The 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.
Cohen, Allan S & Kim, Seock-ho. (1993). A comparison of Lord's !x-2 and Raju's area measures in detection of DIF. Applied Psychological Measurement, 17, 39-52. doi:10.1177/014662169301700109
Cohen, Allan S.; Kim, Seock-ho.
A comparison of Lord's x² and Raju's area measures in detection of DIF.
Retrieved from the University of Minnesota Digital Conservancy,
Content distributed via the University of Minnesota's Digital Conservancy may be subject to additional license and use restrictions applied by the depositor.