Statistical comparisons of heavy metal pollutants between seven regions of the Polish exclusive economic zone |
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| Authors: | Ross M Renner |
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| Institution: | 1. School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
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| Abstract: | This paper addresses three intractable difficulties associated with the statistical analysis of compositional data, such as percentages or ppm. These are: (1) that such data do not follow multivariate normal distributions thus rendering inappropriate, standard parametric statistical tests and estimation procedures, (2) the covariance/correlation coefficients between specific pairs of components are determined in whole or in part by the presence or absence of other components, and, (3) the negative bias property. That is, at least one covariance and therefore at least one correlation, must be negative, hence the remaining correlations are prevented from ranging freely between ?1 and +1. It follows that correlation coefficients formed from compositional data are not only not absolute, but also frequently spurious. Standard multivariate procedures based on them are unreliable, and intrinsic associations between components inferred from strong positive correlations in particular, are potentially false. In a recent 2009 paper, it was reported that 59 surface sediment samples from 7 regions in the Polish exclusive economic zone had been chemically analyzed for 16 elements. Enrichment factors together with crude correlation coefficients between selected elements were presented. All these quantities were computed from the initial raw compositional data resulting from the chemical analyses In this paper, a statistical procedure is presented which is distinctly different to the enrichment factor computations based on the same raw compositional data. The procedure generates a log-ratio measure of the abundance of each element in each of the seven regions, thus enabling comparisons of relative levels of pollution between the regions. Although the two techniques are quite unrelated, it is shown that in general, extremely high or low measures of the relative abundances in the regions are associated with correspondingly high or low values of the enrichment factors in the same regions that were reported in the 2009 paper. That is, the statistical analysis confirms the results of the enrichment factor data in the identification of the most to the least polluted regions. In an additional analysis, the residue term was excluded from each sediment sample by rescaling the 16 element concentrations to sum to 100%, thus forming 59 residue-free sub-compositions. Crude correlation coefficients were computed for pairs of elements of this sub-compositional data. These revealed that certain correlations based on the initial raw data that were reported in the 2009 paper for the same pairs of elements, were not only inconsistent, but sometimes also contradictory. Such contradictions imply that intrinsic geochemical element associations inferred in that paper from such correlations were false. |
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