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Doctoral Thesis
DOI
https://doi.org/10.11606/T.11.1981.tde-20210104-195626
Document
Author
Full name
Antônio Francisco Iemma
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1981
Supervisor
Title in Portuguese
Análise de experimentos em parcelas subdivididas com tratamentos principais dispostos em blocos incompletos balanceados
Keywords in Portuguese
ANÁLISE DE VARIÂNCIA
DELINEAMENTO EXPERIMENTAL
MODELOS MATEMÁTICOS
Abstract in Portuguese
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
Title in English
Analysis of split-plot experiments with main treatments disposed in balanced incomplete block
Keywords in English

Abstract in English
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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Publishing Date
2021-01-07
 
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