Analysis of Variance and Covariance
How to Choose and Construct Models
for the Life Sciences
C. PATRICK DONCASTER and ANDREW J. H. DAVEY
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: |
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 |