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2.4 Generalisation to dissimilarities
Of course, in many applications that we will encounter (especially in the case of community data)...
2.3 Multivariate Levene’s test (Bumpus’ sparrows)
proposed doing an analysis of variance (ANOVA) on the absolute values of deviations of observati...
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...
1.34 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...
1.32 Repeated measures (Victorian avifauna, revisited)
While randomised blocks, latin squares and split-plot designs lack spatial replication, a special...
1.31 Split-plot designs (Woodstock plants)
Another special case of a design lacking appropriate replication is known as a split-plot design....
1.30 Designs that lack replication (Plankton net study)
A topic related to the issue of pooling is the issue of designs that lack replication. Familiar e...
1.29 Pooling or excluding terms
For a given design file, PERMANOVA, by default, will do a partitioning according to all terms tha...
1.28 Estimating components of variation
The EMS’s also yield another important insight: they provide a direct method to get unbiased esti...
1.27 Nested design (Holdfast invertebrates)
We have seen how a crossed design is identifiable by virtue of every level of one factor being pr...
1.24 Exchangeable units
The denominator mean square of the pseudo-F ratio for any particular term in the analysis is impo...
1.25 Inference space and power
It is worthwhile pausing to consider how the above tests correspond to meaningful hypotheses for ...
1.6 Test by permutation
An appropriate distribution for the pseudo-F statistic under a true null hypothesis is obtained b...
1.23 Constructing $F$ from EMS
The determination of the EMS’s gives a direct indication of how the pseudo-F ratio should be cons...
1.22 Expected mean squares (EMS)
An important consequence of the choice made for each factor as to whether it be fixed or random i...
1.20 Fixed vs random factors (Tasmanian meiofauna)
All of the factors considered so far have been fixed, but factors can be either fixed or random. ...