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The power of two sample tests
Rózsahegyi, Dominik ; Maciak, Matúš (advisor) ; Komárek, Arnošt (referee)
Two-sample tests are one of commonly used statistical tools with which we make decisions if experimentally obtained data from different populations satisfy pre-specified statement. Suitability of using them could be dedicated by the power of test, which states for probability of rejection of invalid statement. The reader gets to know with terms of hypothesis testing which are necessary for introduction of tests. The second chapter introduce tests which could be used when analysed data are complete. If some observations are not exactly known, we call them censored and it is more suitable to use tests listed in the third chapter. We estimate the power for tests in simulations and observe its behavior with different conditions. 1
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The power of two sample tests
Rózsahegyi, Dominik ; Maciak, Matúš (advisor) ; Nagy, Stanislav (referee)
Two-sample tests are commonly used in practice, for example in scientific sphere or financial sectors. The power of test is also an important feature and express probability that the test will reject invalid null hypothesis. In this work we introduce four basic tests in which we compare some parameters of two popu- lations. The reader gets to know with basic terms of hypothesis testing which are necessary for introduction of tests. For each test we use simulation for estima- tion of the power and observe its behavior with different distributions of samples, ranges or selected null and alternative hypothesis. Based on obtained results we compare chosen tests and discuss suitability for using them in different cases. 1
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Permutation Tests of Statistical Hypotheses
Veselý, Zdeněk ; Jurečková, Jana (advisor) ; Jarušková, Daniela (referee)
Title: Permutation Tests of Statistical Hypotheses Author: Zdeněk Veselý Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Jana Jurečková DrSc., Department of Probability and Mathematical Statistics Abstract: This thesis presents permutation tests concept. Permutation test is demonstrated as response to testing problems where it is inconvenient to make any deeper presumptions on data probability distribution. For some of these problems it is even the only exact solution. The construction of permutation test is described in the thesis as well as approach to search of the most powerful tests to specific alternatives. In the second part of the thesis there are comparisons of powers of parametric, permutation and rank test using simulations. The result is that power of parametric and permutation test are very similar most of the times and that confirms that permutation tests are useful tool for praxis. Keywords: Permutation tests, Exact tests, Hypothesis testing, Power of tests
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Normality and its testing
Hájek, Štěpán ; Bašta, Milan (advisor) ; Klebanov, Lev (referee)
This thesis is concerned with normality and its testing. We often encounter with this topic when using statistical tests and models. Among others, examples such as t tests, analysis of variance and linear regression might be given. In this thesis these tests and models are overviewed and the consequences of the violation of the normality assumption are briefly mentioned. The following section describes statistical tests of normality. For example Shapiro-Wilk test or Anderson-Darling test are explored. For each test of normality is given test statistic and conditions for rejection of the null hypothesis. The last section provides a simulation study. The first part of this study is devoted to exploring whether the empirical relative frequency of Type I error corresponds to the nominal significance level of the test. The second part of the simulation study explores the power of normality tests against various alternatives. The results are summarized and discussed. 1
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Statistical tests power analysis
Kubrycht, Pavel ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This Thesis deals with the power of a statistical test and the associated problem of determining the appropriate sample size. It should be large enough to meet the requirements of the probabilities of errors of both the first and second kind. The aim of this Thesis is to demonstrate theoretical methods that result in derivation of formulas for minimum sample size determination. For this Thesis, three important probability distributions have been chosen: Normal, Bernoulli, and Exponential.
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Statistical methods for evaluation of sensorial data
Kozielová, Magda ; Kříž, Oldřich (referee) ; Michálek, Jaroslav (advisor)
\par The thesis deals with the statistical evaluation of data gained by the sensory analysis of the foodstuff. It brings a selection of the suitable statistical tests, a detailed analysis of these tests and their comparision based on the particular power functions for given parameters. As an important part of the thesis, there is a creating of custom software for the evaluating of sensorial data.
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Power analysis
Král, Ondřej ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This thesis examines the issues of analysis of statistical power of a test. It introduces a subject of hypotheses testing which is closely related. The goal is to expose the effect of parameters' alteration on the power test size. By using an application on examples, the thesis graphically illustrates the differences caused by the parameters' alteration. The results show how is the power of a test influenced by the effect of type one error, type two error, the number of observations, the formulation of alternative hypothesis and effect size on test power. The thesis further elaborates on effect size forms. In conclusion, all the explained theories are tested by an example that illustrates the size, which is achieved by changing the parameter.
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Analysis of variance in R
Švejdová, Klára ; Matějka, Martin (advisor) ; Sobíšek, Lukáš (referee)
The bachelor thesis focuses on the One-way ANOVA and its nonparametric counterpart the Kruskal-Wallis test. The aim of this bachelor thesis is to analyse the ANOVA's test validity and power in case of assumptions (e. g. normal distribution, homoscedasticity and sample size) violations. The conclusions of the One-way ANOVA are compared with the Kruskal-Wallis test. The analysis is performed using Monte Carlo simulations implemented in the statistical software R. Based on the simulations, it is found out that the One-Way ANOVA is not significantly sensitive to the violation of normality, if the homoscedasticity assumption is met within each of four samples. On the other hand it is found out that the One-Way ANOVA is significantly sensitive to the violation of homoscedasticity at the particular specification. The Kruskal-Wallis test yields in better results if the homoscedasticity assumption is violated. In case that the One-Way ANOVA and the Kruskal-Wallis test are valid, the ANOVA provides higher power of the test.
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