EFFECT OF THE ABILITY DISTRIBUTION SHAPE ON THE GENERALIZED MANTEL-HAENSZEL STATISTICS USED FOR DIF DETECTION
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Abstract
The main objective of this simulation study was to explore the effect of shape of the θ distribution on the generalized nominal and ordinal Mantel-Haenszel statistics used for detecting DIF in polytomous items. The variables manipulated were: trait ( θ), distribution shape (normal, positively skewed, and platykurtic), θ distribution difference between the reference and the focal group (equal and unequal), sample size (500/ 500 and 500/250 examinees in the reference/focal group), and DIF conditions (No DIF, constant and shift-high DIF patterns). The generalized ordinal Mantel-Haenszel statistic was calculated using integer and log-rank scores. The results show: a) a little impact of the θ distribution shape on the performance of all the statistics, and b) the advantages of employing log-rank scores, especially when the items show a shift-high DIF pattern.
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