Analysis of Variance and Covariance

 

How to Choose and Construct Models

for the Life Sciences

 

 

 

C. PATRICK DONCASTER and ANDREW J. H. DAVEY

 

 

 

 

 

 

Datasets and analyses to supplement the book

 

 

 

 

 

 

ISBN-13: 9780521684477

 

 

In association with the NHBS bookstore and the British Ecological Society, the publishers have committed to donate 200 copies of this book to underprivileged users on the Gratis book scheme

 


Book contents

 

Preface

page viii

Introduction to analysis of variance

1

What is analysis of variance?

1

How to read and write statistical models

2

General principles of ANOVA

7

Assumptions of ANOVA

14

How to distinguish between fixed and random factors

16

Nested and crossed factors, and the concept of replication

21

Uses of blocking, split plots and repeated measures

25

Uses of covariates

29

How F-ratios are constructed

35

Use of post hoc pooling

38

Use of quasi F-ratios

40

Introduction to model structures

42

Notation

43

Allocation tables

43

Examples

46

Worked example 1: Nested analysis of variance

47

Worked example 2: Cross-factored analysis of variance

49

Worked example 3: Split plot, pooling and covariate analysis

51

Key to types of statistical models

57

How to describe a given design with a statistical model

58

1 One-factor designs

61

1.1 One-factor model

62

2 Nested designs

67

2.1 Two-factor nested model

68

2.2 Three-factor nested model

72

3 Fully replicated factorial designs

76

3.1 Two-factor fully cross-factored model

78

3.2 Three-factor fully cross-factored model

86

3.3 Cross-factored with nesting model

98

3.4 Nested cross-factored model

109

4 Randomised-block designs

115

4.1 One-factor randomised-block model

121

4.2 Two-factor randomised-block model

128

4.3 Three-factor randomised-block model

134

5 Split-plot designs

141

5.1 Two-factor split-plot model (i)

146

5.2 Three-factor split-plot model (i)

150

5.3 Three-factor split-plot model (ii)

154

5.4 Split-split-plot model (i)

158

5.5 Split-split-plot model (ii)

163

5.6 Two-factor split-plot model (ii)

167

5.7 Three-factor split-plot model (iii)

170

5.8 Split-plot model with nesting

173

5.9 Three-factor split-plot model (iv)

176

6 Repeated-measures designs

179

6.1 One-factor repeated-measures model

187

6.2 Two-factor repeated-measures model

190

6.3 Two-factor model with repeated measures on one cross factor

195

6.4 Three-factor model with repeated measures on nested cross factors

200

6.5 Three-factor model with repeated measures on two cross factors

205

6.6 Nested model with repeated measures on a cross factor

214

6.7 Three-factor model with repeated measures on one factor

220

7 Unreplicated designs

229

7.1 Two-factor cross factored unreplicated model

230

7.2 Three-factor cross factored unreplicated model

232

Further Topics

237

Balanced and unbalanced designs

237

Restricted and unrestricted mixed models

242

Magnitude of effect

244

A priori planned contrasts and post hoc unplanned comparisons

245

Choosing experimental designs

248

Statistical power

248

Evaluating alternative designs

250

How to request models in a statistics package

258

Best practice in presentation of the design

260

Troubleshooting problems during analysis

264

Glossary

271

Bibliography

281

Index of all ANOVA models with up to three factors

284

Index

 286