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Selected random variables transformations used in classical linear regression
Tejkal, Martin ; Michálek, Jaroslav (referee) ; Hübnerová, Zuzana (advisor)
Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací.
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Functional ANOVA
Dolník, Viktor ; Dvořák, Jiří (advisor) ; Nagy, Stanislav (referee)
We introduce the concept of functional data and the problem of functional analysis of variance, which differs from the univariate case in the fact that random functions, not random variables, are the subject of comparison. We continue by deriving an asymptotic test for functional one-way ANOVA from the elementary univariate F-test. We describe the simulation envelope test, whose global version suffers from the multiple comparisons problem. Then, an ordering is defined, based on which we create the rank envelope test, a stronger alternative to the simulation envelope test. We also describe how the rank test can be interpreted graphically. Using the rank envelope test, we devise another test for functional one-way ANOVA, which is also graphically interpretable and thus does not need a post-hoc analysis to identify which groups caused rejection of the null hypothesis. We compare the one-way ANOVA tests on a real-case study and a simulation study. 1
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Examination of k regression lines
Drozen, Alan ; Zvára, Karel (advisor) ; Omelka, Marek (referee)
In the present work we study the problem of k regression lines in the general linear model. First we describe the general linear model with a multivariate normal distribution of errors and we show some of its basic characteristics. Then we introduce a model with k regression lines. Further, we describe a test for testing the hypothesis of two regression lines being parallel and another one for testing all or some of the k regression lines being parallel or identical. Then we derive the test of the submodel of the general linear model and analyze issues such as the power of this test, the submodel of another submodel, the orthogonality and reparametrization. We show geometric interpretations of the general linear model and of the submodel test as well. In the subsequent part, we focus on nonparametric tests. We present four permutation tests for testing the submodel in the general linear model. Finally we perform numerical simulation to find out whether the tests match the required size and to determine their power.
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Milk and milk products in the diet of Youth (11 - 15 aged) of Primary School Domažlice, Komenského 17
Rybárová, Petra ; Váchová, Alena (advisor) ; Kovaříková, Miroslava (referee)
This thesis is concerned on the theme Milk and dairy products in nutrition of pupils aged 11 to 15 years. The theoretical part is based on the chemical composition of milk of general aspect and there are characterized some chosen kinds of dairy products and their effects on human health. The practical part is concerned on the research of being some statistically significant differences in consumption of milk and dairy products of the point of view of gender, age and access to milk and diary products in the families. The research is further based on the finding of the levels of probands'knowledge about the composition and the influence of milk to the human organism. The research sample is formed by 240 pupils of Secondary school in Domažlice, Komenského 17. The results show neither the gender, age or access to milk and diary products in the families do not affect the consumption of milk and dairy products of individual probands. The education unit whose aim is to increase the knowledge about milk of second graders in elementary schools is proposed on basis of identified facts.
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Diagnosis of selected competencies of track and field coach
Kapcová, Michaela ; Janák, Vladimír (advisor) ; Holánek, Michal (referee)
Title: Diagnosis of selected competencies of track and field coach of youth Objectives: The main aim of the thesis is to diagnose selected competences of a coach of youth athletics and to verify the hypothesis about the connection between performance and the aspiration of coaches. Methods: The thesis used qualitative methods of research and psychological testing. The qualitative methods used were testing, observation and research. Psychological testing was in the form of TATSO test. Finally, the statistical method F-test was used Results: The results of the work will be a useful source of information for the Czech Athletic Association in the development of curricula for trainers and will also be an indicator for athletic clubs, which organize youth trainers. Keywords: Athletics, coach of youth, coach competencies, TATSO test, F-test, ČAS, Czech Athletic Association, aspiration, level of aspiration
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Functional ANOVA
Dolník, Viktor ; Dvořák, Jiří (advisor) ; Nagy, Stanislav (referee)
We introduce the concept of functional data and the problem of functional analysis of variance, which differs from the univariate case in the fact that random functions, not random variables, are the subject of comparison. We continue by deriving an asymptotic test for functional one-way ANOVA from the elementary univariate F-test. We describe the simulation envelope test, whose global version suffers from the multiple comparisons problem. Then, an ordering is defined, based on which we create the rank envelope test, a stronger alternative to the simulation envelope test. We also describe how the rank test can be interpreted graphically. Using the rank envelope test, we devise another test for functional one-way ANOVA, which is also graphically interpretable and thus does not need a post-hoc analysis to identify which groups caused rejection of the null hypothesis. We compare the one-way ANOVA tests on a real-case study and a simulation study. 1
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The ability to assess the physical endurance of students
Bohata, Pavel ; Bunc, Václav (advisor) ; Hlavička, Petr (referee)
Title: The ability to assess the physical endurance of students Objectives: Goal of this bachelor's thesis is to diagnose the endurance assumptions and determine the values of body mass index of students at second degree of primary schools. Another goal is in analyzing the results of students with common range of education and students with extended range of music education and aesthetics. Subsequently will follow comparison of analyzed results with goal of finding out statistical difference which is significant between endurance assumptions and the body mass index. Methods: The thesis is conducted in the form of quantitative research. The level of endurance assumptions is determined by multi-stage fitness test (Leger test) and by the values of BMI based on anthropometric characteristics. Results are evaluated in a form of histograms and tables. Analysis is performed by using a F-test and a t- test. The choosen test samples are students of two schools which first one is with common range of education and the second one is with extended range of music education and aesthetics. Resulsts: From evaluated and compared results is obvious that there is no statistically significant difference and therefore can't be said that students with extended music education and aesthetics would reach worse results in...
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Milk and milk products in the diet of Youth (11 - 15 aged) of Primary School Domažlice, Komenského 17
Rybárová, Petra ; Váchová, Alena (advisor) ; Kovaříková, Miroslava (referee)
This thesis is concerned on the theme Milk and dairy products in nutrition of pupils aged 11 to 15 years. The theoretical part is based on the chemical composition of milk of general aspect and there are characterized some chosen kinds of dairy products and their effects on human health. The practical part is concerned on the research of being some statistically significant differences in consumption of milk and dairy products of the point of view of gender, age and access to milk and diary products in the families. The research is further based on the finding of the levels of probands'knowledge about the composition and the influence of milk to the human organism. The research sample is formed by 240 pupils of Secondary school in Domažlice, Komenského 17. The results show neither the gender, age or access to milk and diary products in the families do not affect the consumption of milk and dairy products of individual probands. The education unit whose aim is to increase the knowledge about milk of second graders in elementary schools is proposed on basis of identified facts.
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Examination of k regression lines
Drozen, Alan ; Zvára, Karel (advisor) ; Omelka, Marek (referee)
In the present work we study the problem of k regression lines in the general linear model. First we describe the general linear model with a multivariate normal distribution of errors and we show some of its basic characteristics. Then we introduce a model with k regression lines. Further, we describe a test for testing the hypothesis of two regression lines being parallel and another one for testing all or some of the k regression lines being parallel or identical. Then we derive the test of the submodel of the general linear model and analyze issues such as the power of this test, the submodel of another submodel, the orthogonality and reparametrization. We show geometric interpretations of the general linear model and of the submodel test as well. In the subsequent part, we focus on nonparametric tests. We present four permutation tests for testing the submodel in the general linear model. Finally we perform numerical simulation to find out whether the tests match the required size and to determine their power.
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Selected random variables transformations used in classical linear regression
Tejkal, Martin ; Michálek, Jaroslav (referee) ; Hübnerová, Zuzana (advisor)
Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací.
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