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The Standardized S-X 2 Statistic for Assessing Item Fit.

Zhuangzhuang Han1, Sandip Sinharay1, Matthew S Johnson1

  • 1Educational Testing Service, Princeton NJ, USA.

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Summary
This summary is machine-generated.

Researchers often use the S-X^2 statistic for item fit assessment. A modified version, based on the Rao-Robson chi^2 statistic, reduces the number of items incorrectly flagged for misfit.

Keywords:
Orlando-Thissen statisticPearson’sRao-Robson’s modifieditem response theory model fitstatistic

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Area of Science:

  • Psychometrics
  • Statistical modeling

Background:

  • The S-X^2 statistic is widely used for item fit assessment in statistical analyses.
  • It faces limitations due to the Chernoff-Lehmann problem, lacking a known asymptotic null distribution.

Purpose of the Study:

  • To address the limitations of the S-X^2 statistic.
  • To propose a modified statistic with improved properties for item fit assessment.

Main Methods:

  • Development of a modified S-X^2 statistic.
  • Utilizing the modified Rao-Robson chi^2 statistic as a basis.
  • Conducting simulation studies and real data analyses.

Main Results:

  • The modified statistic demonstrates improved performance compared to the original S-X^2 statistic.
  • Fewer items were flagged for misfit when using the modified statistic.
  • The proposed method offers a more reliable approach to item fit assessment.

Conclusions:

  • The modified S-X^2 statistic provides a viable alternative for item fit assessment.
  • This modification helps to mitigate issues associated with the Chernoff-Lehmann problem.
  • The findings support the use of the modified statistic in psychometric research and practice.