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3.6 Vector overlays
A new feature of the PERMANOVA+ add-on package is the ability to add vector overlays onto graphic...
3.5 Negative eigenvalues
The sharp-sighted will have noticed a conundrum in the output given for the Victorian avifauna sh...
3.4 Example: Victorian avifauna
As an example, consider the data on Victorian avifauna at the level of individual surveys, in the...
3.3 Mechanics of PCO
To construct axes that maximise fitted variation (or minimise residual variation) in the cloud of...
3.2 Rationale
It is difficult to visualise patterns in the responses of whole sets of variables simultaneously....
2.12 Dispersion in crossed designs (Cryptic fish)
When two factors are crossed with one another, there may be several possible hypotheses concernin...
2.11 Dispersion in nested designs (Okura macrofauna)
In many situations, the experimental design is not as simple as a one-way analysis among groups. ...
2.10 Small sample sizes
There is one necessary restriction on the use of PERMDISP, which is that the number of replicate ...
2.9 Dispersion as beta diversity (Norwegian macrofauna)
When used on species composition (presence/absence) data in conjunction with certain resemblance ...
2.8 Choice of measure
An extremely important point is that the test of dispersion is going to be critically affected by...
2.7 Ecological example (Tikus Island corals)
An ecological example of the test for homogeneity is provided by considering a study by on coral...
2.6 Test based on medians
Levene’s test (for univariate data) can be made more robust (i.e. less affected by outliers) by u...
2.4 Generalisation to dissimilarities
Of course, in many applications that we will encounter (especially in the case of community data)...
2.2 Rationale
There are various reasons why one might wish to perform an explicit test of the null hypothesis o...
1.38 Environmental impacts
Some further comments are appropriate here regarding experimental designs to detect environmental...
1.37 Asymmetrical designs (Mediterranean molluscs)
Although a previous section has been devoted to the analysis of unbalanced designs, there are som...
1.36 Linear combinations of mean squares (NZ fish assemblages)
Several aspects of the above analysis demonstrate its affinity with unbalanced designs. Note that...
1.35 Designs with covariates (Holdfast invertebrates, revisited)
A topic that is related (perhaps surprisingly) to the topic of unbalanced designs is the analysis...
1.16 Additivity
Central to an understanding of what an interaction means for linear models25 is the idea of addit...
1.34 Types of sums of squares (Birds from Borneo)
When the design is unbalanced, there will be a number of different ways to do the partitioning, w...