Preface

1 Introduction to Design

1.1 Introduction
1.2 The Control of Independent, Dependent, and Supplementary Variables
1.3 Experimental Design Basics

2 Principles of Estimation and Inference: Means and Variances

2.1 Basic Terminology in Sampling
2.2 Basic Terminology in Statistical Estimation
2.3 Basic Terminology in Testing Statistical Hypotheses
2.4 Variables with Normal Distributions
2.5 Other Distributions — Chi-Square, t, and F
2.6 Inferences Concerning Means
2.7 Inferences Concerning Pairs of Means

3 Design and Analysis of Single-Factor Experiments: Completely Randomized Design

3.1 Introduction
3.2 Definitions and Numerical Example
3.3 Structural Model: Model I (Fixed Constants)
3.4 Methods of Deriving Estimates and Their Expected Values: Model I
3.5 Structural Model — Model II (Variance-Component Model)
3.6 Analysis of Variance Assumptions
3.7 Transformations
3.8 Unequal Sample Sizes
3.9 Power, Treatment Effect Size, and the Determination of Sample Size
3.10 Comparisons Among Treatment Means
3.11 Methods of Error Control for Sets of Multiple Comparisons
3.12 Comparing Comparison Methods
3.13 Treatment Magnitude — Dependent Variable Relationships: Trend Analysis and Strength of Association
3.14 Randomized Complete-Block Designs
3.15 Exercises

4 Single-Factor Experiments Having Repeated Measures on the Same Elements

4.1 Introduction
4.2 Notation and Computational Procedures
4.3 Numerical Example
4.4 Analysis of Variance Assumptions for Repeated Measures Designs
4.5 Statistical Models and the Assumptions
4.6 Measures of Association and Power
4.7 Hotelling's T² Multivariate Analysis of Data That Do Not Meet the Circularity Assumption
4.8 Topics Closely Related to Repeated-Measures Anova
4.9 Exercises

5 Design and Analysis of Factorial Experiments: Completely Randomized Designs

5.1 General Purpose
5.2 Terminology and Notation
5.3 Structural Model
5.4 Estimating Elements of the Model
5.5 Principles for Constructing F Ratios
5.6 Higher-Order Factorial Experiments
5.7 Estimation and Tests of Significance for Three-Factor Experiments
5.8 Simple Effects and Their Tests
5.9 Geometric Interpretation of Higher-Order Interactions
5.10 Individual Comparisons
5.11 Partition of Main Effects and Interaction into Trend Components
5.12 The Case n = 1 and a Test for Nonadditivity
5.13 The Choice of a Scale of Measurement and Transformations
5.14 Nested Factors (Hierarchal Designs)
5.15 Split-Plot Designs
5.16 Rules for Deriving the Expected Values of Mean Squares
5.17 Quasi F Ratios
5.18 Preliminary Tests on the Model and Pooling Procedures
5.19 Replicated Experiments
5.20 Unequal Cell Frequencies
5.21 Estimation of the Magnitude of Experimental Effects and Statistical Power
5.22 Exercises

6 Factorial Experiments — Computational Procedures and Numerical Examples

6.1 General Purpose
6.2 p x q Factorial Experiment Having n Observations Per Cell
6.3 p x q Factorial Experiment — Unequal Cell Frequencies
6.4 Effect of Scale Measurement on Interaction
6.5 p x q x r Factorial Experiment Having n Observations Per Cell
6.6 Computational Procedures for Nested Factors
6.7 Factorial Experiment with a Single Control Group
6.8 Test for Nonadditivity
6.9 Computation of Trend Components
6.10 General Computational Formulas for Main Effects and Interaction
6.11 Missing Data
6.12 Special Computational Procedures when all Factors have Two Levels
6.13 Unequal Cell Frequencies — Least-Squares Solution
6.14 Analysis of Variance in Terms of Polynomial Progression
6.15 Exercises

7 Multifactor Experiments Having Repeated Measures on the Same Elements

7.1 General Purposes
7.2 Two-Factor Experiment with Repeated Measures on One Factor
7.3 Three-Factor Experiment with Repeated Measures (Case I)
7.4 Three-Factor Experiment with Repeated Measures (Case II)
7.5 Other Multifactor Repeated-Measure Plans
7.6 Tests on Trends
7.7 Unequal Group Size
7.8 Measures of Association and Statistical Power
7.9 Exercises

8 Factorial Experiments in which some of the Interactions are Confounded

8.1 General Purpose
8.2 Assigning Treatments to Blocks
8.3 Methods for Obtaining and Confounding Interaction Components
8.4 Simplified Computational Procedures for 2^k Factorial Experiments
8.5 Designs for 2^k Experiments
8.6 Designs for 3^k Experiments
8.7 Mixed Designs
8.8 Fractional Replications
8.9 Exercises

9 Latin Squares and Related Designs

9.1 Definition and Enumeration of Latin Squares
9.2 Uses of Latin Squares
9.3 Analysis of Latin-Square Designs — No Repeated Measures
9.4 Analysis of Greco-Latin Squares
9.5 Analysis of Latin Squares — Repeated Measures
9.6 Exercises

10 Analysis of Covariance

10.1 General Purpose
10.2 Single-Factor Experiment
10.3 Multiple Covariates
10.4 Factorial Experiment
10.5 Analysis of Covariance — Repeated Measures
10.6 Exercises

A Random Variables

A.1 Random Variables and Probability Distributions
A.2 Normal distribution
A.3 Gamma and Chi-Square Distributions
A.4 Beta and F Distributions
A.5 Student's t Distribution
A.6 Bivariate Normal Distributions
A.7 Multivariate Normal Distribution
A.8 Distribution of Quadratic Forms

B Vector and Matrix Algebra

B.1 Vectors and Matrices
B.2 Vector and Matrix Equality
B.3 Matrix Transposition
B.4 Vector and Matrix Addition and Subtraction
B.5 Vector and Matrix Multiplication
B.6 Matrix Inversion
B.7 Linear Transformations and Solving Linear Equations
B.8 Basic Statistical Operations

C Linear Models: Regression and the Analysis of Variance

C.1 Linear Relations: Least-Squares Procedures
C.2 The General Linear Model
C.3 The General Linear Model and the Analysis of Variance

D Tables

E Topics Closely Related to the Analysis of Variance

E.1 Use of Analysis of Variance to Estimate
E.2 Analysis of Variance for Ranked Data
E.3 Dichotomous Data
E.4 Kruskal–Wallis H Test
E.5 Contingency Table with Repeated Measures
E.6 Comparing Treatment Effects with a Control
E.7 General Partition of Degrees of Freedom in a Contingency Table

References

Index