
Testing independence in twobytwo tables
Obukhov, Andrey ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
The main purpose of this work is to describe three wellknown statistical tests of independence in twobytwo contingency tables. We will deeply study chi squared test of independence, Fisher's exact test and Barnard's test and apply them on examples. Also we will describe, in general, categorical variables, which are often analysed using a multinomial distribution. At the end we will apply tests on the examples, using data simulated from a multinomial and binomial distribution. 1


Testing independence in twobytwo tables
Obukhov, Andrey ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
The main purpose of this work is to describe three wellknown statistical tests of independence in twobytwo contingency tables. We will deeply study chi squared test of independence, Fisher's exact test and Barnard's test and apply them on examples. Also we will describe, in general, categorical variables, which are often analysed using a multinomial distribution. At the end we will apply tests on the examples, using data simulated from a multinomial and binomial distribution. 1


Statistical tests in stratified fourfold tables
Vook, Peter ; Komárek, Arnošt (advisor) ; Omelka, Marek (referee)
This paper deals with statistical tests in stratified fourfold tables. Several tests of conditional indepen dence are derived in it. A test of homogeneous association is also described. At first, contingency tables with arbitrary dimensions and multinomial distribution are defined. Then we continue with a description of fourfold tables and their binomial representation. In the next section we deal with an odds ratio and its asymptotic distribution. Formal definition of stratification and relevant terms follows afterwards. In the next chapter a derivation of test statistics for conditional independence tests including the wellknown CochranMantelHaenszel test based on a hypergeometric distribution can be found. This chapter also includes a description of BreslowDay test of homogeneous association. A numerical simulation of chosen tests is performed eventually. 1


Tests for Paired Categorical Data
Míchal, Petr ; Komárek, Arnošt (advisor) ; Omelka, Marek (referee)
In this paper we deal with paired categorical data. We will test marginal ho mogeneity and symmetry of corresponding probability table. At first, we describe multinomial distribution and contingency tables. In the next section, we deal with dichotomic paired categorical data, we derive McNemar's test and describe test for small sample sizes. Further, we state tests for general paired categorical data, Stuart's and Bhapkar's test are described. We then state test derived by Bowker, which is used for testing symmetry of probability table. In the last section, we show simulations of McNemar's test in software R. 1


Statistical Analysis of Sample with Small Size
Holčák, Lukáš ; Hübnerová, Zuzana (referee) ; Karpíšek, Zdeněk (advisor)
This diploma thesis is focused on the analysis of small samples where it is not possible to obtain more data. It can be especially due to the capital intensity or time demandingness. Where the production have not a wherewithall for the realization more data or absence of the financial resources. Of course, analysis of small samples is very uncertain, because inferences are always encumbered with the level of uncertainty.


Contingency table analysis from questionnaire survey data of drivers
Velacková, Barbora ; Šulc, Zdeněk (advisor) ; Pecáková, Iva (referee)
The bachelor thesis deals with the contingency table analysis from questionnaire survey data of drivers. The data were obtained from the agency Data Collect s.r.o., which conducted the survey in 2014. The aim of the thesis is to analyse the behaviour of drivers and their habits, which could increase the risk of accidents. The thesis is divided into two main parts; in the first one, methods of contingency table analysis are described; in the second one, the presented analyses are applied to the survey data. Firstly, the behaviour of single and young drivers is analysed, then the differences between men and women drivers. Calculations were made using the software SPSS and MS Excel, in which all the graphs and tables were made.


The analysis of dependence of the material deprivation of the households in the Czech Republic on the selected indicators
Cafourková, Magdalena ; Řezanková, Hana (advisor) ; Pecáková, Iva (referee)
The aim of this thesis is to analyse the material deprivation of the households with regard to the selected indicators, i.e. the costs that the household spends on housing, a region where the household is located, the number of the members and the dependent children in the household, age and sex of a head of the household, and economic activity and education level of the members of the household. The thesis aims not only to prove the dependence among the selected indicators but also to quantify this dependence by using the odds ratio. The individual effect of all variables was proven except of the one related to the number of the dependent children. It was also demonstrated that the factors constituting a threat for the households by a material deprivation rate vary by the different age groups. However, it can be concluded that across all the age groups, the material deprivation rate is determined by the sex of a head of the household, education level of the members of the household, and the costs that the household spends on housing.


Nonlinear Trend Modeling in the Analysis of Categorical Data
Kalina, Jan
This paper studies various approaches to testing trend in the context of categorical data. While the linear trend is far more popular in econometric applications, a nonlinear modeling of the trend allows a more subtle information extraction from real data, especially if the linearity of the trend cannot be expected and verified by hypothesis testing. We exploit the exact unconditional approach to propose alternative versions of some trend tests. One of them is the test of relaxed trend (Liu, 1998), who proposed a generalization of the classical Cochran Armitage test of linear trend. A numerical example on real data reveals the advantages of the test of relaxed trend compared to the classical test of linear trend. Further, we propose an exact unconditional test also for modeling association between an ordinal response and nominal regressor. Further, we propose a robust estimator of parameters in the logistic regression model, which is based on implicit weighting of individual observations. We assess the breakdown point of the newly proposed robust estimator.


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.


Statistical inference for categorical data analysis
Kocáb, Jan ; Pecáková, Iva (advisor) ; Coufalová, Petra (referee)
This thesis introduces statistical methods for categorical data. These methods are especially used in social sciences such as sociology, psychology and political science, but their importance has increased also in medical and technical sciences. In the first part there is mentioned statistical inference for a proportion. Here is written about classical, exact and Bayesian methods for estimating and hypothesis testing. If we have a large sample then we can approximate exact distribution by normal distribution but if we have a small sample cannot use this approximation and it is necessary to use discrete distribution which makes inference more complicated. The second part deals with two categorical variables analysis in contingency tables. Here are explained measures of association for 2 x 2 contingency tables such as difference of proportion and odds ratio and also presented how we can test independence in the case of large sample and small one. If we have small sample we are not allowed to use classical chisquared tests and it is necessary to use alternative methods. This part contains variety of exact tests of independence and Bayesian approach for the 2 x 2 table too. In the end of this part there is written about a table for two dependent samples and we are interested whether two variables give identical results which occurs when marginal proportions are equal. In the last part there are methods used on data and discussed results.
