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Master's Dissertation
DOI
https://doi.org/10.11606/D.11.1978.tde-20240301-151847
Document
Author
Full name
Marinéia de Lara Haddad
Institute/School/College
Date of Defense
Published
Piracicaba, 1978
Supervisor
Title in Portuguese
Estudo sobre parcela perdida em delineamentos em parcelas subdivididas
Keywords in Portuguese
DELINEAMENTO EXPERIMENTAL
MODELOS MATEMÁTICOS
PARCELAS
Abstract in Portuguese
Neste trabalho fizemos um estudo sobre parcela perdida em delineamentos em parcelas subdivididas. Consideramos os casos em que a parcela perdida é composta de duas, três e até k subparcelas, com k > 3. Determinamos, através da minimização da soma de quadrados do resíduo (b) [SQR(b)] e da soma de quadrados do resíduo (a) [SQR(a)], fórmulas para as estimativas das subparcelas que compõem a parcela perdida. Através do método do resíduo condicional, determinamos a expressão da correção da soma de quadrados dos tratamentos T (SQT), dada por: (Descrito na Dissertação). Demonstramos também que a soma de quadrados de blocos e a soma de quadrados dos tratamentos T′ são as usuais, ou seja; são determinadas ignorando-se a parcela perdida. A soma de quadrados da interação TxT′ também foi ajustada através do método do resíduo condicional. A SQR(a) e a SQR(b) estão corretamente estimadas, pois a estimativa da parcela perdida oferece uma contribuição nula para essas somas de quadrados. Para cada parcela perdida a SQR(a) perde um grau de liberdade e a SQR(b) perde tantos quantas forem as subparcelas que compõem a parcela perdida.
Abstract in English
This work deals with a study of missing plot in the split plot design. It considers the case where the plot contains two, three up to k subplots, with k > 3. Through minimization of SSR(a) and SSR(b) we determined the formulas for the estimates of the subplots which composes the missing plot. By the use of the conditional residuals method we calculated the expression for correcting the SST, given by: (See Dissertation). From this expression it follows that SST is always over estimated. We also demonstrate that SSB and SST′ are the usual ones, that is, they are determined by ignoring the missing plot. The SSTxT′ was adjusted by the method of conditional residuals. The values of SSR(a) and SSR(b) are correctly estimated, since the estimate of the missing plot offers a null contribution to these sum of squares. For each missing plot the SSR(a) loses one degree of freedom, and the reduction in the degrees of freedom for SSR(b) is equivalent to the number of subplots in the missing plot.
 
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724558.pdf (2.42 Mbytes)
Publishing Date
2024-03-14
 
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