Univariate Aspects

The total mean values of the investigated territories are shown in Tab. 7-1. It can be seen that the variation range of the elemental content amounts to three orders of magnitude. Territorial or even loading structures of the sampling points at the receptor sites cannot be recognized in the adequate univariate, or even bivariate graphical representations. 

Element Mean value Minimum value Maximum value 

The representation of total sedimented particulates and of some elemental precipitation shows only very strongly scattered seasonal variation (Fig. 7-2) this can be interpreted as follows  

The large variance of the elemental depositions, also demonstrated by the very uncertain temporal courses of the elemental deposition rate (Fig. 7-2), strongly limits visual inspection of the obtained data, the interpretation can be subjective only. Otherwise practically all simple correlation coefficients are significant. Both facts show that it seems to be useful to apply advanced statistical methods to attempt recognition of possible existing data structures which may enable the characterization of pollutant loading and the possible identification of emission sources. 

The principle of unsupervised learning consists in the partition of a data set into small groups to reflect, in advance, unknown groupings [YARMUZA, 1980] (see also Section 5.3). The results of the application of methods of hierarchical agglomerative cluster analysis (see also [HENRION et al., 1987]) were representative of the large palette of mathematical algorithms in cluster analysis. 

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W.J. Meissen and L.M.C. Buydens, Aspects of multi-layer feed-forward neural networks influencing the quality of the fit of univariate non-linear relationships. Anal. Proc., 32 (1995) 53-56. 

SOME PRACTICAL ASPECTS OF TH E SELECTION OF UNIVARIATE DISTRIBUTIONS... 

In rivers and streams heavy metals are distributed between the water, colloidal material, suspended matter, and the sedimented phases. The assessment of the mechanisms of deposition and remobilization of heavy metals into and from the sediment is one task for research on the behavior of metals in river systems [IRGOLIC and MARTELL, 1985]. It was hitherto, usual to calculate enrichment factors, for instance the geoaccumulation index for sediments [MULLER, 1979 1981], to compare the properties of elements. Distribution coefficients of the metal in water and in sediment fractions were calculated for some rivers to find general aspects of the enrichment behavior of metals [FOR-STNER and MULLER, 1974]. In-situ analyses or laboratory experiments with natural material in combination with speciation techniques are another means of investigation [LANDNER, 1987 CALMANO et al., 1992], Such experiments manifest univariate dependencies for the metals and other components, for instance between different metals and nitrilotriacetic acid [FORSTNER and SALOMONS, 1991], but the interactions in natural systems are often more complex. 

Before discussing some applications, a few basic aspects on univariate statistics will be presented. A large amount of information exists regarding this field, and more details can be found in the original literature (e.g. [70,71]). Also a variety of computer packages performing statistical data analysis is available (e.g. [71a]). 

One other aspect of raw separations data is the sheer number of variables measured for each sample. When a univariate detector is used for a 15 min separation, operating with an... 

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