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 Fratios are constructed 
35 
Use of post hoc pooling 
38 
Use of quasi Fratios 
40 
Introduction to model structures 
42 
Notation 
43 
Allocation tables 
43 
Examples 
46 
Worked example 1: Nested analysis of
variance 
47 
Worked example 2: Crossfactored
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 Onefactor designs 
61 
1.1 Onefactor model 
62 
2 Nested designs 
67 
2.1 Twofactor nested model 
68 
2.2 Threefactor nested model 
72 
3 Fully replicated factorial designs 
76 
3.1 Twofactor fully crossfactored
model 
78 
3.2 Threefactor fully crossfactored
model 
86 
3.3 Crossfactored with nesting model

98 
3.4 Nested crossfactored model 
109 
4 Randomisedblock designs 
115 
4.1 Onefactor randomisedblock model

121 
4.2 Twofactor randomisedblock model

128 
4.3 Threefactor randomisedblock
model 
134 
5 Splitplot designs 
141 
5.1 Twofactor splitplot model (i) 
146 
5.2 Threefactor splitplot model (i)

150 
5.3 Threefactor splitplot model
(ii) 
154 
5.4 Splitsplitplot model (i) 
158 
5.5 Splitsplitplot model (ii) 
163 
5.6 Twofactor splitplot model (ii) 
167 
5.7 Threefactor splitplot model
(iii) 
170 
5.8 Splitplot model with nesting 
173 
5.9 Threefactor splitplot model
(iv) 
176 
6 Repeatedmeasures designs 
179 
6.1 Onefactor repeatedmeasures
model 
187 
6.2 Twofactor repeatedmeasures
model 
190 
6.3 Twofactor model with repeated
measures on one cross factor 
195 
6.4 Threefactor model with repeated
measures on nested cross factors 
200 
6.5 Threefactor model with repeated
measures on two cross factors 
205 
6.6 Nested model with repeated
measures on a cross factor 
214 
6.7 Threefactor model with repeated
measures on one factor 
220 
7 Unreplicated designs 
229 
7.1 Twofactor cross factored
unreplicated model 
230 
7.2 Threefactor 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 