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Improving the Crossing-SIBTEST Statistic for Detecting Non-uniform DIF

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  • R. Philip Chalmers

    (The University of Georgia)

Abstract

This paper demonstrates that, after applying a simple modification to Li and Stout’s (Psychometrika 61(4):647–677, 1996) CSIBTEST statistic, an improved variant of the statistic could be realized. It is shown that this modified version of CSIBTEST has a more direct association with the SIBTEST statistic presented by Shealy and Stout (Psychometrika 58(2):159–194, 1993). In particular, the asymptotic sampling distributions and general interpretation of the effect size estimates are the same for SIBTEST and the new CSIBTEST. Given the more natural connection to SIBTEST, it is shown that Li and Stout’s hypothesis testing approach is insufficient for CSIBTEST; thus, an improved hypothesis testing procedure is required. Based on the presented arguments, a new chi-squared-based hypothesis testing approach is proposed for the modified CSIBTEST statistic. Positive results from a modest Monte Carlo simulation study strongly suggest the original CSIBTEST procedure and randomization hypothesis testing approach should be replaced by the modified statistic and hypothesis testing method.

Suggested Citation

  • R. Philip Chalmers, 2018. "Improving the Crossing-SIBTEST Statistic for Detecting Non-uniform DIF," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 376-386, June.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:2:d:10.1007_s11336-017-9583-8
    DOI: 10.1007/s11336-017-9583-8
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    References listed on IDEAS

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    1. Louis Guttman, 1945. "A basis for analyzing test-retest reliability," Psychometrika, Springer;The Psychometric Society, vol. 10(4), pages 255-282, December.
    2. G. Kuder & M. Richardson, 1937. "The theory of the estimation of test reliability," Psychometrika, Springer;The Psychometric Society, vol. 2(3), pages 151-160, September.
    3. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    4. Hsin-Hung Li & William Stout, 1996. "A new procedure for detection of crossing DIF," Psychometrika, Springer;The Psychometric Society, vol. 61(4), pages 647-677, December.
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    Cited by:

    1. R. Philip Chalmers, 2018. "Model-Based Measures for Detecting and Quantifying Response Bias," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 696-732, September.

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