The Power of Crossing SIBTEST.

Crossing SIBTEST or CSIB is designed to detect crossing differential item functioning (DIF) as well as unidirectional DIF. A theoretical formula for the power of CSIB is derived based on the asymptotic distribution of the test statistic under the null and alternative hypotheses. The derived power formula provides insights on the factors that influence the CSIB power, including DIF effect size, standard error, and sample size. The power formula and those influencing factors are further discussed in the context of the item response theory (IRT) three parameter logistic model (3PL) model. Simulation results show the consistency between the theoretical power and the observed rejection rate. The power of CSIB is compared with the unidirectional SIBTEST in theory and through simulation.