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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...