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2.5 $P$-values by permutation
The other hurdle that must be cleared is to recognise that, in line with the philosophy of all of...
2.3 Multivariate Levene’s test (Bumpus’ sparrows)
proposed doing an analysis of variance (ANOVA) on the absolute values of deviations of observati...
1.24 Exchangeable units
The denominator mean square of the pseudo-F ratio for any particular term in the analysis is impo...
1.15 Interpreting interactions
What do we mean by an “interaction” between two factors in multivariate space? Recall that for a ...
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...
1.3 Huygens’ theorem
This partitioning is fine and perfectly valid for Euclidean distances. But what happens if we wis...
A1 Acknowledgements
We wish to thank our many colleagues, whose ongoing research has supported this work by providing...
5.6 Cross-validation
The procedure of pulling out one sample at a time and checking the ability of the model to correc...
2.13 Concluding remarks
PERMDISP is designed to test the null hypothesis of no differences in dispersions among a priori ...
1.21 Components of variation
For any given ANOVA design, PERMANOVA identifies a component of variation for each term in the mo...
9.7 Variability weighting
describe a similar idea to dispersion weighting for use when the data are continuous biological ...
1.9 Summary
A framework has been outlined of three categories of technique (univariate, graphical/distributio...