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Testing independence in two-by-two tables
Obukhov, Andrey ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
The main purpose of this work is to describe three well-known statistical tests of independence in two-by-two 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
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Testing independence in two-by-two tables
Obukhov, Andrey ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
The main purpose of this work is to describe three well-known statistical tests of independence in two-by-two 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
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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
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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 chi-squared 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.
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Possibilities of the graphical analysis of categorical data
Rytíř, Michal ; Pecáková, Iva (advisor) ; Löster, Tomáš (referee)
The goal of my work was described the possibilities of the graphical analysis of categorical data. The first part is about clarifying the concept of categorical data and the rules of charting; the second part about the column and the pie chart, which are used most frequently. The last part presents graphical displays which often have variety properties and they are not used in normal commercial statistical programs. For example they allow a visual test of the hypothesis of independence. These are fourfold displays, sieve diagram, trilinear plot and mosaic display.
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A comparison of statistical packages such as SPSS, STATISTICA, and SAS Enterprise Guide.
Torboněnko, Natalja ; Řezanková, Hana (advisor) ; Pecáková, Iva (referee)
The purpose of this bachelor thesis is to compare three statistical software packages when applied to analysis of categorical data. These packages are SPSS, STATISTICA , and SAS Enterprise Guide. They provide a wide variety of statistical and graphical techniques, and enable users to obtain the results of statistical procedures, without requiring programming. The comparison between these packages were based upon some features such as data input, capability to define missing values, value labels, producing a frequency tables (including multiple response), making a bar graphs, descriptive statistics, Binomial test, Chi-square goodness-of-fit test.
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