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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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Distance-based testing
Solnický, Radek ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
When analyzing ecological data, one considers traditional multivariate techniques to be unsuitable. The use of dissimilarity coefficients and distance matrices is a way, how to solve this problem. In this work we present some of these coefficients and distance-based tests: Mantel test, several versions of ANOSIM and MRPP tests and distance-based test for homogeneity of multivariate dispersions. We focus on relationships among these tests and illustrate the use with an example. We also discuss the difficulties of interpretation of the results of these tests.
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Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
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Snow depth variability at the plot scale: Assesment of topography and vegetation influence
Murdychová, Pavlína ; Jeníček, Michal (advisor) ; Pevná, Hana (referee)
Snow depth variability at the plot scale: Assesment of topography and vegetation influence Abstract This master thesis deals with the evaluation of snow depth variability at the plot scale. It focuses on influence of topography and vegetation factors as slope, exposure, curvature, solar radiation and leaf area index. There is also assesment the impact of the size scale. Measurement was carried out in period of accumulation and snowmelt in winter 2014/2015 in the Krkonoše Mountains on Hanapetrova glade. To evaluate the effect of selected factors on variability of snow depth there was used multiple linear regresion and other descriptive statistical methods. The research shows that the variability of snow depth during the accumulation is greater in forest which is probably due to vegetation. The dependency was not confirmed by regression analysis. Higher variability of snow cover in the forest was also observed in the melting period. The variability of snow cover increased in the forest in general. The results show that the snow depth variability decreasses with increasing grid size. Keywords: snow accumulation, snowmelt, topography, vegetation, multivariate analysis
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Distance-based testing
Solnický, Radek ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
When analyzing ecological data, one considers traditional multivariate techniques to be unsuitable. The use of dissimilarity coefficients and distance matrices is a way, how to solve this problem. In this work we present some of these coefficients and distance-based tests: Mantel test, several versions of ANOSIM and MRPP tests and distance-based test for homogeneity of multivariate dispersions. We focus on relationships among these tests and illustrate the use with an example. We also discuss the difficulties of interpretation of the results of these tests.
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Methods of analysing multivariate contingency tables
Šulc, Zdeněk ; Pecáková, Iva (advisor) ; Coufalová, Petra (referee)
This thesis occupies with a relationship of two significant methods of analyzing multivariate contingency tables, namely correspondence analysis and loglinear models. The thesis is divided into three parts. The first one is dedicated to basic terms of categorical data analysis, mainly to contingency tables and their distributions. Primarily, the emphasis is placed on their multidimensional form. The second part presents tools and techniques of both methods in a scope needed for their practical use and interpretation of their results. A practical application of both methods is included in the third part which is presented on the data from a market research. This part describes settings for both analyses in a statistical software SPSS and the subsequent interpretation of their outputs. A comparison of analyzed methods in terms of their use can be found in the conclusion.
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Synanthropic flora of villages on altitudinal gradient in southern part of the Czech Republic
JENČOVÁ, Dana
The study is a floristic survey of 131 villages in southern part of South Bohemia. In total 27.773 floristic records were collected with occurence of 585 taxa of wild vascular plants recorded, 548 taxa were further used in statistical analyses. Environmental factors with potencial effect on village flora composition and diversity were recorded along or extracted from various sources. Relations of diversity (number of species) and environmental factors were studied. Species composition was compared with these variables using multivariate statistical methods.
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