The Power of Crossing SIBTEST

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Differential item functioning (DIF) is crucial for test fairness.
• Existing methods like SIBTEST primarily focus on unidirectional DIF.
• Detecting crossing DIF requires specialized statistical approaches.

Purpose of the Study:

• To introduce and theoretically derive the power of the Crossing SIBTEST (CSIB) statistic.
• To investigate factors influencing CSIB's statistical power.
• To compare CSIB's power with unidirectional SIBTEST.

Main Methods:

• Derivation of a theoretical power formula for CSIB based on asymptotic distribution.
• Analysis of factors including DIF effect size, standard error, and sample size.
• Application within the Item Response Theory (IRT) three-parameter logistic (3PL) model framework.
• Monte Carlo simulations to compare theoretical power with observed rejection rates.

Main Results:

• A novel theoretical power formula for CSIB was successfully derived.
• Simulation results confirmed the accuracy of the theoretical power formula.
• Key factors influencing CSIB power were identified and quantified.
• CSIB demonstrated comparable or superior power to unidirectional SIBTEST in certain scenarios.

Conclusions:

• CSIB is a viable statistical method for detecting both crossing and unidirectional DIF.
• The derived power formula offers valuable insights for test developers and researchers.
• Understanding the factors influencing CSIB power can optimize its application in educational and psychological assessments.