Identifying Different Item Response Curves.

A method is presented for determining whether or not two three-parameter item characteristic curves differ significantly from each other. The method may be used within the context of item response theory to detect evidence of item compromise, change with time, or group-specific differences e.g., bias. Approximate sampling distributions are given for the test statistic. Two modes of use are distinguished, an exploratory mode in which items are identified for further scrutiny, and a confirmatory mode in which the method may be applied to individual items with higher precision. Demonstrations with actual and simulated data are reported. The method involves the derivation of a measure analogous to chi-square, called a sum of squares SOS measure. The SOS measures integrate the difference between item response curves and assess the statistical significance of the resulting area based not only on its magnitude but also on the accuracy with which the two curves were estimated. Author