Linear multivariate statistical methods are widely used for analysing data sets which consist of a large number of variables. These techniques, which include principal component analysis, factor analysis, canonical correlation analysis, redundancy analysis and discriminant analysis, all produce a set of new variables, commonly called 'factors', according to some criterion which differs for different techniques. Among these techniques, principal component analysis is one of the most popular techniques used for reducing the dimensions of the multivariate data set. In many applications, when Principal Component Analysis (PCA) is performed on a large number of variables, the interpretation of the results is not simple. The derived eigenvectors of the sample covariance or correlation matrix are not necessarily in a simple form, with all coefficients either 'large' or 'negligible'. To aid interpretation, it is fairly common practice to rotate the retained set of components, often using orthogonal rotation. The purpose of rotation is to simplify structure, and thus to make it easier to interpret the low-dimensional space represented by the retained set of components. Thus, quantification of simplicity is a two step process. The first set involves the extraction of the feature from the data called components, while the second stage uses a rotation method to simplify the structure. One of the two main purposes of this thesis is to combine into one step these two separate stages of dimension reduction (finding the components) and simplification (rotation). This goal is achieved by combining these two objectives in the form of a single function leading to what we call Simplified Components (SCs). Another objective is to discover which of the many possible criteria suggested in factor analysis can be adopted in the proposed procedure of SCs. Thus, a simplified one-step procedure of SCs is proposed, using four measures of simplicity, namely varimax, quartimax, orthomax and equamax indices.

<p>The use of traditional univariate analyses for comparing groups in high-dimensional genomic studies, such as the ordinary t-test that is typically used to compare two independent groups, might be suboptimal because of methodological challenges including multiple testing problem and failure to incorporate correlation among genes. Hence, multivariate methods are preferred for the joint analysis of a group or set of variables. These methods aim to test for differences in average values of a set of variables across groups. The variables that make the set could be determined statistically (using exploratory methods such as cluster analysis) or biologically (based on membership to known pathways). In this thesis, the traditional One-Way Multivariate Analysis of Variance (MANOVA) method and a robustifed version of MANOVA (Robustifed MANOVA) are compared with respect to Type I error rates and power through a simulation study. We generated data from multivariate normal as well as multivariate gamma distributions with different parameter settings. The methods are illustrated using a real gene expression data. In addition, we investigated a popular method known as Gene Set Enrichment Analysis (GSEA), where sets of genes (variables) that belong to known biological pathways are considered jointly and assessed whether or not they are "enriched" with respect to their association with a disease or phenotype of interest. We applied this method to a real genotype data.</p> / Master of Science (MSc)

1990 - 2008 Fertility factors in the disctrict of Most in 2000-2010 period Abstract The objective of this study was to find causes of regional fertility differences and context with social and economic indicators. Then to find situation of district of Most in regional comparison and social and economic causes of fertility developement in this district in 2000-2010 period. In first descriptive part there was made the comparative analysis of age structure and fertility indicators in Czech republic, Ústí region and district of Most. The result is different values of the fertility indicators (intensity and timing) and also younger age structure. In the second part were found social and economic factors of regional fertility differences and factors in district of Most with multivariate statistical methods. The cluster analysis confirmed the differences of district of Most and border of North Bohemia too. For use factor analysis and canonical correlation analysis the conclusion was the important factor of regional differences is especially education, but also availability and quality of housing, economic level. Less importace of religion. In the district of Most are important factors of education and indicators of economic level. Key words: fertility factors, regional fertility differences, district of Most,...

This thesis is intent on the introduction to problems of statistical approach to research tasks. It focuses on research assignments, position of research worker and statistician while analyzing, ways of gathering data files and problems connected with them, main types of multivariate statistical methods and possible views of their classification. Moreover, this work includes overview of examples of research assignments, possibilities of their solutions and related data files. First chapter describes statistical approach to the research assignments, and the second one shows concrete examples of these assignments. The enclosed CD includes data files to most of the statistical examples.

Ranunculus trichophyllus agg. (thread-leaved water crowfoot) represents a taxonomically challenging group of aquatic plants in which the presence of several significantly different genotypes and the genome size variation have been recently revealed. The results of previous studies suggest that cryptic taxa occur in this group, being so far overlooked due to considerable morphological reduction and extensivephenotypic plasticity. In this thesis, the variation and genetic relationships of four morphologically similar homophyllous water-crowfoot species was critically assessed in the area of Central Europe, using a combination of modern biosystematic methods (flow cytometry, direct DNA sequencing, morphometric analyses), specially focusing on the complex of R. trichophyllus.. The genome size analysis via flow cytometry was confirmed as a suitable method for determining the studied species; further, several hybrid combinations were revealed using this approach. However, recent interspecific hybridization is rather infrequent in the interest group. The results of DNA analyses indicate an importance of hybridization events in the evolution of sect. Batrachium: all the polyploid taxa studied are probably of allopolyploid origin. Two cryptic taxa within the traditionally recognized species R. trichophyllus have...

<p>Uzorci zemlji&scaron;ta iz pov&scaron;inskog sloja dubine 0 - 10 cm<br />prikupljeni su sa 121 lokacije na gradskom području Novog<br />Sada. Ispitivano područje obuhvatilo je povr&scaron;inu (4 x 5)km²,<br />koja je podeljena na mrežna polja veličine (400 x 400) m^2&nbsp;i u&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />svakom polju uzet je po jedan uzorak. Za 121 uzorak<br />gradskog zemlji&scaron;ta Novog Sada ispitana su fizičko-hemijska<br />svojstva zemlji&scaron;ta, ukupni i pristupačni sadržaj metala (As,<br />Co, Cr, Cu, Mn, Ni, Pb, Zn) i njihova prostorna raspodela.<br />Konturne mape prostorne raspodele metala u zemlji&scaron;tu<br />dobijene su kori&scaron;ćenjem interpolacijske metode običnog<br />kriginga. Za pojedine uzorke izvr&scaron;eno je razdvajanje čestica<br />po veličinama frakcionisanjem u vodi pomoću sita različitih<br />veličina i identifikovani su minerali prisutni u frakciji prah +<br />glina. Aktivnosti radionuklida &bdquo;unsupported&rdquo;²¹⁰Pb i ¹³⁷Cs<br />određene su za jedan deo uzoraka zemlji&scaron;ta u Novom Sadu i<br />za uzorke zemlji&scaron;ta pored fabrike akumulatora u Somboru.<br />Ispitana je i vertikalna distribucija stabilnog i radioaktivnog<br />Pb u zemlji&scaron;tu.</p><p>Na 14 lokacija u Novom Sadu prikupljeno je 35 uzoraka<br />snega direktno sa asfaltnih puteva i sa zemljanih povr&scaron;ina u<br />okolini puteva i na pe&scaron;ačkim ostrvima. Raspodela čestica po<br />veličinama i ukupne koncentracije metala (Al, Ca, Cu, Fe, K,<br />Na, Mn, Ni, Pb, Zn) određene su analizom filtriranih uzoraka,<br />a za 4 uzorka ispitana je morfologija čestica i urađena<br />semikvantitativna analiza čestica u suvoj materiji.</p><p>Prilikom obrade rezultata merenja primenjene su metode<br />deskriptivne statistike i multivarijacione statističke analize u<br />cilju identifikacije izvora zagađenja i određivanja povezanosti<br />između samih metala i drugih parametara.</p> / <p>A total of 121 surface soil samples were collected&nbsp;across the central part of Novi Sad covering a surface&nbsp;area (4 km x 5 km). The physicochemical properties,&nbsp;pseudo total and available metal concentrations (As,&nbsp;Co, Cr, Cu,&nbsp; Mn, Ni, Pb, and Zn) were determined.&nbsp;Contour maps of spatial distribution of the investigated&nbsp;metals were obtained using ordinary&nbsp; kriging&nbsp;interpolation method. Separation of different particle&nbsp;<br />size fractions by wet sieving&nbsp; and identification of&nbsp;minerals in the clay and silt fraction for some soil&nbsp;samples were performed.&nbsp; Specific activities of&nbsp;radionuclides &ldquo;unsupported&rdquo; ²¹⁰Pb and ¹³⁷Cs were&nbsp;measured in forty soil samples collected in urban area&nbsp;of Novi Sad and industrial area of Sombor (near a&nbsp;battery manufacturer).&nbsp; Vertical distribution of stable and&nbsp;radioactive&nbsp; Pb for&nbsp; two samples from the industrial soil&nbsp;was examined.</p><p>Thirty five snow samples were collected at fourteen&nbsp;locations near crossroads in Novi Sad. The samples&nbsp;were taken directly from the road surface and from the&nbsp;ground surface in the vicinity of roads and on&nbsp;pedestrian islands. Particle size distribution and &nbsp;total&nbsp;concentration of the metals (Al, Ca, Cu, Fe, K, Na, Mn,&nbsp;Ni, Pb, Zn) were &nbsp;determined for filtered samples. Semi-quantitative analysis of the particles was &nbsp;conducted and&nbsp;morphology of the particles was examined for dry&nbsp;matter of four snow samples.&nbsp;</p><p>Methods of descriptive and multivariate statistics and&nbsp;geostatistics were carried out for &nbsp;the analysis and&nbsp;interpretation of the data.</p>

The presented thesis discusses the basic analysis methods of arteriovelocitograms. The core of this work rests in classification of signals and contribution to possibilities of noninvasive diagnostic methods for evaluation patients with peripheral ischemic occlusive arterial disease. The classification employs multivariate statistical methods and principles of neural networks. The data processing works with an angiographic verified set of arteriovelocitogram dates. The digital subtraction angiography classified them into 3 separable classes in dependence on degree of vascular stenosis. Classification AVG signals are represented in the program by the 6 parameters that are measured on 3 different places on each patient’s leg. Evaluation of disease appeared to be a comprehensive approach at signals acquired from whole patient’s leg. The sensitivity of clustering method compared with angiography is between 82.75 % and 90.90 %, specificity between 80.66 % and 88.88 %. Using neural networks sensitivity is in range of 79.06 % and 96.87 %, specificity is in range of 73.07 % and 91.30 %.