The Standardized S-X ² Statistic for Assessing Item Fit

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.