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The best policy to avoid confusion is to use precise, unique species and sample labels (typically, the sample label would be a conglomeration of all the different study design factors and a replicate number). However, conflicting desirable criteria can sometim...

Perhaps the greatest benefit of the strict label matching in PRIMER is the ability to Tools>Merge assemblage data when two sets of samples, taken at different times or places, are not recorded on a common data sheet, with predetermined taxonomic categories. Sp...

The subject of missing data has arisen several times already (Sections 1, 3, 5) and the point made that the terminology and sheet entry Missing! refers only to variables (usually environmental -type variables) that are not recorded for some samples. It does no...

Tools>Missing is designed to operate only on matrices for which: a) assumptions of multivariate normality can be made; b) there are many fewer variables than samples, so that there are enough data values to be able to estimate the parameters representing means...

Transformation options for the Clyde environmental matrix, Clyde environment, are discussed in more detail in the following (PCA) section, but the tool to carry out separate transforms on sets of variables, Pre-Treatment>Transform(individual), rather than tran...

The following section (on PCA) will discuss further the choice of particular transformations to avoid the sensitivity of PCA (and Euclidean distances in general) to outliers in some environmental variables, but choice of individual transformations is often a w...

Ranking is also a menu option when the active sheet is a resemblance (Tools>Rank distance), but it operates a little differently. This time, all elements of the triangular matrix are ranked together, rather than separate ranking of the rows or columns of the r...

The Clyde environment sheet has samples as rows and variables as columns. This is the opposite of the ecological matrices typically seen so far, such as Clyde macrofauna biomass, in which rows are the variables (species). The environment matrix is displayed ac...

Unlike previous versions, in PRIMER 7 the Transform(individual) routine has been moved to a more convenient – and logical – position in the Pre-treatment menu. Its routine use is therefore covered in Section 4, and its application has been seen several times a...

For an example of an Expression combining two (or more) variables, use the Clyde environmental sheet but copy it (Tools>Duplicate), which is always a good idea when experimenting! The aim is to create a new variable (column) which is the C:N ratio, so first Ed...

Similarly, expressions can combine samples, or even factors (or indicators) on those samples (or variables) – and expressions can even incorporate different worksheets. In fact some of the most useful applications of complex expressions are in combinations of ...

A useful variation of this, but one which needs more care, is to compute average body mass of each species in each sample. This is simply B/A, but needs to cater for the many cases when A (and B) are zero and a simple ratio is undefined. With active sheet Clyd...

Transforming resemblances remains in the Tools menu in PRIMER 7, since it is not an option for pre-treatment of data matrices prior to resemblance calculation (which characterises the other items on the Pre-treatment menu). Although not commonly required, it f...

Tools operations on resemblances which are discussed elsewhere are: a) Dissim and Unravel in Sections 5 & 6 – the former turns similarity into dissimilarity, or vice-versa, and the latter creates a single column of entries from unravelling rows of the triangul...

PRIMER uses the term environmental variables as a shorthand for a wide variety of data types (including biological data!), extending well beyond the archetypal case of physical or chemical measurements made on the environment surrounding an assemblage sample....

Normalisation (subtracting the mean and dividing by the standard deviation, for each variable), and subsequent selection of Euclidean distance or PCA, operates more effectively the closer the data is to approximate (multivariate) normality. The latter is not a...

PCA is an ordination method in which samples, regarded as points in the high-dimensional variable space (11-d here) are projected onto a best-fitting plane, or other low-dimensional solution – the user can specify how many principal components (new axes) are r...

Though the vector overlay has a tendency to clutter the plot, the changing contaminant load along this E-W transect of sampling sites (Fig. 1.5 in CiMC) is clear. The end points S1 and S12 lie close together and there is a strong trend from S1 to the dump cent...

The final table in the results window is headed Principal Component Scores – these can instead be sent to a new worksheet by checking (✓Scores to worksheet) in the Analyse>PCA dialog, which facilitates their further use in PRIMER. An example would be to comput...

Many of the options for manipulating PCA configurations are exactly the same as for MDS plots, covered extensively in Section 8, so will not be repeated – only features that differ will be shown. General rotation is not allowed in a PCA: directions have define...