Multivariate statistical investigations

Interrelationships or dependences between different substances in the water and their presumed influencing factors are analyzed on the basis of corre- 

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Application of multivariate statistics to fatty acid data from the Tyrolean Iceman and other mummies is a mosaic stone in the investigation of this mid-European ancestor, which is still a matter of research (Marota and Rollo 2002 Murphy et al. 2003 Nerlich et al. 2003). The iceman is on public display in the South Tyrol Museum of Archaeology in Bolzano, Italy, stored at —6°C and 98% humidity, the conditions as they probably were during the last thousands of years. 

Chemometrics, as defined by Kowalski (1), includes the application of multivariate statistical methods to the study of chemical problems. SIMCA (Soft Independent Method of Class Analogy) and other multivariate statistical methods have been used as tools in chemometric investigations. SIMCA, based on principal components, is a multivariate chemometric method that has been applied to a variety of chemical problems of varying complexity. The SIMCA-3B program is suitable for use with 8- and 16-bit microcomputers. 

A high-throughput analytical technique such as NMR has promise of adoption to investigate the metabolite content of vegetables. This information combined with multivariate statistical analysis is expected to offer a conclusive and exhaustive idea of quality discrimination and prediction with high reliability for new samples. In the field of fresh cut fruits and vegetables, demands for quality determination are increasing over the past decade. 

The concept of the PCSA method is general and this method should be applicable to many types of multivariate calibration techniques. As near-infrared and other spectroscopic methods are developed further for noninvasive in vivo clinical measurements, it is critical to understand the chemical basis of measurement selectivity. Unfortunately, calibration models generated from multivariate statistics are typically accepted without further investigation. Application of the PCSA method can help to establish the chemical or spectroscopic basis of predicted concentrations. 

In environmental chemistry in particular it cannot be the last step of the investigation to produce data tables on pollutant concentrations. Multivariate statistical methods offer a tool for the investigation of the multifactorial and complex events in the environment. 

Commonly the compromising conditions of routine environmental monitoring lead to restrictions on the accuracy and the precision of sampling and analysis. The purpose of this section is to show that under these conditions multivariate statistical methods are a useful tool for qualitative extraction of new information about the degree of stress of the investigated areas, and for identification of emission sources and their seasonal variations. The results represented from investigation of the impact of particulate emissions can, in principle, be transferred to other environmental analytical problems, as described in the following case studies. 

The application of different multivariate statistical methods enables clarification of the changes of the heavy metal pattern within the test area examined here. A multivariate change of the heavy metal content of the test field from the upper left to the lower right part of the area can be demonstrated in the example investigated. 

The purpose of this case study is to investigate the following two questions by means of multivariate statistical methods ... 

Polar biomarkers have also been investigated by NMR (SO) in postmortem BT samples. These samples were treated with perchloric acid, and metabolic extracts were analyzed to compare AD with amyotrophic lateral sclerosis (ALS) (80). After multivariate statistical analysis of the 8 AD and the 11 ALS samples, a high score in the statistical parameters of OPLS was obtained with the exclusion of 1 AD sample. Increased concentration of branched amino acids, alanine, acetate, glutamine, glutamate, and glyceropho-sphocholine in AD patients was observed when compared to ALS (80). 

Due to their persistent silica skeletons and their diversity, diatom remains provide a good record of past and present environmental conditions. Cameron (2004) recently showed that they could be used to compare samples that had been in contact with water and for the investigation of time of death in drowning. Through the recent advances in analytical quality control and use of multivariate statistics, their use in forensics is likely to develop further. In a similar way, phytoliths (the plant opal silica structure that accumulates in some plants) have been used to differentiate soils with otherwise similar mineralogy (Marumo and Yanai 1986). 

It is logical to consider whether the majolica sherds which were found in Mexico City could have been fabricated of local clay. Fortunately data on clays and related pottery from the Valley of Mexico has been collected at Brookhaven National Laboratory over many years. The ceramic material, which had previously been anlyzed by Harbottle and Sayre in collaboration with other investigators, consisted of Precolumbian artifacts. The pottery and the clays from two archaeological sites within the Valley, Teotihuacan, and Tlatilco were all basically similar in composition, although the clays and pottery from the two separate sites could be diflFerentiated through a subtle multivariate statistical analysis. It is likely that the entire Valley of Mexico is underlain with clay bed of moderately uniform trace impurity composition, and hence if the composition of the Mexico City majolica sherds was similar to that of ceramics and clay from Teotihuacan or Tlatilco, it would be probable that the majolica was fabricated from clays originating somewhere within the Valley of Mexico. 

Besides the descriptive values, it is also interesting to know the correlations between the two groups of variables (rXi,Yj)- The multivariate statistical methods for this data matrix are Canonical Correlation Analysis (CCA) to investigate the relationship between both sets of variables, and Multivariate Regression with a view to predicting the values of the response variables in the Y-block in function of the variables in the X-block, using a mathematical model. 

Differentiation between the stereoisomeric dexamethasone and betamethasone (Figure 13.2) has been investigated in detail [47-49]. While De Wasch et al. [47] differentiated from differences in relative abundances, Antignac et al. [48] proposed the use of multivariate statistical techniques, based on principal component analysis. Baseline separation between betamethasone, dexamethasone, and various related esters was reported by Arthur et al. [49] using a Cg column and a step gradient. 

Because analyses of water quality usually involve the collection of data on several variables, multivariate statistical analyses often are relevant. For example, multivariate analysis of variance (MANOVA) and discriminant analysis were used by Alden (1997) to investigate water quality trends in Chesapeake Bay. 

Vrakas, D., Panderi, I., Hadjipavlou-Litina, D. and Tsantili-Kakoulidou, A. (2005) Investigation of the relationships between log P and various chromatographic indices for a series of substituted coumarins. Evaluation of their similarity/ dissimilarity using multivariate statistics. QSAR Comb. Sci., 24, 254-260. 

An example of a three-way multiblock problem was published in the area of multivariate statistical process control of batch processes [Kourti et al. 1995], Suppose, e.g., that the feed of a batch process is characterized by a composition vector of length L. If / different batch runs have been completed this results in a matrix X (I x L) of feed characteristics. The process measurements are collected in Z (I x J x K) having I batches, J variables and measured at K time points each. The M different end product quality measurements are collected in Y (/ x M). Investigating if there is a connection between X, Z and Y is a common task in process analysis. 

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