CUSUM-based person-fit statistics for adaptive testing

Edith van Krimpen-Stoop, R.R. Meijer

Research output: Book/ReportReportProfessional

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Item scores that do not fit an assumed item response theory model may cause the latent trait value to be estimated inaccurately. Several person-fit statistics for detecting nonfitting score patterns for paper-and-pencil tests have been proposed. In the context of computerized adaptive tests (CAT), the use of person-fit analysis has hardly been explored. In this study, new person-fit statistics are proposed, and critical values for these statistics are derived from existing statistical theory. Statistics are proposed that are sensitive to runs of correct or incorrect item scores and are based on all items administered in a CAT or based on subsets of items, using observed and expected item scores and using cumulative sum (CUSUM) procedures. The theoretical and empirical distributions of the statistics are compared and detection rates are investigated. Results show that the nominal and empirical Type I error rates are comparable for CUSUM procedures when the number of items in each subset and the number of measurement points are not too small. Detection rates of CUSUM procedures were superior to other fit statistics. Applications of the statistics are discussed.
Original languageEnglish
Place of PublicationEnchede
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages25
Publication statusPublished - 1999

Publication series

NameOMD Research Report
PublisherUniversity of Twente, Faculty of Educational Science and Technology


  • Adaptive Testing
  • Computer Assisted Testing
  • IR-103774
  • Item Response Theory
  • METIS-136388
  • Estimation (Mathematics)


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