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.
Highlights
The Mantel-Haenszel methods constitute one of the most popular nonparametric differential item functioning (DIF) detection procedures
Type Below, we briefly present the generalized Mantel-Haenszel statistics used in this study
The main topics investigated by the present research was: (a) how the distribution shapes affects the performance of both QGMH(1) and QGMH(2) statistics; and (b) the effect of log-rank score assigned to the response variable on the QGMH(2) statistic
Summary
The Mantel-Haenszel methods constitute one of the most popular nonparametric differential item functioning (DIF) detection procedures. In the case of polytomous items, generalizations of the MH chi-squared statistic have been used for detecting DIF: the generalized Mantel-Haenszel test - GMH (MANTEL and HAENSZEL, 1959; ZWICK et al, 1993a) and the Mantel test (MANTEL, 1963; ZWICK et al, 1993a). They found that the use of log-rank scores instead of the usual integer scores increased the power of QGMH(2) for detecting the shift-high. This topic has received little attention given that studies on DIF have routinely employed integer scores
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