Analysis and Design of Experiments: Analysis of Variance and Analysis of Variance Designs

This book is a mathematically rigorous extensive discussion of an important area in modern mathematics: design of experiments, or the analysis of variance and variance designs as statistical procedures. Emphasis is upon rigorous mathematical treatment, including proofs, formula derivation, and principles of statistical inference. The first six chapters of this book cover the theory of the analysis of variance, with full discussion of chi square distribution, F distribution functions, analysis of variance in one-way and r-way classification, and distribution of variance ratio when the null hypothesis is false, with inclusion of Tang's tables. Experimental design is treated in chapters on Latin squares and incomplete balanced block designs, Galois fields and orthogonal Latin squares, construction of incomplete balanced block designs, factorial experiments, and randomized designs, blocks and quasi-factorial designs. Non-orthogonal data are considered in a separate chapter, while analysis of covariance, interblock estimates and variance are also considered. Includes 14 pages of useful tables.