Univariate statistical evaluation

The empirical distribution of measured values can be described in terms of 

As a rule the substances contained in water are not symmetrically distributed since, as already mentioned, they consist of various strata of a population, which are not always equally represented. Time-dependent fluctuations in a univariate, time-dependent approach entail a loss of information, since the temporal dynamics cannot be adequately described. 

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The initial multivariate analysis consisted of a principal component analysis on the raw data to determine if any obvious relationships were overlooked by univariate statistical analysis. The data base was reviewed and records containing missing data elements were deleted. The data was run through the Statistical Analysis System (SAS) procedure PRINCOMP and the results were evaluated. 

Several applications of univariate statistical analysis for data evaluation in Py-MS are known [73]. One such application is the evaluation of reproducibility of a replicate of an analysis for the peak intensity at a given m/z value. If a series of measurements are made on identical specimens, this will provide a sample xi, X2...Xn. This sample will allow the calculation of parameters such as the mean m and the standard deviation s. By comparing the value s for different m/z values it is possible to select those m/z that are more reproducible (smaller s). 

In univariate statistics a key question discussed previously was to evaluate how close the values of p and m are for a certain population and an experimental m. The answer to this question is used as a model for significance tests. One main tool used to evaluate statistical data is the distribution function, which describes the distribution of measurements about their mean. In other words, the distribution function gives the... 

The book follows a rational presentation structure, starting with the fundamentals of univariate statistical techniques and a discussion on the implementation issues in Chapter 2. After stating the limitations of univariate techniques, Chapter 3 focuses on a number of multivariate statistical techniques that permit the evaluation of process performance and provide diagnostic insight. To exploit the information content of process measurements even further. Chapter 4 introduces several modeling strategies that are based on the utilization of input-output process data. Chapter 5 provides statistical process monitoring techniques for continuous processes and three case studies that demonstrate the techniques. 

Statistical dimensions number of variables (manifest or latent) taken into account in evaluation. Statistical dimensions define the type of data handling and evaluation, e.g. univariate, bivariate, multivariate... 

Combining data from stream sediment analyses with data on historic mining areas, the emission risks of old mine waste sites are evaluated systematically throughout Austria. Univariate and multivariate statistics serve to identify areas with naturally, or anthropogenically, elevated heavy metal concentrations (Fig. 4). Lead and zinc mineralization for... 

Multivariate statistical methods should be preferred for evaluating such multidimensional data sets since interactions and resulting correlations between the water compounds have to be considered. Fig. 8-1, which shows the univariate fluctuations in the concentrations of the analyzed compounds, illustrates the large temporal and local variability. Therefore in univariate terms objective assessment of the state of pollutant loading is hardly possible. 

Sediment analyses are useful for characterization of pollution over a long period [MULLER, 1981]. Assessment of the state of a river and of the interactions between the components can be made by application of multivariate statistical methods only, because the strongly scattering territorial and temporal courses [FORSTNER and MULLER, 1974 FORSTNER and WITTMANN, 1983] are not compatible with many univariate techniques. FA shall serve as a tool for the recognition of variable structures and for the differentiated evaluation of the pollution of both river water and sediment [GEISS and EINAX, 1991 1992],... 

In addition to the usual statistical methods based on univariate descriptors (mean, median, and standard deviation) and analysis of variance, multivariate techniques of statistics and chemometrics are increasingly being used in data evaluation. Whereas the former are more rigorous in theoretical background and assumptions, the latter are useful in the presentation of the data, pattern recognition, and multivariate calibrations. Several good monographs on chemometrics are available (see for example [58-61]). 

The tools of chemometrics encompass not only the familiar (univariant) methods of statistics, but especially the various multivariant methods, together with a package of pattern-recognition methods for time-series analyses and all the known models for signal detection and signal processing. Chemometric methods of evaluation have now become an essential part of environmental analysis, medicine, process analysis, criminology, and a host of other fields. 

Hagenhoff [145] has given a quantitative description of organic SIMS. Various strategies for quantification have been developed internal standards (limited applicability, because of elaborate preparational steps mostly in liquid phases), univariate and multivariate quantification. In the latter cases quantification is achieved by normalisation to uncharacteristic peaks e.g. hydrocarbons), to a sum of characteristic peaks e.g. in mixtures) or to the overall spectral intensity. Promising results concerning quantification of SIMS data can be obtained by evaluation of peak intensity ratios and by means of multivariate statistical methods. Using internal standards an accuracy of the quantification of better than 10% can be reached [146]. 

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