In the following Chapters 1 to 7, we will describe all common models with up to three treatment factors for seven principal classes of ANOVA design:

1. One-factor – replicate measures at each level of a single explanatory factor;

2. Nested – one factor nested in one or more other factors;

3. Factorial – fully replicated measures on two or more crossed factors;

4. Randomised blocks – repeated measures on spatial or temporal groups of sampling units;

5. Split plot – treatments applied at multiple spatial or temporal scales;

6. Repeated measures – subjects repeatedly measured or tested in temporal or spatial sequence;

7. Unreplicated factorial – a single measure per combination of two or more factors.

For each model we provide the following information:

• The model equation;

• The test hypothesis;

• A table illustrating the allocation of factor levels to sampling units;

• Illustrative examples;

• Any special assumptions;

• Guidance on analysis and interpretation;

• Full analysis of variance tables showing all sources of variation, their associated degrees of freedom, components of variation estimated in the population, and appropriate error mean squares for the F-ratio denominator;

• Options for pooling error mean square terms.

As an introduction to Chapters 1 to 7, we first describe the notation used, explain the layout of the allocation tables, present some worked examples and provide advice on identifying the appropriate statistical model.

Notation

Chapters 1 to 3 describe fully randomised and replicated designs. This means that each combination of levels of categorical factors (A, B, C) is assigned randomly to n sampling units (S′), which are assumed to be selected randomly and independently from the population of interest.