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On the mid-right of the main dialog for BEST, the box headed (Correlation method:) now offers three non-parametric choices and one parametric correlation: Spearman rank, Weighted Spearman rank, Kendall tau and Pearson, covered in equations (11.3), (11.4) and (...

The final area of the main BEST dialog, headed Permutations, which carries out the global BEST test for statistical significance of the best matching combination of variables, is deferred until later in this section. The Next > button, under (Method•BIOENV), g...

The Next > button now takes you to a Results dialog box, which controls two features of the BEST results window, the quantity of output and how the explanatory variables are identified. For a run of BIOENV, (Results detail: Brief or Normal) will output just tw...

A study of diatom assemblages (abundances of 193 species) at 17 sites in the lagoons of Messol-ongi, Aitoliko and Kleissova in Eastern Central Greece was undertaken by Danielidis DB (1991), Ph.D. thesis, Univ Athens. At each site, a suite of 11 water-column da...

The question of statistical significance testing on the results of the Bio-Env (or BVStep) procedure naturally arises. Section 14 describes Analyse>RELATE, a (non-parametric) form of Mantel test. For any two independently-derived resemblance matrices, defining...

Another technique for linking sample patterns based on assemblage data to a suite of environmental (or other) explanatory variables was also discussed in Clarke KR et al 2008 J Exp Mar Biol Ecol 366: 56-69 (see the last topic in Chapter 11, CiMC). The well-est...

The Analyse>Cluster>LINKTREE routine has a number of features that are designed to mesh to the PRIMER approach. Firstly, as seen for unconstrained UNCTREE clustering (Section 6), each successive split of the biotic samples into two groups (of potentially unequ...

Continuing the lagoon diatom study, having first selected (highlighting then Select>Highlighted) the optimal 3-variable set (Sal, PO$_4$, In-N), from the above BEST run, in Messolongi environment, and again with the diatom resemblance matrix as the active shee...

Low values of B% correspond to samples which are rather close together on the MDS plot and the question naturally arises as to whether these samples should be split at all – is there any evidence that the biological assemblages differ among the sites 5, 7, 11,...

Note that LINKTREE is able to tolerate some missing data in the abiotic matrix – the piecemeal form of LINKTREE’s conclusions lends itself to analysing what¬ever complete matrix is available locally, i.e. within each created subdivision. But distortions in int...

The BEST routine in the previous section introduced the concept of measuring how closely related two sets of multivariate data are, for a matching set of samples, by calculating a rank correlation coefficient (Spearman’s $\rho$, Kendall etc) between all the el...

Model matrices corresponding to more complicated structures than simple seriation or cyclicity need first to be constructed by the user and then entered to RELATE in the same way as any other resemblance matrix being matched to the active sheet. There are at l...

A permutation test can be applied to the matching coefficient $\rho$ between any two resemblance matrices which are independently derived, with all sample labels in the active matrix matched with (some) labels in the supplied resemblances. As remarked in the p...

The Phuket coral-reef assemblages at equi-spaced positions down an onshore-offshore gradient (transect A) from Phuket Island, were seen previously in Sections 8, 9 and 11. Open the workspace Phuket ws, or if not available open just Phuket coral cover 83-87 fr...

Given the breakdown of the serial gradient structure for 1987, is it now the case that the pattern of change down the transect has nothing at all in common with that for 1983? To answer that question requires a further run of RELATE, but of the two similarity ...

A new feature in PRIMER 7 parallels that discussed for the BEST analysis of the previous section, namely a secondary factor is supplied, e.g. (✓Within levels of factor         ), which turns this into a 2-way RELATE test. The matching statistic $\rho$ – wheth...

Return to the macrofaunal data set from the Ekofisk oilfield, with workspace Ekofisk ws last saved in C:\ Examples v7\Ekofisk macrofauna in Section 9, following an ordered 1-way ANOSIM test (with replication) on the similarity matrix B-C on sq rt from data Eko...

The conclusion is, of course, consistent with the different, but closely-related, ordered ANOSIM statistic R$^{\text Oc}$ = 0.67 (p<0.01%), calculated in Section 9. It is relatively easy to show algebraically that the unordered ANOSIM statistic – here R = 0.55...

A RELATE test could equally well have been carried out between the Ekofisk community pattern and a matching (abiotic) resemblance matrix computed not from the surrogate for increased impact – the nearness of the sites to the oil-field centre – but from a set ...

As an example of Tools>Expand Samples on a data matrix (or Tools>Expand on a resemblance matrix, since the expansion can be equally well achieved either before or after the computation of Euclidean distance in this situation) we shall use the Exe nematode stud...