Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences

by C. Patrick Doncaster , Andrew J. H. Davey

• ISBN13: 9780521865623
• ISBN10: 052186562X
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-10-22
• Publisher: Cambridge University Press

Summary

Analysis of variance (ANOVA) is a core technique for analysing data in the Life Sciences. This reference book bridges the gap between statistical theory and practical data analysis by presenting a comprehensive set of tables for all standard models of analysis of variance and covariance with up to three treatment factors. The book will serve as a tool to help post-graduates and professionals define their hypotheses, design appropriate experiments, translate them into a statistical model, validate the output from statistics packages and verify results. The systematic layout makes it easy for readers to identify which types of model best fit the themes they are investigating, and to evaluate the strengths and weaknesses of alternative experimental designs. In addition, a concise introduction to the principles of analysis of variance and covariance is provided, alongside worked examples illustrating issues and decisions faced by analysts.

Author Biography

Andrew J. H. Davey is an Environmental Scientist at the UK Water Research Centre.

Table of Contents

Preface	p. ix
Introduction to analysis of variance	p. 1
What is analysis of variance?	p. 1
How to read and write statistical models	p. 2
General principles of ANOVA	p. 7
Assumptions of ANOVA	p. 14
How to distinguish between fixed and random factors	p. 16
Nested and crossed factors, and the concept of replication	p. 21
Uses of blocking, split plots and repeated measures	p. 25
Uses of covariates	p. 29
How F-ratios are constructed	p. 35
Use of post hoc pooling	p. 38
Use of quasi F-ratios	p. 40
Introduction to model structures	p. 42
Notation	p. 43
Allocation tables	p. 43
Examples	p. 46
Nested analysis of variance	p. 47
Cross-factored analysis of variance	p. 49
Split-plot, pooling and covariate analysis	p. 51
Key to types of statistical models	p. 57
How to describe a given design with a statistical model	p. 58
One-factor designs	p. 61
One-factor model	p. 62
Nested designs	p. 67
Two-factor nested model	p. 68
Three-factor nested model	p. 72
Fully replicated factorial designs	p. 76
Two-factor fully cross-factored model	p. 78
Three-factor fully cross-factored model	p. 86
Cross-factored with nesting model	p. 98
Nested cross-factored model	p. 109
Randomised-block designs	p. 115
One-factor randomised-block model	p. 121
Two-factor randomised-block model	p. 128
Three-factor randomised-block model	p. 134
Split-plot designs	p. 141
Two-factor split-plot model (i)	p. 146
Three-factor split-plot model (i)	p. 150
Three-factor split-plot model (ii)	p. 154
Split-split-plot model (i)	p. 158
Split-split-plot model (ii)	p. 163
Two-factor split-plot model (ii)	p. 167
Three-factor split-plot model (iii)	p. 170
Split-plot model with nesting	p. 173
Three-factor split-plot model (iv)	p. 176
Repeated-measures designs	p. 179
One-factor repeated-measures model	p. 187
Two-factor repeated-measures model	p. 190
Two-factor model with repeated measures on one cross factor	p. 195
Three-factor model with repeated measures on nested cross factors	p. 200
Three-factor model with repeated measures on two cross factors	p. 205
Nested model with repeated measures on a cross factor	p. 214
Three-factor model with repeated measures on one factor	p. 220
Unreplicated designs	p. 229
Two-factor cross factored unreplicated model	p. 230
Three-factor cross factored unreplicated model	p. 232
Further Topics	p. 237
Balanced and unbalanced designs	p. 237
Restricted and unrestricted mixed models	p. 242
Magnitude of effect	p. 244
A priori planned contrasts and post hoc unplanned comparisons	p. 245
Choosing experimental designs	p. 248
Statistical power	p. 248
Evaluating alternative designs	p. 250
How to request models in a statistics package	p. 258
Best practice in presentation of the design	p. 260
Troubleshooting problems during analysis	p. 264
Glossary	p. 271
References	p. 281
Index of all ANOVA models with up to three factors	p. 284
Index	p. 286
Categories of model	p. 288
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