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#### 1.19 Contrasts

In some cases, what is of interest in a particular experimental design is not necessarily the com...

#### 1.18 Additional assumptions

Recall that we assume for the analysis of a one-way design by PERMANOVA that the multivariate obs...

#### 1.17 Methods of permutations

As for the one-way case, the distribution of each of the pseudo-F ratios in a multi-way design is...

#### 1.16 Additivity

Central to an understanding of what an interaction means for linear models25 is the idea of addit...

#### 1.15 Interpreting interactions

What do we mean by an “interaction” between two factors in multivariate space? Recall that for a ...

#### 1.12 Monte Carlo P-values (Victorian avifauna)

In some situations, there are not enough possible permutations to get a reasonable test. Consider...

#### 1.14 Two-way crossed design (Subtidal epibiota)

The primary advantage of PERMANOVA is its ability to analyse complex experimental designs. The pa...

#### 1.13 PERMANOVA versus ANOSIM

The analysis of similarities (ANOSIM), described by is also available within PRIMER and can be u...

#### 1.11 Pair-wise comparisons

Pair-wise comparisons among all pairs of levels of a given factor of interest are obtained by doi...

#### 1.10 Running PERMANOVA

To run PERMANOVA on the Ekofisk data, click on the resemblance matrix and select PERMANOVA+ > PER...

#### 1.9 Creating a design file

We shall formally test the hypothesis of no differences in community structure among the four gro...

#### 1.8 One-way example (Ekofisk oil-field macrofauna)

Our first real example comes from a study by , who studied changes in community structure of soft...

#### 1.7 Assumptions

Recall that for traditional one-way ANOVA, the assumptions are that the errors are independent, t...

#### 1.3 Huygens’ theorem

This partitioning is fine and perfectly valid for Euclidean distances. But what happens if we wis...

#### 1.2 Partitioning

We shall begin by considering the balanced one-way (single factor) ANOVA experimental design. A f...

#### 0.4 Changes from DOS to PERMANOVA+ for PRIMER

The new Windows interface All of the original DOS routines have been fully re-written, translat...

#### 0.3 Introduction to the methods of PERMANOVA+

Rationale PERMANOVA+ is an add-on package which extends the resemblance-based methods of PRIMER t...

#### A3 Index to mathematical notation and symbols

Matrices and vectors A = matrix containing elements $a _ {ij} = - \frac{1}{2} d _ {ij} ^ 2 $ B =...

#### A1 Acknowledgements

We wish to thank our many colleagues, whose ongoing research has supported this work by providing...

#### 5.15 Comparison of methods using SVD

The relationship between dbRDA and CAP can also be seen if we consider their formulation using si...