Oehlert Gary W. A First Course in Design and Analysis of Experiments

University of Minnesota, 2010. — 679 p. — ISBN: 0-7167-3510-5.Oehlert's text is suitable for either a service course for non-statistics graduate students or for statistics majors. Unlike most texts for the one-term grad/upper level course on experimental design, Oehlert's new book offers a superb balance of both analysis and design, presenting three practical themes to students:
when to use various designs;
how to analyze the results;
how to recognize various design options.Also, unlike other older texts, the book is fully oriented toward the use of statistical software in analyzing experiments.Researchers use experiments to answer questions. Typical questions might Experiments be: answer questions
Is a drug a safe, effective cure for a disease? This could be a test of how AZT affects the progress of AIDS.
Which combination of protein and carbohydrate sources provides the best nutrition for growing lambs?
How will long-distance telephone usage change if our company offers a different rate structure to our customers?
Will an ice cream manufactured with a new kind of stabilizer be as palatable as our current ice cream?
Does short-term incarceration of spouse abusers deter future assaults?
Under what conditions should I operate my chemical refinery, given this month’s grade of raw material?
This book is meant to help decision makers and researchers design good experiments, analyze them properly, and answer their questions.Why Experiment?
Components of an Experiment.
Terms and Concepts.
Outline.
More About Experimental Units.
More About Responses.
Randomization and Design.
Randomization Against Confounding.
Randomizing Other Things.
Performing a Randomization.
Randomization for Inference.
The paired t-test.
Two-sample t-test.
Randomization inference and standard inference.
Further Reading and Extensions.
Problems.
Completely Randomized Designs.
Structure of a CRD.
Preliminary Exploratory Analysis.
Models and Parameters.
Estimating Parameters.
Comparing Models: The Analysis of Variance.
Mechanics of ANOVA.
Why ANOVA Works.
Back to Model Comparison.
Side-by-Side Plots.
Dose-ResponseModeling.
Further Reading and Extensions.
Problems.
Looking for Specific Differences—Contrasts.
Contrast Basics.
Inference for Contrasts.
Orthogonal Contrasts.
Polynomial Contrasts.
Further Reading and Extensions.
Problems.
Multiple Comparisons.
Error Rates.
Bonferroni-Based Methods.
The Scheff.e Method for All Contrasts.
Pairwise Comparisons.
Displaying the results.
The Studentized range.
Simultaneous confidence intervals.
Strong familywise error rate.
False discovery rate.
Experimentwise error rate.
Comparisonwise error rate.
Pairwise testing reprise.
Pairwise comparisons methods that do not control.
combined Type I error rates.
Confident directions.
Comparison with Control or the Best.
Comparison with a control.
Comparison with the best.
Reality Check on Coverage Rates.
A Warning About Conditioning.
Some Controversy.
Further Reading and Extensions.
Problems.
Checking Assumptions.
Assumptions.
Transformations.
Assessing Violations of Assumptions.
Assessing nonnormality.
Assessing nonconstant variance.
Assessing dependence.
Fixing Problems.
Accommodating nonnormality.
Accommodating nonconstant variance.
Accommodating dependence.
Effects of Incorrect Assumptions.
Effects of nonnormality.
Effects of nonconstant variance.
Effects of dependence.
Implications for Design.
Further Reading and Extensions.
Problems.
Power and Sample Size.
Approaches to Sample Size Selection.
Sample Size for Confidence Intervals.
Power and Sample Size for ANOVA.
Power and Sample Size for a Contrast.
More about Units and Measurement Units.
Allocation of Units for Two Special Cases.
Further Reading and Extensions.
Problems.
Factorial Treatment Structure.
Factorial Structure.
Factorial Analysis: Main Effect and Interaction.
Advantages of Factorials.
Visualizing Interaction.
Models with Parameters.
The Analysis of Variance for Balanced Factorials.
General Factorial Models.
Assumptions and Transformations.
Single Replicates.
Pooling Terms into Error.
Hierarchy.
Problems.
A Closer Look at Factorial Data.
Contrasts for Factorial Data.
Modeling Interaction.
Interaction plots.
One-cell interaction.
Quantitative factors.
Tukey one-degree-of-freedom for nonadditivity.
Further Reading and Extensions.
Problems.
Further Topics in Factorials.
Unbalanced Data.
Sums of squares in unbalanced data.
Building models.
Testing hypotheses.
Empty cells.
Multiple Comparisons.
Power and Sample Size.
Two-Series Factorials.
Contrasts.
Single replicates.
Further Reading and Extensions.
Problems.
Random Effects.
Models for Random Effects.
Why Use Random Effects?
ANOVA for Random Effects.
Approximate Tests.
Point Estimates of Variance Components.
Confidence Intervals for Variance Components.
Assumptions.
Power.
Further Reading and Extensions.
Problems.
Nesting, Mixed Effects, and ExpectedMean Squares.
Nesting Versus Crossing.
Why Nesting?
Crossed and Nested Factors.
Mixed Effects.
Choosing a Model.
Hasse Diagrams and Expected Mean Squares.
Test denominators.
Expected mean squares.
Constructing a Hasse diagram.
Variances of Means and Contrasts.
Unbalanced Data and Random Effects.
Staggered Nested Designs.
Problems.
Complete Block Designs.
Blocking.
The Randomized Complete Block Design.
Why and when to use the RCB.
Analysis for the RCB.
How well did the blocking work?
Balance and missing data.
Latin Squares and Related Row/Column Designs.
The crossover design.
Randomizing the LS design.
Analysis for the LS design.
Replicating Latin Squares.
Efficiency of Latin Squares.
Designs balanced for residual effects.
Graeco-Latin Squares.
Further Reading and Extensions.
Problems.
Incomplete Block Designs.
Balanced Incomplete Block Designs.
Intrablock analysis of the BIBD.
Interblock information.
Row and Column Incomplete Blocks.
Partially Balanced Incomplete Blocks.
Cyclic Designs.
Square, Cubic, and Rectangular Lattices.
Alpha Designs.
Further Reading and Extensions.
Problems.
Factorials in Incomplete Blocks—Confounding.
Confounding the Two-Series Factorial.
Two blocks.
Four or more blocks.
Analysis of an unreplicated confounded two-series.
Replicating a confounded two-series.
Double confounding.
Confounding the Three-Series Factorial.
Building the design.
Confounded effects.
Analysis of confounded three-series.
Further Reading and Extensions.
Problems.
Split-Plot Designs.
What Is a Split Plot?
Fancier Split Plots.
Analysis of a Split Plot.
Split-Split Plots.
Other Generalizations of Split Plots.
Repeated Measures.
Crossover Designs.
Further Reading and Extensions.
Problems.
Designs with Covariates.
The Basic Covariate Model.
When Treatments Change Covariates.
Other Covariate Models.
Further Reading and Extensions.
Problems.
Fractional Factorials.
Why Fraction?
Fractioning the Two-Series.
Analyzing a k−q.
Resolution and Projection.
Confounding a Fractional Factorial.
De-aliasing.
Fold-Over.
Sequences of Fractions.
Fractioning the Three-Series.
Problems with Fractional Factorials.
Using Fractional Factorials in Off-Line Quality Control.
Designing an off-line quality experiment.
Analysis of off-line quality experiments.
Further Reading and Extensions.
Problems.
Response Surface Designs.
Visualizing the Response.
First-Order Models.
First-Order Designs.
Analyzing First-Order Data.
Second-Order Models.
Second-Order Designs.
Second-Order Analysis.
Mixture Experiments.
Designs for mixtures.
Models for mixture designs.
Further Reading and Extensions.
Problems.
On Your Own.
Experimental Context.
Experiments by the Numbers.
Final Project.A Linear Models for Fixed Effects.
A. Models.
A. Least Squares.
A. Comparison of Models.
A. Projections.
A. Random Variation.
A. Estimable Functions.
A. Contrasts.
A. The Scheffe Method.
A. Problems.
B Notation.
C Experimental Design Plans.
C. Latin Squares.
C. Standard Latin Squares.
C. Orthogonal Latin Squares.
C. Balanced Incomplete Block Designs.
C. Efficient Cyclic Designs.
C. Alpha Designs.
C. Two-Series Confounding and Fractioning Plans.
D. Tables.