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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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Analysis of Variance with Random Effects
Hamerníková, Iva ; Komárek, Arnošt (advisor) ; Pešta, Michal (referee)
The aim of this thesis is to describe and derive the test of analysis of variance with random effects. At first we introduce a summary of results from the theory of probability which will be important in future derivations. Then we define the one-way classification model with fixed effects and propose the test statistics to test the equality of group means. In the following part we define the one-way classification model with random effects and derive properties of observations in this model. Under the assumption of balanced data we define sums of squares and derive their properties, which allow us to use them to create the test statistic. Finally we will use simulations in R to verify whether the ANOVA test with random effects observes the significance level when normality assumptions are violated.
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Multiple comparison with controls
Sychova, Maryna ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
The main theme of the diploma thesis is description of multiple comparison methods, which are used to compare pairs of means or medians. At the beggining we define multiple testing and describe methods that control the probability of first type error at level α. The Šidák method and the prerequi- sites required for its use are described in detail. The work also includes a brief description of analysis of variance and an overview of several methods of multiple comparison. Additionally, the method of multiple comparison with control, its modifications and practical implementation is presented.
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Porovnání kvality hroznů a vína z ruční a mechanizované sklizně u odrůdy Sauvignon blanc
Žáková, Iveta
Machine harvesting is the most widely expanded vineyard mechanization practices today. Foreign research into the effects of mechanization demonstrated that the grape quality was unaffected, in some cases, improved with the introduction of machine harvesting. In 2015 within the framework of this diploma work the experiment was performed by Sauvignon blanc. All data were subjected to Analysis of variance at P < 0,05. Although statistical differences were found in the grapes by total acidity and type of harvesting, statistical differences were not found in wine. Wine produced from machine grape harvesting were more fruity in sensory analysis.
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Analysis of variance when the assumption of homoscedasticity is violated
Zavadilová, Anna ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
The method known as analysis of variance of simple sort offers a possibility of how to test equality of mean values of several random selections. At the same time, however, it requires the random selections to originate from normal distribution and to meet the condition of homoscedasticity, i.e. the requirement of identity of variances. The aim of this Thesis is to analyse consequences of violation of the assumptions of normality and homoscedasticity of the input data. The first part of the Thesis presents an overview of the course of the method based on the analysis of variance with standard assumptions. It is followed by the deriving of asymptotic distribution of test statistics, supposing the validity of the null hypothesis of identity of mean values in the case that neither the normality of input data nor the identity of variances is supposed. The findings are then applied to several special cases. The final part of the Thesis deals with a simulation study describing the influence of non-fulfilment of assumptions imposed on the test significance level. Powered by TCPDF (www.tcpdf.org)
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Variance and Covariance Analysis with an application to financial data
Hájková, Anna ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
This Bachelor Thesis is dedicated to analysis variance and co- variance with and application to financial data. The aim of this thesis is to inform about multidimensional ANOVA and to show its connection with one- dimensional ANOVA, which is a part of standart statistical textbooks. Other part describes the analysis of covariance. For the better understanding, most of methods are applicated to financial data in the program Mathematica 8.0 1
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Subjective assessment of disturbing noise from gramophone records
Vlašín, Martin ; Martinásek, Zdeněk (referee) ; Rášo, Ondřej (advisor)
The bachelor thesis is focused on distortion that occurs by playing gramophone records. Due to functional principle of turntable and due to origin of individual distortion, which may occur while playing records, were selected two most significant and most frequently occurring distortion. For these distortion is studied their effect on subjective assessment of audio record. From data obtained from participants in the listening test was performed statistical analysis, also test of reliability and detection of any possible errors occurring in the assessments of individual listeners. The conclusions from results confirmed differences between two distortions and also between different audio samples on the subjective perception of the quality of audio experience for listener.
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Statistical analysis of real manufacturing process data
Kučerová, Barbora ; Mrázková, Eva (referee) ; Bednář, Josef (advisor)
Tématem této diplomové práce je statistická regulace výrobního procesu. Cílem bylo analyzovat data z reálného technologického procesu revolverového vstřikovacího lisu. Analýza byla provedena za užití statistického testování hypotéz, analýzy rozptylu, obecného lineárního modelu a analýzy způsobilosti procesu. Analýza dat byla provedena ve statistickém softwaru Minitab 16.
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Effective operation of up-to-date waste-to-energy units
Cafourková, Tereza ; Pavlas, Martin (referee) ; Touš, Michal (advisor)
The main content of this thesis is a suggestion of computing system for efficient energy manufacture. The introduction devotes to description of up-to-date waste-to-energy units (EVO), it concentrates on Incinerator of municipal wastes of TERMIZO a.s., specifically. In the main body of this work is the data analysis of factory journal that has been implemented, results have been used as mathematical model output value. These activities are necessary for computing system suggestion. Resulting optimization of batch wasting plan with maximum economic effect for entrepreneur is the main output of this work. Conclusion consists of environmental and economic evaluation of operation of up-to-date waste-to-energy units and offers another optimization posibility.
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Statistical data evaluation
Fadrný, Tomáš ; Koška, Petr (referee) ; Maroš, Bohumil (advisor)
This diploma thesis evaluates and processes data from final device checks. All the devices are similar types of thermal overcurrent relays by the ABB company. For appropriate statistical data processing, the Minitab 14 statistical software was used and various statistical methods were applied. Results are always listed for each device type and each method used. The diploma thesis is divided into two parts. The first one analyzes the methods used and the second part states the method results. There is also an overall evaluation of the processed data.
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