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This book introduces modern methods for estimating and analysing factorial experiments, including a new Hadamard matrix-based technique for 2n designs. It covers confounded, asymmetrical, and supersaturated 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.
Preface
Author Biography
Factorial experiments
Introduction
Factorial experiments
Assumptions made in the analysis of variance models
Contrast
Simple and main effects of a 2n factorial experiment
23 factorial experiments
Total number of main effects and interaction effects in 2n factorial experiments
Estimating main effects and interaction effects
General analysis of 2k factorial experiment in r replications
Advantages of factorial experiments
Factorial experiments with n factors each at three levels
Introduction
32 factorial experiments
The 33 factorial experiment
General analysis of a 3k factorial experiment in r replications
42 symmetrical factorial experiments
General analysis of Sk factorial experiment in r replications
Confounding in factorial experiments
Introduction
Confounding
ANOVA table of confounded factorial experiments
Generalized confounded interactions
Types of confounding
Required number of replications for 2n a balanced factorial experiment confounded into two blocks per replication
Comparison between complete, partial, and balanced confounding factorial experiments
Methods for constructing confounded factorial experiments with n factors each at two levels
Construction of confounding factorial experiments with n factors each at two levels saving two factor interactions
Method for constructing confounding factorial experiments with n factors each at three levels
The Das method of confounding for n factors each at three levels
Construction of confounded factorial experiments with n factors each at three levels saving two-factor interactions
Balanced confounding of 33 factorial experiments confounded into blocks of size 9
Balanced confounding of 34 factorial experiments into blocks of size 9
Confounding in factorial experiments with a single replication
Double confounding
The identification of confounded interactions in symmetrical factorial experiments
Introduction
Identification of confounded interactions for confounding in 2n factorial experiments confounded into blocks of sizes 2n-1
Alternate method for the identification of confounded interactions for 2n factorial experiments confounded into blocks of size 2r
The identification of confounded interactions in a 3n factorial experiment with three blocks per replication
3n factorial experiments with more than three blocks per replication
Another method of identifying confounded interactions in 3n factorial experiments confounded into blocks of size 3n-1
Identification of confounded interactions for 3n factorial experiments confounded into blocks of size 3r
Sn factorial experiments confounded in Sr block sizes
Fractional factorial design
Introduction
Construction of (1/Sk) fraction of 2n fractional factorial experiment
Method of construction of half fraction of 27 factorial experiment
Method of construction of a quarter fraction of 25 factorial experiment
Plan of the quarter fraction of 26 factorial experiment
Construction of (1/Sk) fraction of 3n fractional factorial experiment
Asymmetrical factorial designs and their confounding
Introduction
Main effect and interaction effect of asymmetrical factorial experiments
Two factors at two levels and one factor at three levels
Two factors each at three levels and one factor at two levels
Analysis of asymmetrical factorial experiment when n factors are at two levels and m factors are at three levels
Analysis of asymmetrical factorial experiments when n factors are at three levels and m factors are at two levels
Three factors N, P, and K at levels 2, 3, and 4, respectively
Analysis of asymmetrical factorial experiment Sn1 × Sm2 × St3
Confounding in asymmetrical factorial experiments
Asymmetrical factorial experiments and pseudo-factors
Applications of factorial experiments
Introduction
Factorial experiments for balanced incomplete block designs
Construction of balanced incomplete block design using confounding factorial experiment
Factorial experiments for partially balanced incomplete block designs
Singular group divisible designs from 3n factorial experiments
Group divisible designs using blocks of same PBIB designs as level codes of factorials
Group divisible designs from the level of three factors of a factorial experiment
Group divisible design with a smaller number of blocks
Construction of an efficiency-balanced design using factorial experiment
Variance-balanced design
Pairwise-balanced designs
Supersaturated designs and factorial experiments
Orthogonal main effect plans and factorial experiments
Orthogonal arrays and factorial experiments
Application of fractional factorial designs
Introduction
Method of construction of a partially balanced array
Orthogonal arrays from a half fraction of a sn factorial experiment
Partially balanced arrays from a half fraction of a 2n factorial experiment
Balanced incomplete block designs from a half fraction of a 2n fractional factorial experiment
Partially balanced incomplete block designs from a half fraction of a 2n fractional factorial design with r = 2
Variance balanced designs from fractional factorial experiments
(1/S) fraction of Sn fractional factorial experiments
Analysis of factorial experiments using R
Introduction
Analysis of variance of 23 factorial experiments using R
Analysis of variance of 24 factorial experiments using R
Analysis of variance of 32 factorial experiments using R
Analysis of variance of 33 factorial experiments using R
References
Index