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#### 4.4 Simple linear regression (Clyde macrofauna)

In our first example of DISTLM, we will examine the relationship between the Shannon diversity (H...

#### 4.3 Partitioning

Consider an (N × p) matrix of response variables Y, where N = the number of samples and p = the n...

#### 4.2 Rationale

Just as PERMANOVA does a partitioning of variation in a data cloud described by a resemblance mat...

#### 3.1 General description

Key references Method: , PCO is a routine for performing principal coordinates analysis () ...

#### 2.1 General description

Key reference Method: PERMDISP is a routine for testing the homogeneity of multivariate dis...

#### 1.1 General description

Key references Method: , Permutation techniques: , PERMANOVA is a routine for testing the...

#### 3.9 PCO versus MDS

We recommend that, for routine ordination to visualise multivariate data on the basis of a chosen...

#### 3.8 Distances among centroids (Okura macrofauna)

In chapter 1, the difficulty in calculating centroids for non-Euclidean resemblance measures was ...

#### 3.7 PCO versus PCA (Clyde environmental data)

Principal components analysis (PCA) is described in detail in chapter 4 of . As stated earlier, P...

#### 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...

#### 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...

#### 2.5 $P$-values by permutation

The other hurdle that must be cleared is to recognise that, in line with the philosophy of all of...