Four statistics used for the analysis of categorical data were observed in the presence of many zero cell frequencies in two way classification contingency tables. The purpose of this study was to determine the effect of many zero cell frequencies upon the distribution properties of each of the four statistics studied. It was found that Light and Margolin's C and Pearson's Chi-square statistic closely approximated the Chi-square distribution as long as less than one-third of the table cells were empty. It was found that the mean and variance of Kullbach's 21 were larger than the expected values in the presence of few empty cells. The mean for 21 was found to become small in the presence of large numbers of empty cells. Ku's corrected 21 statistic was found, in the presence of many zero cell frequencies, to have a much larger mean value than would be expected in a Chi-square distribution. Kullback's 21 demonstrated a peculiar distribution change in the presence of large numbers of zero cell frequencies. 21 first enlarged, then decreased in average value.

Two methods of analyzing multi-dimensional frequency data are detailed. The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴi's and ϴj's. The ϴi's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴij are not zero, then the ϴi's are analogous to a main effect in a 2m factorial analysis, (m = number of factors or classifications). The ϴif's may be interpreted as a measure and direction of the two factor relationships. These ϴij are analogous to partial or adjusted phi-coefficients. The second method discussed assumes a multinomial distribution and the statistics are developed from an Information Theoretic Approach. Each hypothesis is tested using twice the minimum discrimination information statistic (m.d.i.s), 2I. From the null hypothesis it is possible to estimate unique cell probabilities by an iterative metod. Then 2 is equal to 2 (sample frequencies) log (sample frequencies) - 2 (expected frequencies) log (expected frequencies). (141 pages)

This thesis is composed of two parts. The first part pertains to tree-based models. The second part deals with multiple testing in large-scale contingency tables. Tree-based models have gained enormous popularity in statistical modeling and data mining. We propose a novel tree-pruning algorithm called frontier-based tree-pruning algorithm (FBP). The new method has an order of computational complexity comparable to cost-complexity pruning (CCP). Regarding tree pruning, it provides a full spectrum of information. Numerical study on real data sets reveals a surprise: in the complexity-penalization approach, most of the tree sizes are inadmissible. FBP facilitates a more faithful implementation of cross validation, which is favored by simulations. One of the most common test procedures using two-way contingency tables is the test of independence between two categorizations. Current test procedures such as chi-square or likelihood ratio tests provide overall independency but bring limited information about the nature of the association in contingency tables. We propose an approach of testing independence of categories in individual cells of contingency tables based on a multiple testing framework. We then employ the proposed method to identify the patterns of pair-wise associations between amino acids involved in beta-sheet bridges of proteins. We identify a number of amino acid pairs that exhibit either strong or weak association. These patterns provide useful information for algorithms that predict secondary and tertiary structures of proteins.

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.

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.

Clinical Assisted Reproductive Technology (ART) practices seek to make improvements in embryo quality and resultant procedural success rates. There is a significant variance in live birth rates among clinics nationwide. The goal of this thesis is make comparisons of embryo quality among clinics and understand these differences. This analysis focuses on the stage between egg retrieval and embryo transfer. Because the currently accepted embryo scoring methods are not directly proportional to performance, a new scoring methodology is proposed and applied. Data provided by the Society for Assisted Reproductive Technology (SART) consisting of 36,836 patient cycles from 40 anonymous clinics nationwide is considered. After necessary reductions are made, the data is anatomized to link each embryo transferred to an implantation probability. A score is generated for each morphology grouping based on the average implantation rate of that group. This score is used as the basis for clinic comparisons. Top-performing clinics (in terms of live birth rates in patients agedold) are then shown to both produce embryos of higher score and achieve better results from embryos of identical morphology.

This paper describes the "strucplot" framework for the visualization of multi-way contingency tables. Strucplot displays include hierarchical conditional plots such as mosaic, association, and sieve plots, and can be combined into more complex, specialized plots for visualizing conditional independence, GLMs, and the results of independence tests. The framework's modular design allows flexible customization of the plots' graphical appearance, including shading, labeling, spacing, and legend, by means of "graphical appearance control" functions. The framework is provided by the R package vcd.

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.

O problema de testar hipóteses sobre proporções marginais de uma tabela de contingência assume papel fundamental, por exemplo, na investigação da mudança de opinião e comportamento. Apesar disso, a maioria dos textos na literatura abordam procedimentos para populações independentes, como o teste de homogeneidade de proporções. Existem alguns trabalhos que exploram testes de hipóteses em caso de respostas dependentes como, por exemplo, o teste de McNemar para tabelas 2 x 2. A extensão desse teste para tabelas k x k, denominado teste de homogeneidade marginal, usualmente requer, sob a abordagem clássica, a utilização de aproximações assintóticas. Contudo, quando o tamanho amostral é pequeno ou os dados esparsos, tais métodos podem eventualmente produzir resultados imprecisos. Neste trabalho, revisamos medidas de evidência clássicas e bayesianas comumente empregadas para comparar duas proporções marginais. Além disso, desenvolvemos o Full Bayesian Significance Test (FBST) para testar a homogeneidade marginal em tabelas de contingência bidimensionais e multidimensionais. O FBST é baseado em uma medida de evidência, denominada e-valor, que não depende de resultados assintóticos, não viola o princípio da verossimilhança e respeita a várias propriedades lógicas esperadas para testes de hipóteses. Consequentemente, a abordagem ao problema de teste de homogeneidade marginal pelo FBST soluciona diversas limitações geralmente enfrentadas por outros procedimentos. / Tests of hypotheses for marginal proportions in contingency tables play a fundamental role, for instance, in the investigation of behaviour (or opinion) change. However, most texts in the literature are concerned with tests that assume independent populations (e.g: homogeneity tests). There are some works that explore hypotheses tests for dependent proportions such as the McNemar Test for 2 x 2 contingency tables. The generalization of McNemar test for k x k contingency tables, called marginal homogeneity test, usually requires asymptotic approximations. Nevertheless, for small sample sizes or sparse tables, such methods may occasionally produce imprecise results. In this work, we review some classical and Bayesian measures of evidence commonly applied to compare two marginal proportions. We propose the Full Bayesian Significance Test (FBST) to investigate marginal homogeneity in two-way and multidimensional contingency tables. The FBST is based on a measure of evidence, called e-value, which does not depend on asymptotic results, does not violate the likelihood principle and satisfies logical properties that are expected from hypothesis testing. Consequently, the FBST approach to test marginal homogeneity overcomes several limitations usually met by other procedures.

O problema de testar hipóteses sobre proporções marginais de uma tabela de contingência assume papel fundamental, por exemplo, na investigação da mudança de opinião e comportamento. Apesar disso, a maioria dos textos na literatura abordam procedimentos para populações independentes, como o teste de homogeneidade de proporções. Existem alguns trabalhos que exploram testes de hipóteses em caso de respostas dependentes como, por exemplo, o teste de McNemar para tabelas 2 x 2. A extensão desse teste para tabelas k x k, denominado teste de homogeneidade marginal, usualmente requer, sob a abordagem clássica, a utilização de aproximações assintóticas. Contudo, quando o tamanho amostral é pequeno ou os dados esparsos, tais métodos podem eventualmente produzir resultados imprecisos. Neste trabalho, revisamos medidas de evidência clássicas e bayesianas comumente empregadas para comparar duas proporções marginais. Além disso, desenvolvemos o Full Bayesian Significance Test (FBST) para testar a homogeneidade marginal em tabelas de contingência bidimensionais e multidimensionais. O FBST é baseado em uma medida de evidência, denominada e-valor, que não depende de resultados assintóticos, não viola o princípio da verossimilhança e respeita a várias propriedades lógicas esperadas para testes de hipóteses. Consequentemente, a abordagem ao problema de teste de homogeneidade marginal pelo FBST soluciona diversas limitações geralmente enfrentadas por outros procedimentos. / Tests of hypotheses for marginal proportions in contingency tables play a fundamental role, for instance, in the investigation of behaviour (or opinion) change. However, most texts in the literature are concerned with tests that assume independent populations (e.g: homogeneity tests). There are some works that explore hypotheses tests for dependent proportions such as the McNemar Test for 2 x 2 contingency tables. The generalization of McNemar test for k x k contingency tables, called marginal homogeneity test, usually requires asymptotic approximations. Nevertheless, for small sample sizes or sparse tables, such methods may occasionally produce imprecise results. In this work, we review some classical and Bayesian measures of evidence commonly applied to compare two marginal proportions. We propose the Full Bayesian Significance Test (FBST) to investigate marginal homogeneity in two-way and multidimensional contingency tables. The FBST is based on a measure of evidence, called e-value, which does not depend on asymptotic results, does not violate the likelihood principle and satisfies logical properties that are expected from hypothesis testing. Consequently, the FBST approach to test marginal homogeneity overcomes several limitations usually met by other procedures.