This book summarizes all the methods to analyze high-dimensional data that are obtained through applying an experimental design in the life, food and chemical sciences, especially those developed in recent years. It includes information on: Basic and established theories on linear models from a mathematical and statistical perspective; Available methods and their mutual relationships, including coverage of ASCA, APCA, PC-ANOVA, ASCA+, LiMM-PCA and RM-ASCA+, and PERMANOVA, as well as various alternative methods and extensions; Applications in metabolomics, microbiome, gene expression, proteomics, food science, sensory science, and chemistry; Commercially available and open-source software for application of these methods.