Appendices | PRIMER-e Learning Hub

A1 Acknowledgements

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

A2 References

Akaike (1973) Akaike H. 1973. ‘Information theory as an extension of the maximum l...

A3 Index to mathematical notation and symbols

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

A4 Index to data sets used in examples

Below is an index to the data sets used in examples, listed in order of appearance in the text. W...

0.1 Title page

0.2 Contact details and installation of the PERMANOVA+ software

0.3 Introduction to the methods of PERMANOVA+

0.4 Changes from DOS to PERMANOVA+ for PRIMER

0.5 Using this manual

1.1 General description

1.2 Partitioning

1.3 Huygens’ theorem

1.4 Sums of squares from a distance matrix

1.5 The pseudo-F statistic

1.6 Test by permutation

1.7 Assumptions

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

1.9 Creating a design file

1.10 Running PERMANOVA

1.11 Pair-wise comparisons

1.12 Monte Carlo P-values (Victorian avifauna)

1.13 PERMANOVA versus ANOSIM

1.14 Two-way crossed design (Subtidal epibiota)

1.15 Interpreting interactions

1.16 Additivity

1.17 Methods of permutations

1.18 Additional assumptions

1.19 Contrasts

1.20 Fixed vs random factors (Tasmanian meiofauna)

1.21 Components of variation

1.22 Expected mean squares (EMS)

1.23 Constructing $F$ from EMS

1.24 Exchangeable units

1.25 Inference space and power

1.26 Testing the design

1.27 Nested design (Holdfast invertebrates)

1.28 Estimating components of variation

1.29 Pooling or excluding terms

1.30 Designs that lack replication (Plankton net study)

1.31 Split-plot designs (Woodstock plants)

1.32 Repeated measures (Victorian avifauna, revisited)

1.33 Unbalanced designs

1.34 Types of sums of squares (Birds from Borneo)

1.35 Designs with covariates (Holdfast invertebrates, revisited)

1.36 Linear combinations of mean squares (NZ fish assemblages)

1.37 Asymmetrical designs (Mediterranean molluscs)

1.38 Environmental impacts

2.1 General description

2.2 Rationale

2.3 Multivariate Levene’s test (Bumpus’ sparrows)

2.4 Generalisation to dissimilarities

2.5 $P$-values by permutation

2.6 Test based on medians

2.7 Ecological example (Tikus Island corals)

2.8 Choice of measure

2.9 Dispersion as beta diversity (Norwegian macrofauna)

2.10 Small sample sizes

2.11 Dispersion in nested designs (Okura macrofauna)

2.12 Dispersion in crossed designs (Cryptic fish)

2.13 Concluding remarks

3.1 General description

3.2 Rationale

3.3 Mechanics of PCO

3.4 Example: Victorian avifauna

3.5 Negative eigenvalues

3.6 Vector overlays

3.7 PCO versus PCA (Clyde environmental data)

3.8 Distances among centroids (Okura macrofauna)

3.9 PCO versus MDS

4.1 General description

4.2 Rationale

4.3 Partitioning

4.4 Simple linear regression (Clyde macrofauna)

4.5 Conditional tests

4.6 (Holdfast invertebrates)

4.7 Assumptions & diagnostics

4.8 Building models

4.9 Cautionary notes

4.10 (Ekofisk macrofauna)

4.11 Visualising models: dbRDA

4.12 Vector overlays in dbRDA

4.13 dbRDA plot for Ekofisk

4.14 Analysing variables in sets (Thau lagoon bacteria)

4.15 Categorical predictor variables (Oribatid mites)