Principles of Data Analysis

Usually multivariate analytical information is represented in form of a data matrix  

From the viewpoint of data analysis, these objectives are achieved by means of the following fundamental methods  

In addition, methods of artificial intelligence (artificial neural networks and genetic algorithms) are applied. 

The proceeding of common methods of data analysis can be traced back to a few fundamental principles the most essential of which are dimensionality reduction, transformation of coordinates, and eigenanalysis. 

The principle of reduction of dimensionality will be illustrated schematically. In case that the property (+/—) of an object depends mainly on one 

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The collection of examples is extensive and includes relatively simple data analysis tasks such as polynomial fits they are used to develop the principles of data analysis. Some chemical processes will be discussed extensively they include kinetics, equilibrium investigations and chromatography. Kinetics and equilibrium investigations are often reasonably complex processes, delivering complicated data sets and thus require fairly complex modelling and fitting algorithms. These processes serve as examples for the advanced analysis methods. 

Whatever the analysis of the data may entail, there are some general methods helpful to the analyst. The objective of this chapter is to present a brief introduction to these general methods and principles of data analysis. 

Teo BK (1986) EXAFS basic principles of data analysis. Springer, Berlin... 

This simple example illustrates principles of Bayesian analysis and how it accommodates information from different sources. Real situations and real analyses can be more complicated than our example. For example, when species are tested with chemical A, we might not know their LC50 values exactly instead, we might have estimates of LC50 values. Or we may have data on another similar chemical C. In each case, we would adjust the analysis to accommodate the more complicated situation. 

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis. Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented. 

Deconvolution, the inverse operation of recovering the original function o from the convolution model as given in Eq. (1), employs procedures that almost always result in an increase in resolution of the various components of interest in the data. However, there are many broadening and degrading effects that cannot be explicitly expressed as a convolution integral. To consider resolution improvement alone, it is instructive to consider other viewpoints. The uncertainty principle of Fourier analysis provides an interesting perspective on this question. 

These EDA methods are essentially pictorial and can often be carried out using simple pencil and paper methods. Picturing data and displaying it accurately is an aspect of data analysis which is under utilised. Unless exploratory data analysis uncovers features and structures within the data set there is likely to be nothing for confirmatory data analysis to consider One of the champions of EDA, the American statistician John W. Tukey, in his seminal work on EDA captures the underlying principle in his comment that... 

Principles of Data Quality Control in Chemical Analysis , Analyst Cambridge, 1989, 114, 1497. 

Tnformation about the characteristics of keto-hexoses in solution has been - derived mainly from optical rotatory data (I, 2, 3, 4) and in recent years by application of the principles of conformational analysis (5, 6). In the current study an attempt is made to describe the conformation and composition of these sugars in solution by nuclear magnetic resonance (NMR) spectroscopy, a highly sensitive means for examining stereochemistry and for differentiating between isomeric species. 

The principle of multivariate analysis of variance and discriminant analysis (MVDA) consists in testing the differences between a priori classes (MANOVA) and their maximum separation by modeling (MDA). The variance between the classes will be maximized and the variance within the classes will be minimized by simultaneous consideration of all observed features. The classification of new objects into the a priori classes, i.e. the reclassification of the learning data set of the objects, takes place according to the values of discriminant functions. These discriminant functions are linear combinations of the optimum set of the original features for class separation. The mathematical fundamentals of the MVDA are explained in Section 5.6. 

In the first section will be presented XAS from the physical principles to data analysis and measurements. Then section 2 will be devoted to a discussion of a few examples to illustrate the power and limitations of XAS for gaining structural information. Examples are focused on EXAFS studies on nanocrystalline materials. Detailed reviews for applications on other fields of materials science or for presenting the complementary information available by the study of the X-ray Absorption Near Edge Structure (XANES) part of the X-ray absorption spectrum can be found in a number of books [3-5], A brief overview of the recent development of the technique regarding the use of X-ray microbeams available on the third generation light sources will be finally presented in the last section. 

The objective of the statistical analysis of variances is to separate the effects produced by the dependent variables in the factors of the process. At the same time, this separation is associated with a procedure of hypotheses testing what allows to reject the factors (or groups of factors) which do not significantly influence the process. The basic mathematical principle of the analysis of variances consists in obtaining statistical data according to an accepted criterion. This criterion is complemented with the use of specific procedures that show the particular influence or effects of the grouping criterion on dependent variables. 

B. K. Teo, EXAFS Basic Principles and Data Analysis, Springer Verlag, Berlin (1986) DC Koningsberger, R Prins, X-ray Absorption Principles, Applications, Techniques of EXAFS, SEXAFS and XANES, John Wiley and Sons, New York (1988) P.A. Lee, P.H. Citrin, P. Eisenberger, B.M. Kincaid, Rev. Mod. Phys. 53, 769-806 (1981) T.M. Hayes, J.B. Boyce, Sol St. Phys. 37, 173-351 (1982) E.A. Stern, S.M. Heald, In Handbook of Synchrotron Radiation Vol. 1, Elsevier Science Publishers, Amsterdam, pp 955-1014, (1983) H. Winick, S. Doniach, Synchrotron Radiation Research, Plenum Press, New York (1980). 

In both pulse and phase fluorometries, the most widely used method of data analysis is based on a nonlinear least-squares method. The basic principle of this method is to minimize a quantity which expresses the mismatch between data and fitted function. This quantity is the reduced chisquare defined as the weighted sum of the squares of the deviations of the experimental response R(t ) from the calculated ones... 

There are two simple principles underpinning MIAME. First, microarray data should be annotated in sufficient detail to be of most use to third parties. Second, while the microarray technology is still rapidly developing, it would be counterproductive to try to impose on researchers the use of any particular platforms or software, and any particular methods of data analysis. Instead, the standards should simply require revealing of data in sufficient detail. 

The methods of data analysis described in this book will be of use in fulfilling each of these principles. Without a proper understanding of the statistics of data an analyst cannot hope to deliver results that are fit for purpose. ... 

X-ray fluorescence spectrometry, gas chromatography and neutron activation analysis (NAA). An older book edited by Hofstader, Milner and Runnels on Analysis of Petroleum for Trace Metals (1976), includes one chapter each on principles of trace analysis and techniques of trace analysis and others devoted to specific elements in petroleum products. Markert (1996) presents a fresh approach to sampling, sample preparation, instrumental analysis, data handling and interpretation. The Handbook on Metals in Clinical and Analytical Chemistry, edited by Seiler,... 

Step response. Although we can in principle use any feed concentration time function to determine the RTD, some choices are convenient for ease of data analysis. One of these is the step response. In the step-response experiment, at time zero we abruptly change the feed tracer concentration from steady value co to steady value c/. For convenience we assume cq =. 0. Exercise. 8.4 shows, that, we can easily remove this... 

The Kinetics Toolkit is provided so that you can focus your attention on the underlying principles of the analysis of chemical kinetic data rather than becoming involved in the time-consuming process of manipulating data sets and graph plotting. Full sets of data are provided for most of the examples that are used in the main text and you should, as a matter of course, use the Kinetics Toolkit to follow the analysis that is provided. A number of the Questions, and all of the Exercises, require you to use the Kinetics Toolkit in answering them. 

E. Stem, in X-Ray Absorption Principles, Applications, Techniques of EXAFS, SEX-AFS and XANES (D. C. Koningsberger and R. Prins, eds.), p. 3. Wiley, New York, 1988. B.-K. Teo, EXAFS Basic Principles and Data Analysis. Springer-Verlag, New York, 1986. 

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