Theory of Factorial Experiments

This book introduces modern methods for estimating and analysing factorial experiments, including a new Hadamard matrix-based technique for 2n2^n2n designs. It covers confounded, asymmetrical, and super-saturated designs and demonstrates the use of factorial experiments in constructing various block designs. Practical RStudio implementations are included. The book also explores the analysis of variance for asymmetrical factorial designs and confounded experiments, including single and double confounding schemes. It also offers a practical guide to implementing these methods in RStudio, including worked examples and computation of ANOVA tables. • Introduces a novel method using Hadamard matrices to estimate effects and compute ANOVA tables in 2n2^n2n factorial experiments. • Discusses estimation of effects in ternary symmetrical designs using linear and quadratic contrasts with single degrees of freedom. • Covers estimation techniques and ANOVA computation for asymmetrical factorial and confounded designs. • Demonstrates the use of factorial experiments for constructing BIBDs, PBIBDs, and other complex experimental designs. • Offers practical R code and examples for estimating effects and generating ANOVA tables from real datasets. This book is for graduate students, academic researchers, and applied statisticians in agricultural, industrial, and experimental sciences who seek advanced yet accessible coverage of factorial experiments and their real-world applications.