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Both the Draftsman and Histogram Plots show that several of the Ekofisk abiotic variables are highly right-skewed (tail to the right), and it would be wise, if we are to limit the distorting effects of outliers and normalise the data to a desired common measur...

It is typical of a suite of physico-chemical variables (or biomarkers, water-quality indices etc.) that they are not on comparable measurement scales, unlike assemblage abundances. All multivariate analysis methods are based on resemblances between samples tha...

When variables are on different measurement scales, there is little viable alternative to normalising each variable (as above) thus equalising, in effect, their contributions to the multivariate analysis. When variables are (ostensibly) on the same scale, e.g...

Sediment copepod assemblages (and other fauna) from five creeks of the Fal estuary, SW England, were analysed by Somerfield PJ, Gee JM, Warwick RM 1994, Mar Ecol Prog Ser 105: 79-88. The sediments of this estuary are characterised by high and varying concentr...

There are other cases in which variables (species) might need prior weighting, e.g. when a species is known to be often misidentified, its contribution (and those of the species it is mistaken for) can be reduced by multiplying the entries in the two species t...

Another example might be in attempting to reconcile two different types of data in the same matrix, e.g. counts of motile organisms and area cover of colonial species. These cases can be problematic. One solution is to use a similarity measure such as the Gowe...

Pre-treatment>Variability Weighting is a new option in PRIMER 7, which bears similarities to the idea of Dispersion Weighting. This was introduced by Hallett CS, Valesini FJ, Clarke KR 2012, Ecol Indicat 19: 240-252 in a context where the variables were ‘healt...

The directory C:\Examples v7\N Sea biomarkers holds a data sheet N Sea flounder biomarkers(.pri) of biochemical and histological biomarkers measured concurrently on flounder caught at 5 North Sea sites (labelled S3, S5, S6, S7 and S9), running on a putative co...

The remaining option on the Pre-treatment menu is Cumulate samples, which successively adds up the entries across variables, separately for each sample. It is only appropriate when all variables share a common measurement scale, and when the order in which the...

Sediment particle size data from 6 size ranges at 3 sites (A, B, C), at 2 depths (2m and 5m), and 5 replicate samples from each site/depth combination are in C:\Examples v7\Denmark PSA\ Denmark PSA histogram. The data are already standardised to % composition ...

The smoothing effect can best be seen by Plots>Surface Plot of both Data1 and Data2 sheets – a further graph type new to PRIMER 7, but which should be reserved only for cases such as this, where there is genuine ordering of the variables. Symbols can be added ...

Fundamental to the operation of PRIMER and (explicitly or implicitly) any fully multivariate analysis, is an appropriate definition of resemblance between every pair of samples, based on whether the suite of recorded variables (species, environmental variables...

A detailed discussion of the competing properties of different resemblance matrices is outside this manual’s scope (see L&L, CiMC Chapters 2 & 16, or Clarke KR, Somerfield PJ, Chapman MG 2006, J Exp Mar Biol Ecol 330: 55-80). Novice users are recommended to ta...

The most commonly-used similarity coefficient for biological community analysis, because it obeys many of the ‘natural’ biological guidelines in a way that most other coefficients do not (see CiMC), is the Bray-Curtis similarity, defined between samples 1 and ...

A simple modification to the Bray-Curtis coefficient adjusts its behaviour as samples become vanishingly sparse. Standard Bray-Curtis is undefined for two samples containing no species, and can fluctuate wildly for near-blank samples – two samples containing j...

Data on coral communities at a site in Tikus Island, Thousand Islands, Indonesia, over the years 1981, 83, 84, 85, 87 and 88, were reported by Warwick RM, Clarke KR, Suharsono 1990, Coral Reefs 8: 171-179. Ten replicate transects were examined each year, and t...

Euclidean distance, an appropriate measure for environmental (and other) data types, is defined as: $$ D_1 = \sqrt{ \sum_i \left( y _ {i1} - y_{i2} \right) ^ 2 } $$ where the $y_{i1}$ & $y_{i2}$ result from pre-treatment by transformation (sometimes) and subse...

The remaining of the three choices in the initial list, Measure•Index of Association, is essentially Whittaker’s index of association, which when calculated on samples (the default is always Analyse between•Samples)is simply just Bray-Curtis similarity on a s...

PRIMER 7 allows the user choice of 44 other resemblances, firstly divided into two (mutually exclusive) types: Similarities (including L&L’s S numbers) or Dissimilarities/Distances (including L&L’s D numbers); then most of the same coefficients split instead i...

The distance measures defined by L&L and calculated by PRIMER 7 (in addition to $D_1$) are: $ D_2 = \sqrt{ \frac{1}{p} \sum_i \left( y_{i1} - y_{i2} \right) ^ 2 } \text{ \hspace{25mm} average distance,} $ where the number of species p is fixed for all pairs...