Most distribution free nonparametric methods depend on the ranks or orderings of the individual observations. This dissertation develops methods for the situation when there is only partial information about the ranks available. A random-linear-extension exact test and an empirical version of the random-linear-extension test are proposed as a new way to compare groups of data with partial orders. The basic computation procedure is to generate all possible permutations constrained by the known partial order using a randomization method similar in nature to multiple imputation. This random-linear-extension test can be simply implemented using a Gibbs Sampler to generate a random sample of complete orderings. Given a complete ordering, standard nonparametric methods, such as the Wilcoxon rank-sum test, can be applied, and the corresponding test statistics and rejection regions can be calculated. As a direct result of our new method, a single p-value is replaced by a distribution of p-values. This is related to some recent work on Fuzzy P-values, which was introduced by Geyer and Meeden in Statistical Science in 2005. A special case is to compare two groups when only two objects can be compared at a time. Three matching schemes, random matching, ordered matching and reverse matching are introduced and compared between each other. The results described in this dissertation provide some surprising insights into the statistical information in partial orderings. / Statistics

Made available in DSpace on 2014-08-20T14:38:47Z (GMT). No. of bitstreams: 1 tese_roberson_macedo_de_oliveira.pdf: 1075591 bytes, checksum: e6c23d2f9ba41197a953c043c70e5bc0 (MD5) Previous issue date: 2012-11-14 / The relationship between in vivo characteristics, carcass and meat goats from the region of Camaquã, were evaluated from the analysis of multivariate data. Data from 14 castrated males, born March-April/2009 and sacrificed with 8-9 months of age, originating from the familiar raising unit Casa de Pedra, RS, Brazil (Lot a) for 20 castrated male goats, born in June-July/2008, slaughtered at 11-12 months of age, originating from the familiar raising unit Arroio da Palma, RS, Brazil (Lot b), underwent randomization test and principal component analysis. The test result randomization between lots accepted that the set of variables Lots differ. The principal component analysis using forty-five descriptor variables showed that about 37.75% of the total variation is explained by the first component and 20.83% for the second. When using the 24 descriptors with the highest correlation with the ordination axes observed significant correlations for most variables. The principal component analysis explained more than 75% in the first two components. The characteristics that best explained the object of the study were: chilled carcass weight, hardness, right carcass, chewiness, hot carcass weight, global evaluation, live weight, yield hot carcass. The ordination diagram synthesized information and descriptive variables. The use of multivariate techniques may be recommended to evaluate the goat meat. / As relações entre características in vivo, na carcaça e na carne de cabritos da região do Alto Camaquã, foram avaliadas a partir da análise multivariada de dados. Dados de 14 cabritos machos castrados nascidos entre março e abril de 2009 e abatidos com 8-9 meses de idade (Lote a) e 20 cabritos machos castrados, nascidos entre junho e julho de 2008 e abatidos com 11-12 meses de idade (Lote b), foram submetidos ao teste de aleatorização e a análise por componentes principais. O resultado do teste de aleatorização entre os Lotes aceitou que no conjunto das variáveis os Lotes diferem. A análise por componentes principais utilizando quarenta e cinco variáveis descritoras mostrou que cerca de 37,75% da variação total é explicada pelo primeiro componente e 20,83% pelo segundo. Quando utilizado 24 descritores com maior correlação com os eixos de ordenação observou-se correlações significativas para grande parte das variáveis. A análise por componentes principais explicou mais de 75% nos dois primeiros componentes. As características que melhor explicaram o objeto de estudo foram: peso de carcaça fria, dureza, carcaça direita, mastigabilidade, peso de carcaça quente, avaliação global, peso vivo e rendimento de carcaça quente. O diagrama de ordenação sintetizou a informação e destacou as variáveis que os descrevem. O uso de técnicas de análise multivariada pode ser recomendado para caracterizar e avaliar a carne de cabrito.