The power of approximate degrees of freedom tests in heteroscedastic factorial designs

Several viable approaches have been proposed for conducting factorial analysis when the homogeneous variances assumption is violated. Although robust type I error control and excellent power performance are desirable properties of a test procedure for making statistical inferences, the corresponding power calculations must also be considered to extend its applicability in planning research studies. This article presents the power functions of two approximate degrees of freedom tests within the context of two-way factorial designs. Both theoretical examination and empirical investigation are performed to demonstrate the underlying features of the two approaches. Simulation results showed that the suggested procedures provide remarkably good approximations over a wide range of model configurations. In view of the overall accuracy, the power functions are recommended for enhancing the usefulness of the associated test procedures. To facilitate the adoption of the suggested methodology in factorial research designs, computer code is presented for implementing the described power calculations.