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Planning, Construction, and Statistical Analysis of Comparative Experiments

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ISBN-10: 0471213950

ISBN-13: 9780471213956

Edition: 2004

Authors: Francis G. Giesbrecht, Marcia L. Gumpertz

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This text encapsulates the past 25 years of developments and new techniques for planning and designing experiments. It covers a wide range of applications, including agricultural sciences, animal and biomedical sciences, and industrial and engineering studies.
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Book details

Copyright year: 2004
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/1/2004
Binding: Hardcover
Pages: 693
Size: 6.25" wide x 9.75" long x 1.75" tall
Weight: 2.464
Language: English

Role of Statistics in Experiment Design
Organization of This Book
Representativeness and Experimental Units
Replication and Handling Unexplained Variability
Randomization: Why and How
Ethical Considerations
Review Exercises
Completely Randomized Design
Completely Randomized Design
Assumption of Additivity
Factorial Treatment Combinations
Nested Factors
Review Exercises
Linear Models for Designed Experiments
Linear Model
Principle of Least Squares
Parameterizations for Row--Column Models
Review Exercises
Linear Combinations of Random Variables
Simulating Random Samples
Testing Hypotheses and Determining Sample Size
Testing Hypotheses in Linear Models with Normally Distributed Errors
Kruskal--Wallis Test
Randomization Tests
Power and Sample Size
Sample Size for Binomial Proportions
Confidence Interval Width and Sample Size
Alternative Analysis: Selecting and Screening
Review Exercises
Methods of Reducing Unexplained Variation
Randomized Complete Block Design
Formal Statistical Analysis for the RCBD
Models and Assumptions: Detailed Examination
Statistical Analysis When Data Are Missing in an RCBD
Analysis of Covariance
Review Exercises
Interaction of a Random Block Effect and a Fixed Treatment Effect
Latin Squares
Formal Structure of Latin Squares
Combining Latin Squares
Graeco--Latin Squares and Orthogonal Latin Squares
Some Special Latin Squares and Variations on Latin Squares
Frequency Squares
Youden Square
Review Exercises
Some Standard Latin Squares
Mutually Orthogonal Latin Squares
Possible Youden Squares
Split-Plot and Related Designs
Background Material
Examples of Situations That Lead to Split-Plots
Statistical Analysis of Split-Plot Experiments
Split-Split-Plot Experiments
Strip-Plot Experiments
Comments on Further Variations
Analysis of Covariance in Split-Plots
Repeated Measures
Review Exercises
Incomplete Block Designs
Efficiency of Incomplete Block Designs
Distribution-Free Analysis for Incomplete Block Designs
Balanced Incomplete Block Designs
Lattice Designs
Cyclic Designs
Other Incomplete Block Designs
Review Exercises
Catalog of Incomplete Block Designs
Repeated Treatments Designs
Repeated Treatments Design Model
Construction of Repeated Treatments Designs
Statistical Analysis of Repeated Treatments Design Data
Carryover Design for Two Treatments
Correlated Errors
Designs for More Complex Models
Review Exercises
Factorial Experiments: The 2[superscript N] System
2[superscript N] Factorials
General Notation for the 2[superscript N] System
Analysis of Variance for 2[superscript N] Factorials
Factorial Experiments: The 3[superscript N] System
3 X 3 Factorial
General System of Notation for the 3[superscript N] System
Analysis of Experiments without Designed Error Terms
Techniques That Look for Location Parameters
Analysis for Dispersion Effects
Review Exercises
Confounding Effects with Blocks
Confounding 2[superscript 3] Factorials
General Confounding Patterns
Double Confounding
3[superscript N] System
Detailed Numerical Example: 3[superscript 3] Factorial in Blocks of Nine
Confounding Schemes for the 3[superscript 4] System
Review Exercises
Fractional Factorial Experiments
Organization of This Chapter
Fractional Replication in the 2[superscript N] System
Constructing Fractional Replicates by Superimposing Factors
Foldover Technique
Franklin-Bailey Algorithm for Constructing Fractions
Irregular Fractions of the 2[superscript N] System
Fractional Factorials with Compromised Resolution
A Caution About Minimum Aberration
Direct Enumeration Approach to Constructing Plans
Blocking in Small 2[superscript N-k] Plans
Fractional Replication in the 3[superscript N] System
Review Exercises
Minimum Aberration Fractions without Blocking
Minimum Aberration Fractions with Blocking
Response Surface Designs
Basic Formulation
Some Basic Designs
Statistical Analyses of Data from Response Surface Designs
Blocking in Response Surface Designs
Mixture Designs
Optimality Criteria and Parametric Modeling
Response Surfaces in Irregular Regions
Searching the Operability Region for an Optimum
Examination of an Experimental Problem
Review Exercise
Plackett-Burman Hadamard Plans
Hadamard Matrix
Plackett-Burman Plans
Hadamard Plans and Interactions
Statistical Analyses
Weighing Designs
Projection Properties of Hadamard Plans
Very Large Factorial Experiments
General p[superscript N] and Nonstandard Factorials
Organization of This Chapter
p[superscript N] System with p Prime
4[superscript N] System
4[superscript N] System Using Pseudofactors at Two Levels
6[superscript N] Factorial System
Asymmetrical Factorials
2[superscript N] X 3[superscript M] Plans
Plans for Which Run Order Is Important
Preliminary Concepts
Trend-Resistant Plans
Generating Run Orders for Fractions
Extreme Number of Level Changes
Trend-Free Plans from Hadamard Matrices
Extensions to More Than Two Levels
Small One-at-a-Time Plans
Sequences of Fractions of Factorials
Motivating Example
Foldover Techniques Examined
Augmenting a 2[superscript 4-1] Fraction
Sequence Starting from a Seven-Factor Main Effect Plan
Augmenting a One-Eighth Fraction of 4[superscript 3]
Adding Levels of a Factor
Double Semifold
Planned Sequences
Sequential Fractions
Factorial Experiments with Quantitative Factors: Blocking and Fractions
Factors at Three Levels
Factors at Four Levels Based on the 2[superscript N] System
Pseudofactors and Hadamard Plans
Box-Behnken Plans
Review Exercises
Box-Behnken Plans
Supersaturated Plans
Plans for Small Experiments
Supersaturated Plans That Include an Orthogonal Base
Model-Robust Plans
Multistage Experiments
Factorial Structures in Split-Plot Experiments
Splitting on Interactions
Factorials in Strip-Plot or Strip-Unit Designs
General Comments on Strip-Unit Experiments
Split-Lot Designs
Fractional Factorial Plans for Split-Plot Designs
Orthogonal Arrays and Related Structures
Orthogonal Arrays and Fractional Factorials
Other Construction Methods
Nearly Orthogonal Arrays
Large Orthogonal Arrays
Factorial Plans Derived via Orthogonal Arrays
Product Array Designs
Block Crossed Arrays
Compound Arrays
Experiments on the Computer
Stratified and Latin Hypercube Sampling
Using Orthogonal Arrays for Computer Simulation Studies
Demonstration Simulations