Doncaster C.P., Davey A.J.H. Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences

Cambridge: Cambridge University Press, 2007. — 303 p.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.Introduction to analysis of variance
What is analysis of variance?
How to read and write statistical models
General principles of ANOVA
Assumptions of ANOVA
How to distinguish between fixed and random factors
Nested and crossed factors, and the concept of replication
Uses of blocking, split plots and repeated measures
Uses of covariates
How F-ratios are constructed
Use of post hoc pooling
Use of quasi F-ratios
Introduction to model structures
Notation
Allocation tables
Examples
Worked example 1: Nested analysis of variance
Worked example 2: Cross-factored analysis of variance
Worked example 3: Split-plot, pooling and covariate analysis
Key to types of statistical models
How to describe a given design with a statistical model
One-factor designs
One-factor model
Nested designs
Two-factor nested model
Three-factor nested model
Fully replicated factorial designs
Two-factor fully cross-factored model
Three-factor fully cross-factored model
Cross-factored with nesting model
Nested cross-factored model
Randomised-block designs
One-factor randomised-block model
Two-factor randomised-block model
Three-factor randomised-block model
Split-plot designs
Two-factor split-plot model (i)
Three-factor split-plot model (i)
Three-factor split-plot model (ii)
Split-split-plot model (i)
Split-split-plot model (ii)
Two-factor split-plot model (ii)
Three-factor split-plot model (iii)
Split-plot model with nesting
Three-factor split-plot model (iv)
Repeated-measures designs
One-factor repeated-measures model
Two-factor repeated-measures model
Two-factor model with repeated measures on one cross factor
Three-factor model with repeated measures on nested cross factors
Three-factor model with repeated measures on two cross factors
Nested model with repeated measures on a cross factor
Three-factor model with repeated measures on one factor
Unreplicated designs
Two-factor cross factored unreplicated model
Three-factor cross factored unreplicated model
Further Topics
Balanced and unbalanced designs
Restricted and unrestricted mixed models
Magnitude of effect
A priori planned contrasts and post hoc unplanned comparisons
Choosing experimental designs
Statistical power
Evaluating alternative designs
How to request models in a statistics package
Best practice in presentation of the design
Troubleshooting problems during analysisIndex of all ANOVA models with up to three factors