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Thèse de Doctorat
DOI
https://doi.org/10.11606/T.11.1981.tde-20210104-195626
Document
Auteur
Nom complet
Antônio Francisco Iemma
Adresse Mail
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
Piracicaba, 1981
Directeur
Titre en portugais
Análise de experimentos em parcelas subdivididas com tratamentos principais dispostos em blocos incompletos balanceados
Mots-clés en portugais
ANÁLISE DE VARIÂNCIA
DELINEAMENTO EXPERIMENTAL
MODELOS MATEMÁTICOS
Resumé en portugais
Neste estudo, analisou-se o comportamento dos experimentos em parcelas subdivididas com tratamentos principais dispostos em blocos incompletos balanceados. Para tanto, adotou-se o modelo matemático: yijs = m + ti + bj + e k(ij) + t’s + (tt’) is + e ijs onde, para i=1, 2,..., v; j=1, 2, ..., u ; k=1, 2,..., k, yijs é o valor observado na subparcela que recebeu o s-êsimo tratamento secundário, dentro do i-ésimo tratamento principal, no bloco j; m é o efeito da média geral; ti é o efeito do i-ésimo tratamento principal; bj e o efeito do j-ésimo bloco; e k(ij) é o erro atribuído à k-ésima parcela do bloco j, que recebeu o tratamento principal i: caracterizado como componente do erro (a); t's é o efeito do s-ésimo tratamento secundário; (tt') is é o efeito da interação entre o i-ésimo tratamento principal e o s-ésimo tratamento secundário; eijs é o erro atribuído à observação yijs, caracterizado como componente do erro (b). Ademais, considerou-se a existência de correlação constante, 0, entre duas subparcelas de uma mesma parcela, e independência entre subparcelas de parcelas distintas, resultando (Descrito na Tese). No desenvolvimento da metodologia, supôs-se um ensaio com parcelas subdivididas no qual os v tratamentos principais estivessem presentes em r dos a blocos incompletos balanceados(r
Titre en anglais
Analysis of split-plot experiments with main treatments disposed in balanced incomplete block
Mots-clés en anglais

Resumé en anglais
In this paper, the conduct of the split-plot designs with t he main treatments disposed in balanced incomplete blocks,was analised. For this, the following mathematical model, was used: yijs = m + ti + bj + e k(ij) + t’s + (tt’) is + e ijs wherw, for i=1, 2,..., v; j=1, 2, ..., u ; k=1, 2,..., k, yijs denotes the observation of the subplot containing the s th subtreatment of the i th main treatment in the j th block; m denotes the effect of general mean; ti denotes the effect of the i th main treatment; bj denotes the effect of the j th block; e ij denotes the error inherent at the k th whole-plot of the j th block in the i th mean treatment, characterized with a error (a) component; t's denotes the effect of the s th sub treatment; (tt') is denotes the effect for the interaction between i th main treatment and s th sub treatment; eijs denotes the error inherent at the i-j-s th sub plot, characterized with a error (b) component. Moreover, the presence of constant correlaction, p, between two subplots of sarne plot, and independence among subplots of the distincts plots, was considered, resulting: (See Thesis). ln methodology one split-plot design with the v main treatments disposed in r out of a balanced incomplete block (r< a), where every block was formed by k plots, and every pair of main treatments occurred in λ blocks, was considered. Under these assumptions, the solution of the normal equations, the dispersion matrix for the effects in the mathematical model proposed, the criterion for the usual null hypothesis tests and the criterion of the multiple comparisions by Tukey's test based on linear functions variance, was obtained. Except for constants inherents in the model, two main conclusions were obtained: estimates of main treatments and blocks, obtained in this study, were analogous to those existent in the literature of the balanced incomplete block design; while other estimates were analogous to those correspondents in the split-plot randomized block design.
 
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Date de Publication
2021-01-07
 
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