In this dissertation, the problem of partitioning a set of treatments with respect to a control treatment is considered. Starting in 1950's a number of researchers have worked on this problem and have proposed alternative solutions. In Tong (1979), the authors proposed a formulation to solve this problem and hundreds of researchers and practitioners have used that formulation for the partition problem. However, Tong's formulation is somewhat rigid and misleading for the practitioners, if the distance between the ``good'' and the ``bad'' populations is large. In this case, the indifference zone gets quite large and the undesirable feature of the Tong's formulation to partition the populations in the indifference zone, without any penalty, can potentially lead Tong's formulation to produce misleading partitions. In this dissertation, a generalization of the Tong's formulation is proposed, under which, the treatments in the indifference zone are not partitioned as ``good'' or ``bad'', but are partitioned as a identifiable set. For this generalized partition, a fully sequential and a two-stage procedure is proposed and its theoretical properties are derived. The proposed procedures are also studied via Monte Carlo Simulation studies. The thesis concludes with some non-parametric partition procedures and the study of robustness of the various available procedures in the statistical literature.

Submitted by Silvana Teresinha Dornelles Studzinski (sstudzinski) on 2015-03-26T00:57:22Z No. of bitstreams: 1 CristinaMotaDireito.pdf: 1443424 bytes, checksum: 459171999951a14ed3d4e5b8812a91c7 (MD5) / Made available in DSpace on 2015-03-26T00:57:22Z (GMT). No. of bitstreams: 1 CristinaMotaDireito.pdf: 1443424 bytes, checksum: 459171999951a14ed3d4e5b8812a91c7 (MD5) Previous issue date: 2010 / Nenhuma / O dever constitucional de fundamentar viabiliza a obtenção de uma resposta correta/adequada da decisão, além de ser condição de possibilidade para a validade da decisão. É através da hermenêutica, com a análise do caso concreto, que se pode chegar a uma resposta correta/adequada ao caso. A interpretação da norma não está à mercê do aplicador, razão pela qual as decisões prescindem de leitura hermenêutica no intuito de fazer a correta leitura e aplicação da lei, uma vez que a resposta correta só se dá no caso concreto. A decisão correta deve estar baseada no direito como integridade, à margem da discricionariedade do decisor, que poderia, através do poder criador que lhe atribui a discricionariedade, decidir de acordo com a sua subjetividade. Este é o ponto fulcral do problema da fundamentação e das razões pelas quais ela se transformou, no âmbito do Estado Democrático de Direito, em um direito fundamental do cidadão e em um dever (have a duty) fundamental do juiz e do tribunal. A democracia, portanto, estará ligada umbilicalmente ao controle decisional. Por outro lado, fundamentação não quer dizer “qualquer fundamentação”, assim como não se pode atribuir “qualquer significado a um determinado texto”. A decisão, a partir da hermenêutica filosófica, revela uma faceta completamente antidiscricionária, levando à resposta correta ao caso concreto. A decisão deve demonstrar os critérios que foram utilizados como meio de evidenciar a sua correção e servir como norte para decisões futuras. A falta de fundamentação gera ausência de critérios de decisão, bem como impossibilita um controle externo das decisões. Portanto, por ser garantia do cidadão e ao mesmo tempo limitadora do julgador, a fundamentação é uma garantia fundamental. / The grounding constitutional right turns out to be an effective way to reach a correct/adequate answer to a decision and by also being the condition that enables the decision validation. It is through Hermeneutics together with the analysis of the substantial case that a correct/adequate decision to it can be reached. The interpretation of the norm is not up to the user being this the reason why the decisions ofthe substantial cases prescind from the Hermeneutics reading in order to have the correct understanding and enforcement of the law since the correct answer will only take place at the substantial case. The right decision at the substantial case must be based on law as integrity aside the discretion of the taker, who would be able to decide according tohis subjectivity by using the creative power given by the related discretion power. This is the crucial point of the foundational problem and its reasons why it turned into the citizen ́s fundamental right at the scope of welfare State and also as the fundamental duty of the judge/court. Hence, democracy will be inherently linked to the decision taking control. foundation does not mean any foundation since it cannot be given any meaning at a certain text.. The decision originated at philosophical hermeneutics reveals its entirely anti discretional side leading the correctanswer to the substantial case. The decision must show the criteria used so that it highlights its correction and also provide the direction for the future decisions. The lack of foundation promotes the absence of decisional criteria inasmuch as it hinders an external controlof the decisions. Thus the foundation as a means of the citizen ́s assurance, which is also restricting of the judger is essential garantee.

ANOVA analysis is a classic tool for multiple comparisons and has been widely used in numerous disciplines due to its simplicity and convenience. The ANOVA procedure is designed to test if a number of different populations are all different. This is followed by usual multiple comparison tests to rank the populations. However, the probability of selecting the best population via ANOVA procedure does not guarantee the probability to be larger than some desired prespecified level. This lack of desirability of the ANOVA procedure was overcome by researchers in early 1950's by designing experiments with the goal of selecting the best population. In this dissertation, a single-stage procedure is introduced to partition k treatments into "good" and "bad" groups with respect to a control population assuming some key parameters are known. Next, the proposed partition procedure is genaralized for the case when the parameters are unknown and a purely-sequential procedure and a two-stage procedure are derived. Theoretical asymptotic properties, such as first order and second order properties, of the proposed procedures are derived to document the efficiency of the proposed procedures. These theoretical properties are studied via Monte Carlo simulations to document the performance of the procedures for small and moderate sample sizes.