The area between two item response functions was used to construct two indicators of differential item functioning. The first indicator was designed from the integral of the difference of the two response functions across six standard deviations of ability. The second index was designed from the integral of the square of the difference of the two response functions across the same range of ability. Both indices were developed using the three-parameter item response theory model such that they subsume the two-and one-parameter models as special cases; and both were designed to be sensitive to uniform and non-uniform differential item functioning. The standard errors of the item response theory parameters were used to estimate the standard error of each integral. The ratio of the integral to the estimate of its standard error was shown to be normally distributed using Monte-Carlo data. Hence, both indices provide a multivariate assessment, a z test, of differences in the sets of item response theory parameters
