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| Preface | |
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| Introduction | |
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| Why Experiment? | |
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| Components of an Experiment | |
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| Terms and Concepts | |
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| Outline | |
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| More About Experimental Units | |
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| More About Responses | |
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| Randomization and Design | |
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| Randomization Against Confounding | |
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| Randomizing Other Things | |
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| Performing a Randomization | |
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| Randomization for Inference | |
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| The paired t-test | |
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| Two-sample t-test | |
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| Randomization inference and standard inference | |
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| Further Reading and Extensions | |
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| Problems | |
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| Completely Randomized Designs | |
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| Structure of a CRD | |
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| Preliminary Exploratory Analysis | |
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| Models and Parameters | |
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| Estimating Parameters | |
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| Comparing Models: The Analysis of Variance | |
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| Mechanics of ANOVA | |
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| Why ANOVA Works | |
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| Back to Model Comparison | |
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| Side-by-Side Plots | |
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| Dose-Response Modeling | |
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| Further Reading and Extensions | |
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| Problems | |
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| Looking for Specific Differences--Contrasts | |
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| Contrast Basics | |
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| Inference for Contrasts | |
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| Orthogonal Contrasts | |
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| Polynomial Contrasts | |
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| Further Reading and Extensions | |
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| Problems | |
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| Multiple Comparisons | |
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| Error Rates | |
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| Bonferroni-Based Methods | |
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| The Scheffe Method for All Contrasts | |
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| Pairwise Comparisons | |
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| Displaying the results | |
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| The Studentized range | |
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| Simultaneous confidence intervals | |
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| Strong familywise error rate | |
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| False discovery rate | |
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| Experimentwise error rate | |
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| Comparisonwise error rate | |
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| Pairwise testing reprise | |
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| Pairwise comparisons methods that do not control combined Type I error rates | |
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| Confident directions | |
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| Comparison with Control or the Best | |
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| Comparison with a control | |
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| Comparison with the best | |
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| Reality Check on Coverage Rates | |
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| A Warning About Conditioning | |
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| Some Controversy | |
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| Further Reading and Extensions | |
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| Problems | |
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| Checking Assumptions | |
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| Assumptions | |
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| Transformations | |
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| Assessing Violations of Assumptions | |
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| Assessing nonnormality | |
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| Assessing nonconstant variance | |
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| Assessing dependence | |
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| Fixing Problems | |
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| Accommodating nonnormality | |
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| Accommodating nonconstant variance | |
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| Accommodating dependence | |
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| Effects of Incorrect Assumptions | |
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| Effects of nonnormality | |
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| Effects of nonconstant variance | |
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| Effects of dependence | |
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| Implications for Design | |
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| Further Reading and Extensions | |
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| Problems | |
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| Power and Sample Size | |
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| Approaches to Sample Size Selection | |
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| Sample Size for Confidence Intervals | |
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| Power and Sample Size for ANOVA | |
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| Power and Sample Size for a Contrast | |
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| More about Units and Measurement Units | |
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| Allocation of Units for Two Special Cases | |
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| Further Reading and Extensions | |
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| Problems | |
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| Factorial Treatment Structure | |
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| Factorial Structure | |
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| Factorial Analysis: Main Effect and Interaction | |
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| Advantages of Factorials | |
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| Visualizing Interaction | |
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| Models with Parameters | |
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| The Analysis of Variance for Balanced Factorials | |
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| General Factorial Models | |
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| Assumptions and Transformations | |
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| Single Replicates | |
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| Pooling Terms into Error | |
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| Hierarchy | |
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| Problems | |
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| A Closer Look at Factorial Data | |
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| Contrasts for Factorial Data | |
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| Modeling Interaction | |
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| Interaction plots | |
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| One-cell interaction | |
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| Quantitative factors | |
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| Tukey one-degree-of-freedom for nonadditivity | |
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| Further Reading and Extensions | |
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| Problems | |
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| Further Topics in Factorials | |
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| Unbalanced Data | |
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| Sums of squares in unbalanced data | |
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| Building models | |
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| Testing hypotheses | |
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| Empty cells | |
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| Multiple Comparisons | |
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| Power and Sample Size | |
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| Two-Series Factorials | |
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| Contrasts | |
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| Single replicates | |
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| Further Reading and Extensions | |
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| Problems | |
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| Random Effects | |
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| Models for Random Effects | |
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| Why Use Random Effects? | |
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| ANOVA for Random Effects | |
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| Approximate Tests | |
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| Point Estimates of Variance Components | |
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| Confidence Intervals for Variance Components | |
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| Assumptions | |
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| Power | |
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| Further Reading and Extensions | |
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| Problems | |
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| Nesting, Mixed Effects, and Expected Mean Squares | |
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| Nesting Versus Crossing | |
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| Why Nesting? | |
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| Crossed and Nested Factors | |
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| Mixed Effects | |
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| Choosing a Model | |
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| Hasse Diagrams and Expected Mean Squares | |
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| Test denominators | |
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| Expected mean squares | |
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| Constructing a Hasse diagram | |
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| Variances of Means and Contrasts | |
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| Unbalanced Data and Random Effects | |
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| Staggered Nested Designs | |
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| Problems | |
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| Complete Block Designs | |
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| Blocking | |
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| The Randomized Complete Block Design | |
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| Why and when to use the RCB | |
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| Analysis for the RCB | |
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| How well did the blocking work? | |
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| Balance and missing data | |
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| Latin Squares and Related Row/Column Designs | |
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| The crossover design | |
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| Randomizing the LS design | |
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| Analysis for the LS design | |
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| Replicating Latin Squares | |
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| Efficiency of Latin Squares | |
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| Designs balanced for residual effects | |
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| Graeco-Latin Squares | |
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| Further Reading and Extension | |
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| Problems | |
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| Incomplete Block Designs | |
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| Balanced Incomplete Block Designs | |
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| Intrablock analysis of the BIBD | |
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| Interblock information | |
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| Row and Column Incomplete Blocks | |
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| Partially Balanced Incomplete Blocks | |
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| Cyclic Designs | |
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| Square, Cubic, and Rectangular Lattices | |
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| Alpha Designs | |
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| Further Reading and Extension | |
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| Problems | |
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| Factorials in Incomplete Blocks--Confounding | |
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| Confounding the Two-Series Factorial | |
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| Two blocks | |
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| Four or more blocks | |
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| Analysis of an unreplicated confounded two-series | |
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| Replicating a confounded two-series | |
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| Double confounding | |
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| Confounding the Three-Series Factorial | |
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| Building the design | |
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| Confounded effects | |
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| Analysis of confounded three-series | |
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| Further Reading and Extensions | |
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| Problems | |
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| Split-Plot Designs | |
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| What Is a Split Plot? | |
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| Fancier Split Plots | |
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| Analysis of a Split Plot | |
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| Split-Split Plots | |
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| Other Generalizations of Split Plots | |
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| Repeated Measures | |
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| Crossover Designs | |
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| Further Reading and Extensions | |
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| Problems | |
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| Designs with Covariates | |
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| The Basic Covariate Model | |
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| When Treatments Change Covariates | |
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| Other Covariate Models | |
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| Further Reading and Extensions | |
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| Problems | |
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| Fractional Factorials | |
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| Why Fraction? | |
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| Fractioning the Two-Series | |
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| Analyzing a 2[superscript k-1] | |
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| Resolution and Projection | |
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| Confounding a Fractional Factorial | |
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| De-aliasing | |
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| Fold-Over | |
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| Sequences of Fractions | |
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| Fractioning the Three-Series | |
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| Problems with Fractional Factorials | |
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| Using Fractional Factorials in Off-Line Quality Control | |
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| Designing an off-line quality experiment | |
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| Analysis of off-line quality experiments | |
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| Further Reading and Extensions | |
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| Problems | |
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| Response Surface Designs | |
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| Visualizing the Response | |
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| First-Order Models | |
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| First-Order Designs | |
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| Analyzing First-Order Data | |
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| Second-Order Models | |
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| Second-Order Designs | |
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| Second-Order Analysis | |
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| Mixture Experiments | |
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| Designs for mixtures | |
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| Models for mixture designs | |
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| Further Reading and Extensions | |
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| Problems | |
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| On Your Own | |
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| Experimental Context | |
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| Experiments by the Numbers | |
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| Final Project | |
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| Bibliography | |
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| Linear Models for Fixed Effects | |
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| Models | |
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| Least Squares | |
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| Comparison of Models | |
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| Projections | |
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| Random Variation | |
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| Estimable Functions | |
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| Contrasts | |
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| The Scheffe Method | |
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| Problems | |
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| Notation | |
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| Experimental Design Plans | |
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| Latin Squares | |
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| Standard Latin Squares | |
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| Orthogonal Latin Square | |
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| Balanced Incomplete Block Designs | |
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| Efficient Cyclic Designs | |
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| Alpha Designs | |
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| Two-Series Confounding and Fractioning Plans | |
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| Tables | |
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| Index | |