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Close the World cities worksheet (it will not be needed again) and re-open workspace Morlaix ws, from earlier in this section. It contains the data sheet Morlaix macrofauna abundance, fourth-root transformed and with Bray-Curtis similarity matrix, Resem1, on w...

The mMDS Shepard diagram above strongly suggests a middle course between simple metric and non-metric MDS, which we shall term threshold metric MDS (tmMDS), in which the Shepard plot is fitted by a straight line but not through the origin. It will almost alway...

Though usually greatly inferior to nMDS for typical ordinations from community similarities (e.g. with coefficients from the Bray-Curtis family), purely metric MDS (mMDS) becomes a valuable tool for ordinations based on only a handful of samples, when the info...

The PRIMER 7 nMDS dialog box includes a new option to (✓Fix Collapse). This addresses the problem of indeterminacy in some nMDS plots, when two (or more) groups of samples have very different communities, such that all dissimilarities between the groups are la...

A variation of the above, and a final new PRIMER 7 feature to discuss in this section, is the option to mix, in equal measure, stress functions from two resemblance matrices, in a single nMDS. There are possible applications to data sets in which a single MDS ...

The series of ANOSIM (analysis of similarity) tests, accessed through Analyse>ANOSIM, operate on a resemblance matrix as the active sheet and carry out non-parametric tests for designs which broadly parallel univariate 1- and 2- way ANOVA (analysis of variance...

Return to the W Australian fish diet data, introduced at the start of Section 4 and last seen under the Higher-d & scree plots heading of Section 8, showing MDS plots of dietary categories found in 65 (pooled) gut samples from 7 fish species. If the workspace ...

The table ending the results window gives the pairwise comparisons. For each pair of groups (fish species), the first data column is of pairwise R statistics. These are again a difference of average rank dissimilarities between and within the two groups, scale...

Checking the (✓Pairwise tests to worksheet) box has also sent the above R values to a worksheet in triangular format, which could be a useful layout for tabulating ANOSIM results in a publication. More subtly, this can be regarded as a resemblance matrix (of d...

ANOSIM applies equally well to data on environmental, biomarker or morphometric variables, which might be transformable to approximate normality; it is then a robust alternative to classical multivariate (MANOVA) tests such as Wilks’ lambda. The inevitable sli...

However, for the Ekofisk oil-field study of the last section there is a postulated cause for benthic community change (the presence of an oilfield) and impacts, if any, are expected to result in a monotonic change with increasing distance from the drilling cen...

An example of a 2-way crossed layout was introduced in Section 1, for meiofaunal communities in sediment patches either disturbed or undisturbed by soldier crabs (treatment factor Trt, levels D/U, factor A), over four areas of Tasmanian sandflat (block factor ...

For an example of a 2-way crossed ANOSIM test in a very different context, save and close the above workspace and return to the particle size distributions from Danish sediments introduced at the very end of Section 4 – the workspace Denmark ws in C:\Examples ...

In the unordered 1-way design, replication is essential for any sort of test (otherwise how can you tell whether single samples from groups A, B, C, … are from the same or different communities? – there are no within-group rank dissimilarities to compare with ...

The test for an ordered factor (A) in the 2-way crossed design parallels the construction seen earlier for the 2-way (unordered) crossed case, in that the 1-way R$^\text{O}$ statistic is calculated separately for each level of the other factor (B) and those R...

The 2-way crossed ANOSIM for an unordered factor, and with each combination of the two factors only having a single replicate, is covered in CiMC, Figs. 6.9 to 6.12, firstly for a treatment $\times$ block design and then for the example considered here of site...

Subtidal rocky reefs, at ca 10m depth, at the Calafuria station in the Ligurian Sea, N Italy, were the subject of a clearance and recovery experiment by Airoldi L 2000 Mar Ecol Prog Ser 195: 81-92 (see also Clarke KR, Somerfield PJ, Airoldi L, Warwick RM 2006,...

A dietary study of W Australian fish concerns composition by the volume of taxa (21 broad dietary categories: gastropods, bivalves, annelids, etc.) in the foregut of King Wrasse from one of 4 length-classes, caught in 3 locations in 2 periods of the year and 2...

The 3-way fully nested design has factor C at the lowest level, nested in B at the mid level, which itself is nested in A at the top level, denoted C(B(A)). Factors can again be ordered or not, and the routine is essentially a repeated application of the 2-way...

The two other possible 3-way designs can be written C(A$\times$B) and B$\times$C(A). The first is straight-forward: an example might be of locations (A) each containing the same set of habitat types (B), and within each combination of habitat and location a nu...