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A Statistical Test for Differential Item Pair Functioning

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  • Timo Bechger
  • Gunter Maris

Abstract

This paper presents an IRT-based statistical test for differential item functioning (DIF). The test is developed for items conforming to the Rasch (Probabilistic models for some intelligence and attainment tests, The Danish Institute of Educational Research, Copenhagen, 1960 ) model but we will outline its extension to more complex IRT models. Its difference from the existing procedures is that DIF is defined in terms of the relative difficulties of pairs of items and not in terms of the difficulties of individual items. The argument is that the difficulty of an item is not identified from the observations, whereas the relative difficulties are. This leads to a test that is closely related to Lord’s (Applications of item response theory to practical testing problems, Erlbaum, Hillsdale, 1980 ) test for item DIF albeit with a different and more correct interpretation. Illustrations with real and simulated data are provided. Copyright The Psychometric Society 2015

Suggested Citation

  • Timo Bechger & Gunter Maris, 2015. "A Statistical Test for Differential Item Pair Functioning," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 317-340, June.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:317-340
    DOI: 10.1007/s11336-014-9408-y
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    References listed on IDEAS

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    Cited by:

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    2. K. B. S. Huth & L. J. Waldorp & J. Luigjes & A. E. Goudriaan & R. J. Holst & M. Marsman, 2022. "A Note on the Structural Change Test in Highly Parameterized Psychometric Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1064-1080, September.
    3. Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2024. "DIF analysis with unknown groups and anchor items," LSE Research Online Documents on Economics 121991, London School of Economics and Political Science, LSE Library.
    4. Paul Boeck & Sun-Joo Cho, 2021. "Not all DIF is shaped similarly," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 712-716, September.
    5. Ke-Hai Yuan & Hongyun Liu & Yuting Han, 2021. "Differential Item Functioning Analysis Without A Priori Information on Anchor Items: QQ Plots and Graphical Test," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 345-377, June.
    6. Robert J. Zwitser & S. Sjoerd F. Glaser & Gunter Maris, 2017. "Monitoring Countries in a Changing World: A New Look at DIF in International Surveys," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 210-232, March.
    7. Alexander Robitzsch & Oliver Lüdtke, 2022. "Mean Comparisons of Many Groups in the Presence of DIF: An Evaluation of Linking and Concurrent Scaling Approaches," Journal of Educational and Behavioral Statistics, , vol. 47(1), pages 36-68, February.
    8. Chen, Yunxiao & Li, Chengcheng & Ouyang, Jing & Xu, Gongjun, 2023. "DIF statistical inference without knowing anchoring items," LSE Research Online Documents on Economics 119923, London School of Economics and Political Science, LSE Library.
    9. Ting Wang & Carolin Strobl & Achim Zeileis & Edgar C. Merkle, 2018. "Score-Based Tests of Differential Item Functioning via Pairwise Maximum Likelihood Estimation," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 132-155, March.

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