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DIF Detection With Small Samples: Applying Smoothing Techniques to Frequency Distributions in the Mantel-Haenszel Procedure DIF RMSD

Yu, Lei; Moses, Tim P.; Puhan, Gautam; Dorans, Neil J.
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Report Number:
ETS Research Report
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Subject/Key Words:
Differential Item Functioning (DIF), Small Samples, Mantel Haenszel Technique, Loglinear Smoothing, Root Mean Square Difference (RMSD), Bias


All differential item functioning (DIF) methods require at least a moderate sample size for effective DIF detection. Samples that are less than 200 pose a challenge for DIF analysis. Smoothing can improve upon the estimation of the population distribution by preserving major features of an observed frequency distribution while eliminating the noise brought about by irregular data points. This study applied smoothing techniques to frequency distributions and investigated the impact of smoothed data on the Mantel-Haenszel (MH) DIF detection in small samples. Eight sample-size combinations were randomly drawn from a real data set to make the study realistic and were replicated 80 times to produce stable results.

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