Morris Design of Experiments

An Introduction Based on Linear Models
1. Auflage 2011
ISBN: 978-1-4398-9490-3
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 376 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experimental design as a whole within the structure provided by general linear models, rather than as a collection of seemingly unrelated solutions to unique problems.

The core material can be found in the first thirteen chapters. These chapters cover a review of linear statistical models, completely randomized designs, randomized complete blocks designs, Latin squares, analysis of data from orthogonally blocked designs, balanced incomplete block designs, random block effects, split-plot designs, and two-level factorial experiments. The remainder of the text discusses factorial group screening experiments, regression model design, and an introduction to optimal design. To emphasize the practical value of design, most chapters contain a short example of a real-world experiment. Details of the calculations performed using R, along with an overview of the R commands, are provided in an appendix.

This text enables students to fully appreciate the fundamental concepts and techniques of experimental design as well as the real-world value of design. It gives them a profound understanding of how design selection affects the information obtained in an experiment.

Zielgruppe

Graduate students in statistics taking an experimental design course; statisticians and biostatisticians.

Autoren/Hrsg.

Morris, Max

Fachgebiete

• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Bioinformatik

Inhaltsverzeichnis

Introduction
Example: rainfall and grassland

Basic elements of an experiment
Experiments and experiment-like studies

Models and data analysis

Linear Statistical Models
Linear vector spaces

Basic linear model

The hat matrix, least-squares estimates, and design information matrix
The partitioned linear model

The reduced normal equations

Linear and quadratic forms

Estimation and information

Hypothesis testing and information
Blocking and information

Completely Randomized Designs
Introduction
Models

Matrix formulation

Influence of design on estimation

Influence of design on hypothesis testing

Randomized Complete Blocks and Related Designs
Introduction
A model
Matrix formulation

Influence of design on estimation

Influence of design on hypothesis testing

Orthogonality and "Condition E"

Latin Squares and Related Designs
Introduction
Replicated Latin squares
A model
Matrix formulation

Influence of design on quality of inference

More general constructions: Graeco-Latin squares

Some Data Analysis for CRDs and Orthogonally Blocked Designs

Introduction

Diagnostics
Power transformations

Basic inference
Multiple comparisons

Balanced Incomplete Block Designs
Introduction
A model
Matrix formulation
Influence of design on quality of inference

More general constructions

Random Block Effects

Introduction

Inter- and intra-block analysis

CBDs and augmented CBDs

BIBDs

Combined estimator

Why can information be "recovered"?

CBD reprise

Factorial Treatment Structure
Introduction

An overparameterized model
An equivalent full-rank model

Estimation

Partitioning of variability and hypothesis testing

Factorial experiments as CRDs, CBDs, LSDs, and BIBDs

Model reduction

Split-Plot Designs
Introduction

SPD(R,B)

SPD(B,B)

More than two experimental factors

More than two strata of experimental units

Two-Level Factorial Experiments: Basics
Introduction

Example: bacteria and nuclease

Two-level factorial structure

Estimation of treatment contrasts
Testing factorial effects
Additional guidelines for model editing

Two-Level Factorial Experiments: Blocking
Introduction
Complete blocks

Balanced incomplete block designs

Regular blocks of size 2f-1

Regular blocks of size 2f-2

Regular blocks: general case

Two-Level Factorial Experiments: Fractional Factorials
Introduction

Regular fractional factorial designs

Analysis

Example: bacteria and bacteriocin

Comparison of fractions

Blocking regular fractional factorial designs

Augmenting regular fractional factorial designs
Irregular fractional factorial designs

Factorial Group Screening Experiments

Introduction

Example: semiconductors and simulation

Factorial structure of group screening designs
Group screening design considerations
Case study

Regression Experiments: First-Order Polynomial Models

Introduction

Polynomial models

Designs for first-order models

Blocking experiments for first-order models

Split-plot regression experiments

Diagnostics

Regression Experiments: Second-Order Polynomial Models
Introduction

Quadratic polynomial models

Designs for second-order models

Design scaling and information

Orthogonal blocking

Split-plot designs

Bias due to omitted model terms

Introduction to Optimal Design

Introduction

Optimal design fundamentals

Optimality criteria
Algorithms

Appendices

References

Index

A Conclusion and Exercises appear at the end of each chapter.

Über Autor(innen)

Max D. Morris is a professor in the Department of Statistics and the Department of Industrial and Manufacturing Systems Engineering at Iowa State University. A fellow of the American Statistical Association, Dr. Morris is a recipient of the National Institute of Statistical Sciences Sacks Award for Cross-Disciplinary Research and the American Society for Quality Wilcoxon Prize.