pedagogicheskih testov. M., 2000.
  3. Metod N'jutona // Vikipedija. 2013. URL:'jutona. Data obrashhenija: 20.06.2013.

Information About the Authors

Vladimir K. Voitov, PhD in Engineering, Professor at the Faculty of Information Technology, Moscow State University of Psychology and Education, Moscow, Russia, ORCID:, e-mail:



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