Statistical methods multivariate analysis

Keil, D. et al., Evaluation of multivariate statistical methods for analysis and modeling of immunotoxicology data, Toxicol. Sci. 51, 245, 1999. 

The most commonly employed univariate statistical methods are analysis of variance (ANOVA) and Student s r-test [8]. These methods are parametric, that is, they require that the populations studied be approximately normally distributed. Some non-parametric methods are also popular, as, f r example, Kruskal-Wallis ANOVA and Mann-Whitney s U-test [9]. A key feature of univariate statistical methods is that data are analysed one variable at a rime (OVAT). This means that any information contained in the relation between the variables is not included in the OVAT analysis. Univariate methods are the most commonly used methods, irrespective of the nature of the data. Thus, in a recent issue of the European Journal of Pharmacology (Vol. 137), 20 out of 23 research reports used multivariate measurement. However, all of them were analysed by univariate methods. 

MacGregor, J. F., Marlin, T. E., Kresta, J. V., and Skagerberg, B., Multivariate statistics methods in process analysis and control. In Chemical Process Control, CPCIV, (Y. Arkun and W.H. Ray, eds.). CACHE, AIChE Publishers, New York, 1991. 

PCA [12, 16] is a multivariate statistics method frequently applied for the analysis of data tables obtained from environmental monitoring studies. It starts from the hypothesis that in the group of original data, there is a set of reduced factors or dominant components (sources of variation) which influence the observed data variance in an important way, and that these factors or components cannot be directly measured (they are hidden factors), since no specific sensors exist for them or, in other words, they cannot be experimentally observed. 

Hierarchical Cluster Analysis (HCA) is a multivariate statistical method that can be used assign groundwater samples or monitoring sites to distinct categories (hydrochemical facies). HCA offers several advantages over other methods of... 

Discriminant Analysis (DA) is a multivariate statistical method that generates a set of classification functions that can be used to predict into which of two or more categories an observation is most likely to fall, based on a certain combination of input variables. DA may be more effective than regression for relating groundwater age to major ion hydrochemistry and well construction because it can account for complex, non-continuous relationships between age and each individual variable used in the algorithm while inherently coping with uncertainty in the age values used for... 

Bakraji, E. H., Othman, I., Sarhil, A., and Al-Somel, N. (2002). Application of instrumental neutron activation analysis and multivariate statistical methods to archaeological Syrian ceramics. Journal of Trace and Microprobe Techniques 20 57-68. 

Solvent selection based on cohesion parameters, like those of Hansen [12], and by multivariate statistical methods like principal components analysis are two potential methods that can be used for solvent selection. These effects will be examined further in section 3.6.1. 

Chapter 3 starts with the first and probably most important multivariate statistical method, with principal component analysis (PC A). PC A is mainly used for mapping or summarizing the data information. Many ideas presented in this chapter, like the selection of the number of principal components (PCs), or the robustification of PCA, apply in a similar way to other methods. Section 3.8 discusses briefly related methods for summarizing and mapping multivariate data. The interested reader may consult extended literature for a more detailed description of these methods. 

While in classical statistics (univariate methods) modelling regards only quantitative problems (calibration), in multivariate analysis also qualitative models can be created in this case classification is performed. 

Data have been collected since 1970 on the prevalence and levels of various chemicals in human adipose (fat) tissue. These data are stored on a mainframe computer and have undergone routine quality assurance/quality control checks using univariate statistical methods. Upon completion of the development of a new analysis file, multivariate statistical techniques are applied to the data. The purpose of this analysis is to determine the utility of pattern recognition techniques in assessing the quality of the data and its ability to assist in their interpretation. 

However, it should be emphasized that the statistical methods presented here are no cures for poor data. Irrelevant or erroneous measurement and poorly planned experiments will still be irrelevant, erroneous and poorly planned in spite of any statistical analysis. There are, however, many examples of excellent data that have been seriously mutilated by poor statistical analysis. The aim of this chapter is to present multivariate statistical methods for design and... 

In other words, the application of univariate statistical methods to multivariate data often results in a considerable loss of information and, hence, a loss of power. This is because the assumptions on which the univariate analysis rely are seldom fulfilled (for example, independence between variables). 

There are apparently many multivariate statistical methods partly overlapping in scope [11]. For most problems occurring in practice, we have found the use of two methods sufficient, as discussed below. The first method is called principal component analysis (PCA) and the second is the partial least-squares projection to latent structures (PLS). A detailed description of the methods is given in Appendix A. In the following, a brief description is presented. 

Because data analysis is of central interest, particularly in the application of chemometric methods in the field of environmental research, a rough list of important multivariate statistical methods is given below (Tab. 1-1). 

Caulcutt, R., Boddy, R. Statistics for Analytical Chemists, Chapman and Hall, London, 1983 Chatfield, C., Collins, A.J. Introduction to Multivariate Analysis, Chapman and Hall, London, 1989 Davis, J. C. Statistics and Data Analysis in Geology, 2nd Ed., Wiley, New York, 1986 Dillon, W.R., Goldstein, M. Multivariate Analysis Methods and Applications, Wiley, New York, Chichester, Brisbane, Toronto, Singapore, 1984... 

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