The Effect of Sample Size on the Functioning of the Mantel-Haenszel Statistic

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Abstract
The Mantel-Haenszel (MH) procedure has become one of the most popular procedures for detecting differential item functioning. Valid results with relatively small numbers of examinees are one of the advantages typically attributed to this procedure. In this study, examinee item responses were simulated to contain differentially functioning items, and then were analyzed at five sample sizes to compare detection rates. Results showed the MH procedure missed 25 to 30% of the differentially functioning items when groups of 2000 were used. When 500 or fewer examinees were retained in each group, more than 50% of the differentially functioning items were missed. The items most likely to be undetected were those which were most difficult, those with a small difference in item difficulty between the two groups, and poorly discriminating items.

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