**Introduction **

**Linear Model Basics **

Least squares

Estimation of σ

F-test

One-way layout

Estimation of a subset of parameters

Hypothesis testing for a subset of parameters

Adjusted orthogonality

Additive two-way layout

The case of proportional frequencies

**Randomization and Blocking **

Randomization

Assumption of additivity and models for completely randomized designs

Randomized block designs

Randomized row-column designs

Nested row-column designs and blocked split-plot designs

Randomization model

**Factors**

Factors as partitions

Block structures and Hasse diagrams

Some matrices and spaces associated with factors

Orthogonal projections, averages, and sums of squares

Condition of proportional frequencies

Supremums and infimums of factors

Orthogonality of factors

**Analysis of Some Simple Orthogonal Designs **

A general result

Completely randomized designs

Null ANOVA for block designs

Randomized complete block designs

Randomized Latin square designs

Decomposition of the treatment sum of squares

Orthogonal polynomials

Orthogonal and nonorthogonal designs

Models with fixed block effects

**Factorial Treatment Structure and Complete Factorial Designs **

Factorial effects for two and three two-level factors

Factorial effects for more than three two-level factors

The general case

Analysis of complete factorial designs

Analysis of unreplicated experiments

Defining factorial effects via finite geometries

Defining factorial effects via Abelian groups

More on factorial treatment structure

**Blocked, Split-Plot, and Strip-Plot Complete Factorial Designs **

An example

Construction of blocked complete factorial designs

Analysis

Pseudo factors

Partial confounding

Design keys

A template for design keys

Construction of blocking schemes via Abelian groups

Complete factorial experiments in row-column designs

Split-plot designs

Strip-plot designs

**Fractional Factorial Designs and Orthogonal Arrays **

Treatment models for fractional factorial designs

Orthogonal arrays

Examples of orthogonal arrays

Regular fractional factorial designs

Designs derived from Hadamard matrices

Mutually orthogonal Latin squares and orthogonal arrays

Foldover designs

Difference matrices

Enumeration of orthogonal arrays

Some variants of orthogonal arrays

**Regular Fractional Factorial Designs **

Construction and defining relation

Aliasing and estimability

Analysis

Resolution

Regular fractional factorial designs are orthogonal arrays

Foldovers of regular fractional factorial designs

Construction of designs for estimating required effects

Grouping and replacement

Connection with linear codes

Factor representation and labeling

Connection with finite projective geometry

Foldover and even designs revisited

**Minimum Aberration and Related Criteria **

Minimum aberration

Clear two-factor interactions

Interpreting minimum aberration

Estimation capacity

Other justifications of minimum aberration

Construction and complementary design theory

Maximum estimation capacity: a projective geometric approach

Clear two-factor interactions revisited

Minimum aberration blocking of complete factorial designs

Minimum moment aberration

A Bayesian approach

**Structures and Construction of Two-Level Resolution IV Designs **

Maximal designs

Second-order saturated designs

Doubling

Maximal designs with *N/*4+1 ≤ *n* ≤ *N*/2

Maximal designs with *n = N*/4+1

Partial foldover

More on clear two-factor interactions

Applications to minimum aberration designs

Minimum aberration even designs

Complementary design theory for doubling

Proofs of Theorems 11.27 and 11.28

Coding and projective geometric connections

**Orthogonal Block Structures and Strata **

Nesting and crossing operators

Simple block structures

Statistical models

Poset block structures

Orthogonal block structures

Models with random effects

Strata

Null ANOVA

Nelder’s rules

Determining strata from Hasse diagrams

Proofs of Theorems 12.6 and 12.7

Models with random effects revisited

Experiments with multiple processing stages

Randomization justification of the models for simple block structures

Justification of Nelder’s rules

**Complete Factorial Designs with Orthogonal Block Structures **

Orthogonal designs

Blocked complete factorial split-plot designs

Blocked complete factorial strip-plot designs

Contrasts in the strata of simple block structures

Construction of designs with simple block structures

Design keys

Design key templates for blocked split-plot and strip-plot designs

Proof of Theorem 13.2

Treatment structures

Checking design orthogonality

Experiments with multiple processing stages: the nonoverlapping case

Experiments with multiple processing stages: the overlapping case

**Multi-Stratum Fractional Factorial Designs**

A general procedure

Construction of blocked regular fractional factorial designs

Fractional factorial split-plot designs

Blocked fractional factorial split-plot designs

Fractional factorial strip-plot designs

Design key construction of blocked strip-plot designs

Post-fractionated strip-plot designs

Criteria for selecting blocked fractional factorial designs based on modified wordlength patterns

Fixed block effects: surrogate for maximum estimation capacity

Information capacity and its surrogate

Selection of fractional factorial split-plot designs

A general result on multi-stratum fractional factorial designs

Selection of blocked fractional factorial split-plot designs

Selection of blocked fractional factorial strip-plot designs

Geometric formulation

**Nonregular Designs **

Indicator functions and J-characteristics

Partial aliasing

Projectivity

Hidden projection properties of orthogonal arrays

Generalized minimum aberration for two-level designs

Generalized minimum aberration for multiple and mixed levels

Connection with coding theory

Complementary designs

Minimum moment aberration

Proof of Theorem 15.18

Even designs and foldover designs

Parallel flats designs

Saturated designs for hierarchical models: an application of algebraic geometry

Search designs

Supersaturated designs

**Appendix **

**References **

**Index**