Master's Dissertation
DOI
https://doi.org/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
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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Publishing Date
2008-03-20

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