Applied Psychological Measurement, Volume 17, 1993
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Browsing Applied Psychological Measurement, Volume 17, 1993 by Author "Cohen, Allan S."
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Item A comparison of Lord's x² and Raju's area measures in detection of DIF(1993) Cohen, Allan S.; Kim, Seock-hoThe area between item response functions estimated in different samples is often used as a measure of differential item functioning (DIF). Under item response theory, this area should be 0, except for errors of measurement. This study examined the effectiveness of two statistical tests of this area—a Z test for exact signed area and a Z test for exact unsigned area—for different test length, sample size, proportion of DIF items on the test, and item parameter estimation conditions using the two-parameter model. Errors in detection made using these two statistics were compared with errors made using Lord’s Χ². Differences between all three statistics were relatively small; however, the Χ² statistic was more effective than either of the two Z tests at detecting simulated DIF. The Z test for the exact signed area was the least effective and was the most likely to result in false negative errors. Index terms: area measures, differential item functioning, item response theory, item bias, Lord’s Χ².Item Detection of differential item functioning in the graded response model(1993) Cohen, Allan S.; Kim, Seock-Ho; Baker, Frank B.Methods for detecting differential item functioning (DIF) have been proposed primarily for the item response theory dichotomous response model. Three measures of DIF for the dichotomous response model are extended to include Samejima’s graded response model: two measures based on area differences between item true score functions, and a χ² statistic for comparing differences in item parameters. An illustrative example is presented. Index terms: differential item functioning, graded response model, item response theory.