Scientists from many fields use the General Linear Multivariate Model with both fixed and Gaussian predictors. Three consulting questions motivate a summary of new power and sample size results for variants of this model, including a baseline covariate model, the full model in every cell, and a model with many random predictors.
Conditional power equals power calculated for a specific realization of the predictor values.
Unconditional power equals the expected value of the conditional power with respect to all possible stochastic realizations of the Gaussian predictors. Quantile power is the conditional power for a 'worst case' realization of the random predictors. I demonstrate the utility of the theoretical methods by reviewing the power analyses for a proposed study of transient perinatal hypothyroxinemia, a clinical trial of a drug for bone density, and a genetic analysis.