This paper compares two approximation techniques for detecting differential item functioning (DIF) in an English as a second language (ESL) placement test when the group sizes are too small to use other possible methods (e.g., the three parameter item response theory method). An application of the Angoff delta- plot method (Angoff and Ford, 1973) utilizing the one parameter Rasch model adopted in Chen and Henning (1985), and Scheuneman's chi-square method (Scheuneman, 1979) were chosen because they are among the few methods appropriate for a sample size smaller than 100. Two linguistically and culturally diverse groups (Chinese and Spanish speaking) served as the subjects of this study. The results reveal that there was only marginal overlap between DIF items detected by Chen and Henning's method and Scheuneman's method; the former detected fewer DIF items with less variety than the latter. Moreover, Chen and Henning's method tended to detect easier items with smaller differ ences in p-value between the two groups whereas Scheuneman's method tended to detect items with the opposite features. Implications of these results are discussed.
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