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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...

The Exe environment matrix does not seem (from Plots>Draftsman Plot or Histogram Plot) to contain notable outliers and can safely be used without transformation of individual variables. It does however need Pre-treatment>Normalise Variables – rename it Abiotic...

The other two Model Matrix options are (Type•Cyclicity (factor as cycles)) and (Type•Euclidean 2D). The latter simply calculates, for example, distance between samples in a geographic layout when the x, y co-ordinates of the sample points are not held in a sep...

A 2-way RELATE version of the above test where there are no replicates, and the cyclic factor under test is actually nested within a ‘nuisance’ factor whose effect we want to remove, is given by reverting to the full data sheet for the Loch Etive macrofauna sa...

Veale L et al 2014 J Fish Biol 85: 1320-1354 describe trawl sampling for nearshore estuarine fish in the Leschenault estuary of Western Australia, over 4 regions (B - Basal, L - Lower, U - Upper, A - Apex of the estuary) and 4 seasons (Sp - Spring, S - Summer,...

As seen above, the $\rho$ statistic, which rank correlates the elements of two similarity matrices, can provide a very useful and succinct summary of the extent of agreement between two ordinations (or, to be more precise, of agreement in the high-dimensional ...

Chapter 10 of CiMC gives several examples of aggregating species matrices to higher taxa – using the Tools>Aggregate routine – and the effect this has on the resulting multivariate (and univariate) analyses. We shall illustrate this with the benthic macrofauna...

The illustration below has calculated all combinations of species (sp), genus (gn) and family (fm) level data, under no transform (no), square-root (sqr), fourth-root (4th), log(x+1) (log) transforms and reduction to presence/absence (pa), with similarity shee...

The technique of 2nd stage plots has also been used (Clarke KR, Somerfield PJ, Chapman MG 2006, J Exp Mar Biol Ecol 330: 55-80) to examine the effects of different resemblance coefficient choices on a samples analysis, scaling this in relation to the effects o...

Clarke KR, Somerfield PJ, Chapman MG 2006, J Exp Mar Biol Ecol 330: 55-80 discuss this analysis (and that for several other data sets) in more detail, but to pick out just four general points: a) These 2nd stage plots have common features, irrespective of the ...

A very different way of using 2nd stage matrices is best accessed through the alternative entry option in the dialog box for 2STAGE, namely to specify a single similarity matrix with factors defining a 2-way crossed layout of samples (e.g. of sites and times),...

Open the workspace Phuket ws, of coral cover for the Ko Phuket transect A, in C:\Examples v7\ Phuket corals, or if not available, open the data files Phuket coral cover 83-87, 88-97 and 98-00, and Tools>Merge them (as in Section 11), taking the defaults to p...

In the context of a 2-factor design, PRIMER makes a 2nd stage matrix very simple to produce but it is less easy to understand what it represents! The structure requires that the factors divide the data into a 2-way layout with no replicates in each cell; the i...

The workspace Tees ws was saved in Section 9; if not available open the data Tees macrobenthic abundance from C:\Examples v7\Tees macrobenthos and recalculate Bray-Curtis similarity on the 4th-root transformed abundances for all 192 samples (B-C all), with str...

The Calafuria macroalgal recolonisation experiment monitored the same physical rock patches over one year, having first cleared the (subtidal) rockface. Replicate patches were tracked for 8 different ‘treatments’, namely different times of year for the clearan...

Another situation employing rank correlation ($\rho$) between two resemblance matrices is the BEST (Bio-Env) routine of Section 13, where the biological similarity matrix (‘response’) describes the among-sample relationships of the full community and the secon...

There is one fundamental problem with applying BEST (Bio-Env) in many of the above scenarios: the number of variable combinations from the active matrix that must be considered in a full search increases exponentially with the number of variables. For p variab...

The main application area for the BVStep routine introduced by Clarke KR & Warwick RM 1998, Oecologia 113: 278-289, is what might be termed Bio-Bio, namely searching for subsets of species whose resemblance matrix best matches that of another (fixed) set of sp...

Re-open the Morlaix ws workspace in C:\Examples v7\Morlaix macrofauna from earlier in this section, or since this is all that is needed, just open the data file Morlaix macrofauna abundance into a clear workspace. It consists of 21 sampling times and 251 speci...

On B-C on 4rt, Analyse>BEST>(Method•BVSTEP) & (Worksheet: 4rt data), taking the defaults for all other entries (Spearman correlations, the suggested Bray-Curtis similarity, all 100 species Available for selection, and the permutation test ignored – a test of $...