Contents
1 Introduction
1.1 Basic terminology
1.2 Principles of experimental design
1.3 Randomisation as the basis of inference
1.4 Blocking: the tyre example
1.5 Strategies of experimentation
1.6 Guidelines for designing an experiment
1.7 A short history
1.8 Practice problems
2 Simple comparative experiments
2.1 Sampling distributions
2.2 The two-sample \(t\) test
2.3 Unequal variances
2.4 Checking the assumptions
2.5 Choice of sample size
2.6 The paired comparison design
2.7 Practice problems
3 Single-factor experiments
3.1 The general linear model
3.2 Models for a single-factor experiment
3.3 The analysis of variance
3.4 Estimation
3.5 Model adequacy checking
3.6 Variance-stabilising transformations
3.7 A quantitative factor: the regression model
3.8 Power and sample size
3.9 Practice problems
4 Treatment contrasts and multiple comparisons
4.1 Contrasts
4.2 Orthogonal contrasts
4.3 Multiple comparisons
4.4 Orthogonal polynomials
4.5 Practice problems
5 The randomised complete block design
5.1 The design
5.2 The model and the analysis of variance
5.3 Checking the model
5.4 Relative efficiency
5.5 A missing observation
5.6 Practice problems
6 Latin squares and related designs
6.1 The Latin square design
6.2 Graeco-Latin squares
6.3 Balanced incomplete block designs
6.4 Practice problems
7 Factorial experiments
7.1 Main effects and interaction
7.2 The two-factor factorial design
7.3 One observation per cell
7.4 More than two factors
7.5 Blocking in a factorial design
7.6 Practice problems
8 The \(2^k\) factorial design
8.1 The \(2^2\) design
8.2 The \(2^3\) design and the table of signs
8.3 The general \(2^k\) design
8.4 A single replicate
8.5 Centre points
8.6 Practice problems
9 Blocking and confounding in the \(2^k\) design
9.1 Confounding in two blocks
9.2 Confounding in four or more blocks
9.3 Partial confounding
9.4 Practice problems
10 Two-level fractional factorial designs
10.1 The one-half fraction
10.2 Resolution
10.3 Smaller fractions: the \(2^{k-p}\) design
10.4 Finding the generators of a given design
10.5 De-aliasing: the fold-over
10.6 Practice problems
11 Fixed, random and mixed effects
11.1 Fixed and random factors
11.2 The one-way random effects model
11.3 The two-factor random effects model
11.4 The two-factor mixed model
11.5 Expected mean squares in general
11.6 Practice problems
12 Nested and split-plot designs
12.1 The two-stage nested design
12.2 The split-plot design
12.3 Split plots with random factors
12.4 Practice problems
13 Review problems
13.1 Choosing a design
13.2 Problems
References
References