Please use this identifier to cite or link to this item: http://repositorio.ufla.br/jspui/handle/1/28290
Title: Poder e taxas de erro tipo I de quatro critérios multivariados para o teste de igualdade de efeitos de tratamentos avaliados por meio do método de Monte Carlo
Other Titles: Power and type I error rate of four multivariate críteria for testing equality oftreatments evaluated by means ofthe Monte Carlo*s method.
Authors: Ferreira, Daniel Furtado
Morais, Augusto Ramalho de
Bueno Filho, Júlio Silvio de Sousa
Keywords: Simulação
Wilks
Hotelling
Pillai
Roy
Taxa de erro tipo I
Poder (Ciências sociais)
Agricultura - Experimentação
Monte Carlo, Método de
Estatística experimental
Issue Date: 18-Dec-2017
Publisher: Universidade Federal de Lavras
Citation: CECCHETTI, D. Poder e taxas de erro tipo I de quatro critérios multivariados para o teste de igualdade de efeitos de tratamentos avaliados por meio do método de Monte Carlo. 1999. 59 p. Dissertação (Mestrado em Estatística e Experimentação Agropecuária) - Universidade Federal de Lavras, Lavras, 1999.
Abstract: In the multivariate analysis of variance, four criteria regarded as chiefexist for testing the hypothesis ofequality oftreatment means vectors with approaches by means of the F distribution namely the, criteria by Wilks, Lawley-Hotelling, Roy and that by Pillai. The present work aimed to evaluate, by means ofsimulation, the power and type I error rates ofthese criteria. The language ofthe SAS system - Statistical Analysis System - was utilized to simulate 2000 experiments in severa! situations and in two steps. In the fírst one, the type I error rates were evaluated. For such a number of combinations were done, by takmg into account the number oftreatments equal to 5,10 and 20, replication number equal to 3 and 5, number of variables equal 2 and 3 and variation coefficient of 5, 10 and 20%, fixed, respectively to variables 1, 2 and 3 and still considering the non-existence of effect of treatments. The second step was proceeded under the same condition ofthe fírst one, excepting the manner ofgenerating the effects of treatments. For the treatments effect vectors might be specifíed, successive differences given in function ofthe standard error ofthe parametric means were specifieg. In both steps, the nominal significance leveis of 1% and 5% were adopted. A total of408,000 experimentswas generated. It follows that correlation structure among the variables did not affect the type I error rates, but had they influences upon the powerofthe four criteria. Pillai, Wilks and Hoteiling^ criteria proved similar among them as to the type I error rates. PillaTs criterium was the most rigorous for having presented type I error rate signifícantly (p < 0.05) inferior to the nominal leveis, besides having shown less power. Hotelling's criterion presented trend, in some circumstances, of possessing type I error rates statistically (p < 0.05) superior to the nominal levei and general trend of possessing greater type I error rates than Wilks1 and Pillai's criteria. Roy's criterion has a high power, but the type I error rate were statistically (p < 0.05) higher than nominal rates (a=l% or 5%) in every situation, making their utüization unfeasible. Wilks' criterion is advised as ideal to the tests ofthe equality hypothesis ofthe effect of the means vector of treatments of the multivariate analysis of variance, for presenting type I error rates equal to the nominal leveis of significance and power superior to Pillai's criterion, although it possesses slightly poorer power than Hotelling's criterion.
Description: Esta dissertação/tese está disponível online com base na Resolução CEPE nº 090, de 24 de março de 2015, disponível em http://www.biblioteca.ufla.br/wordpress/wp-content/uploads/res090-2015.pdf, que dispõe sobre a disponibilização da coleção retrospectiva de teses e dissertações online no Repositório Institucional da UFLA, sem autorização prévia dos autores. Parágrafo Único. Caberá ao autor ou orientador a solicitação de restrição quanto à divulgação de teses e dissertações com pedidos de patente ou qualquer embargo similar. Art. 5º A obra depositada no RIUFLA que tenha direitos autorais externos à Universidade Federal de Lavras poderá ser removida mediante solicitação por escrito, exclusivamente do autor, encaminhada à Comissão Técnica da Biblioteca Universitária./ Arquivo gerado por meio da digitalização de material impresso. Alguns caracteres podem ter sido reconhecidos erroneamente.
URI: http://repositorio.ufla.br/jspui/handle/1/28290
Appears in Collections:Estatística e Experimentação Agropecuária - Mestrado (Dissertações)



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