Calculating power for the general linear multivariate model and the general linear mixed model

Power and sample size calculations are an important part of the study design process in biomedical research. Sample size must be large enough to answer the scientific question of interest, while minimizing both the cost of research and the risks to the study participants. We present three papers that extend the theory and methods of power and sample size. In Chapter II, we describe a new method to approximate power for the general linear multivariate model in the presence of Gaussian covariates. Chapter III contains an approximation for the distribution of a sum of inverse Wishart matrices. Chapter IV uses the inverse Wishart theory in a power approximation for the mixed model Wald test with denominator degrees of freedom as described by Kenward and Roger.