The general formulation of a linear combination of population means permits a wide range of research questions to be tested within the context of ANOVA. However, it has been stressed in many research areas that the homogeneous variances assumption is frequently violated. To accommodate the heterogeneity of variance structure, the Welch-Satterthwaite procedure is commonly used as an alternative to the t test for detecting the substantive significance of a linear combination of mean effects. This article presents two approaches to power and sample size calculations for the Welch-- Satterthwaite test. The usefulness and diversity of the suggested techniques are illustrated with two of the potential applications in meta and moderation analyses. The numerical assessments showed that the proposed approaches outperform the existing methods on the accuracy of power calculations and sample size determinations for meta and moderation studies. Computer algorithms are also developed to implement the recommended procedures in actual research designs.