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An information manifold perspective for analyzing test data
McGill University, Montreal, Canada.
Ottawa Hospital Research Institute, Ottawa, Canada.
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE).ORCID iD: 0000-0001-7573-0671
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-5549-8262
2025 (English)In: Applied psychological measurement, ISSN 0146-6216, E-ISSN 1552-3497, Vol. 49, no 3, p. 90-108Article in journal (Refereed) Published
Abstract [en]

Modifications of current psychometric models for analyzing test data are proposed that produce an additive scale measure of information. This information measure is a one-dimensional space curve or curved surface manifold that is invariant across varying manifold indexing systems. The arc length along a curve manifold is used as it is an additive metric having a defined zero and a version of the bit as a unit. This property, referred to here as the scope of the test or an item, facilitates the evaluation of graphs and numerical summaries. The measurement power of the test is defined by the length of the manifold, and the performance or experiential level of a person by a position along the curve. In this study, we also use all information from the items including the information from the distractors. Test data from a large-scale college admissions test are used to illustrate the test information manifold perspective and to compare it with the well-known item response theory nominal model. It is illustrated that the use of information theory opens a vista of new ways of assessing item performance and inter-item dependency, as well as test takers' knowledge.

Place, publisher, year, edition, pages
Sage Publications, 2025. Vol. 49, no 3, p. 90-108
Keywords [en]
entropy, expected sum score, nominal model, scope, score index, spline functions, surprisal, test information, TestGardener
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-233717DOI: 10.1177/01466216241310600ISI: 001380542200001PubMedID: 39713764Scopus ID: 2-s2.0-105001648191OAI: oai:DiVA.org:umu-233717DiVA, id: diva2:1925872
Funder
Wallenberg Foundations, MMW 2019.012Available from: 2025-01-09 Created: 2025-01-09 Last updated: 2025-04-29Bibliographically approved

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Wallmark, JoakimWiberg, Marie

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