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