Baseline study Fish, fry and commercial fishery Nysted Offshore ...

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3.10.2.2.2 Multivariate analysis
When the variables in question (species) are correlated as in the present baseline study,
then the natural choice of method would be a multivariate analysis. If not for the test of
significance, the ordination techniques can be used to explore the structures of the data
and therefore be guidance to the final test of significance.
The choice is between:
• The usual multivariate analysis in a parametric, normal and linear model.
Different aspect about this analysis have been mentioned, but one essential
problem is the requirement for normality and homogeneity of variance now
sharpened as these requirements apply to all variables at the same time. It is a
precondition of the MANOVA test that the number of observations minus one
subtracted from the number of groups should be bigger than the number of
variables (species). If the numbers of observations are at least 2 to 3 times bigger
than the number of variables, then the test is fairly robust to deviations from the
conditions about normality and homogeneity of variance. That is the case in the
present baseline study from Rødsand where approximately 20 different species
were caught.
• The reduction of variables using the ordination technique. A PCA analysis can
extract information from a large number of variables and represent that
information using a smaller number of “synthetic” variables. These variables are
by nature uncorrelated and can be used in univariate analysis. The catch is that it
can be difficult to explain the real picture of the old variables using the new
variables.
• The reduction of number of variables by the use of scientific criteria to create
functional groups of species which abundance and biomass can be tested in uni- or
multivariate models. The obvious method is to make functional groups according
to the expected biological effect in the actual investigation. As an example, it
would be obvious to create a group of species with special attachment to the reef
habitat. One of the effects of such a strategy would be fewer empty samples,
making it easier to fulfil the preconditions to use the parametric
ANOVA/MANOVA.
• Extract various indices or statistics from the original data and use them in uni- or
multivariate analysis. The two fundamental statistics are the total number of
individuals and the total number of species per sample, but there are a number of
diversity indexes etc. available. In general, this method does not provide useful
results because of the difficulties involved in explaining a multidimensional real
world using a model with only one dimension.
• Use the full set of data in a non-parametric multi-step analysis based on measures
of distance. Use permutation analysis to test for significant effects and use tools
based on the calculated distances, in case of significance, to refer the explanation
of the significance back to the particular species. The latter type of investigation
can provide a grouping of species, which might fit the grouping in functional
species.
SEAS. Baseline study – Fish, fry and commercial fishery Dok. nr. 2148-03-001-rev3 2P.doc