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Doctoral Thesis
DOI
https://doi.org/10.11606/T.11.1982.tde-20210104-185946
Document
Author
Full name
Marineia de Lara Haddad
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1982
Supervisor
Title in Portuguese
Estudo sobre parcelas perdidas no delineamento em Quadrado de Youden
Keywords in Portuguese
DELINEAMENTO EXPERIMENTAL
QUADRADO DE YOUDEN
Abstract in Portuguese
O presente trabalho teve como objetivo principal a dedução da análise estatística do delineamento em Quadrado de Youden com perda de uma e de duas parcelas na mesma linha. O modelo matemático considerado foi: ykji = m + lk + cj + ti(j, k) + ekji, ou, admitindo-se que os efeitos de colunas incluem a média geral teórica, e usando-se a forma matricial, Y = Xβ + ε. Através do método dos quadrados mínimos foram determinadas as estimativas dos parâmetros e as suas respectivas somas de quadrados. Eliminando-se do modelo matemático original os efeitos de tratamentos e, posteriormente, os efeitos de linhas, novas somas de quadrados dos parâmetros foram determinadas. Das diferenças entre elas determinaram-se as corretas somas de quadrados de tratamentos e de linhas. Tornando mínima a soma de quadrados do resíduo, SQR, deduziram-se fórmulas para as estimativas das parcelas perdidas. Através do método do resíduo condicional determinaram-se as expressões das correções das somas de quadrados de tratamentos, SQT, e de linhas, SQL. Verificou-se que a SQR está corretamente estimada, pois a estimativa da parcela perdida oferece uma contribuição nula para essa soma de quadrados. Assim sendo, e levando-se em consideração que a SQT foi ajustada para linhas e colunas e a SQL foi ajustada para colunas, concluiu-se que a correta soma de quadrados de colunas é a usual. Foram obtidas também a matriz de dispersão das estimativas dos parâmetros e a fórmula para a variância da estimativa de um contraste entre duas médias de tratamentos ajustadas. Embora não apresentado o estudo sobre os componentes de variância das diversas causas de variação, determinou-se que a SQR perde tantos graus de liberdade quantas forem as parcelas perdidas.
Title in English
Missing plots in the Youden square design
Keywords in English

Abstract in English
The objective of this study was concerned with the development of a statistical analysis for the Youden Square Design with one and two missing plots in the same row. Mathematical model used was: ykji = m + l k + cj + ti(j, k) + ekji, wich in matrix notation, assuming that column effects includes the mean, could be represented by: Y = Xβ + ε. Estimation of parameters and sum of squares were done by least squares. Delecting treatment effects from the original model and row effects two new sum of squares of parameters were determined. By subctration it was calculated correct values for treatment sum of squares and row sum of squares. By minimization of residual sum of squares formulas were developed for estimation of missing plots as well as correct treatment and row sums of squares. Since the treatment sum of squares was adjusted for rows and columns effects and row sum of squares was adjusted for column it was shown that column sum of squares is the usual. It was also determined the matrix dispersion of the parameters estimates and the variance for the contrast between two adjusted treatment means. Degrees of freedom lost by the residual sum of squares was equal to the number of missing plots.
 
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Publishing Date
2021-01-07
 
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