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: 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