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Master's Dissertation
DOI
10.11606/D.11.2008.tde-10032008-175000
Document
Author
Full name
Renata Alcarde
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 2007
Supervisor
Committee
Piedade, Sonia Maria de Stefano (President)
Machado, Amauri de Almeida
Mourão, Gerson Barreto
Title in Portuguese
Fundamentos do diagrama de Hasse e aplicações à experimentação
Keywords in Portuguese
Álgebra
Delineamento experimental
Software estatístico para microcomputador.
Abstract in Portuguese
A crescente aplicação da estatística às mais diversas áreas de pesquisa, tem definido delineamentos complexos, dificultando assim seu planejamento e análise. O diagrama de Hasse é uma ferramenta gráfica, que tem como objetivo facilitar a compreensão da estrutura presente entre os fatores experimentais. Além de uma melhor visualização do experimento o mesmo fornece, através de regras propostas na literatura, os números de graus de liberdade de cada fator. Sob a condição de ortogonalidade do delineamento, podem-se obter também as matrizes núcleo das formas quadráticas para as somas de quadrados e as esperanças dos quadrados médios, propiciando a razão adequada para a aplicação do teste F. O presente trabalho trata-se de uma revisão, fundamentada na álgebra linear, dos conceitos presentes na estrutura do diagrama. Com base nos mesmos, demonstrou-se o desdobramento do espaço vetorial do experimento em subespaços gerados por seus respectivos fatores, de tal modo que fossem ortogonais entre si. E, a fim de exemplificar as regras e o emprego desta ferramenta, utilizaram-se dois conjuntos de dados, o primeiro de um experimento realizados com cabras Saanen e segundo com capim Marandu, detalhando-se a estrutura experimental, demonstrando-se a ortogonalidade entre os fatores e indicando-se o esquema da análise da vari^ancia. Cabe salientar que o diagrama não substitui o uso de softwares, mas tem grande importância quando o interesse está em se comparar resultados e principalmente verificar o quociente adequado para o teste F.
Title in English
Foundations of Hasse diagram and its applications on experimentation
Keywords in English
Experimentation
Graphic tool
Hasse diagram
Orthogonality.
Vectorial subspaces
Abstract in English
The increase of statistics applications on the most diverse research areas has defined complex statistics designs turn its planning and analysis really hard. The Hasse diagram is a graphic tool that has as objective turn the comprehension of the present structure among the experimental factors easiest. More than a better experiment overview, by the rules proposed on the literature, this diagram gives the degrees of freedom for each factor. By the condition of design orthogonality, the nucleus matrix of quadratic form for the sum of squares and the expected values for the mean squares can also be obtained, given the proper ratio for F test application. The present work is a review, with its foundations on linear algebra, of the present's concepts on the diagram structure. With this basis were demonstrated the development of the vectorial space of the experiment in subspaces generated by its own factors, in a way that it was orthogonal within themselves. And, to give examples about the rules and the application of this tool, experimental data of Saanen goats and other set of data of Marandu grazing were used, with a detailed experiment structure, showing the orthogonality within the factors and with an indication of the analysis of variance model. Has to be emphasized that the diagram do not substitute the usage of software but has a great meaning when the interest is about results comparisons and most of all to check the proper quotient for the F test.
 
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renataalacarde.pdf (525.19 Kbytes)
Publishing Date
2008-03-20
 
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