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Master's Dissertation
DOI
https://doi.org/10.11606/D.11.1986.tde-20220208-003906
Document
Author
Full name
Maria Imaculada de Lima Montebelo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1986
Supervisor
Title in Portuguese
Comparações múltiplas no modelo de Gauss-Markov com classificação simples e dados balanceados
Keywords in Portuguese
DADOS BALANCEADOS
MODELO DE GAUSS-MARKOV
Abstract in Portuguese
Aplicou-se técnicas de simulação, através do pacote estatístico SAS (Statistical Analysis System); para estudar o comportamento de nove procedimentos de comparações múltiplas (LSD, Bonferroni, SNK, Tukey, Scheffé, Duncan, Sidák, GT2 e Waller-Duncan), para todas as possíveis comparações entre medias duas a duas. Neste estudo considerou-se o modelo geral de classificação simples de efeitos fixos de análise de variância expressa pelo modelo: Yij = µi + εij, onde: i = 1, 2, ..., k; j = 1, 2, ..., ni; εij, são independentes com N ~ (0, σ2). Utilizou-se 15 configurações de três médias verdadeiras de tratamentos e três coeficientes de variação fixados em 10%, 20% e 40% para amostras de tamanho 10, 5 e 3 tratamentos. Para cada configuração, foram simulados 30 experimentos num total de 450 experimentos. Para cada experimento simulado foram testados todos os possíveis contrastes entre médias duas à duas, com níveis de significância α = 0,01 e α = 0,05, fixos para os procedimentos de Tukey, Scheffé, LSD, Bonferroni, Sidák e GT2 e níveis iniciais α = 0,01 e α = 0,05 para os procedimentos SNK e Duncan. Para o procedimento de Waller-Duncan foram fixados K = 100 e K 500, que aproximam-se de α = 0,05 e α 0,01 respectivamente. Sob as condições em que foi desenvolvido o trabalho, os resultados indicaram que os procedimentos menos sensíveis em apresentarem diferenças reais entre médias de tratamentos, em ordem foram Scheffé, Sidák, GT2, Bonferroni, Tukey. E os mais sensíveis foram os procedimentos de Duncan, Waller-Duncan, LSD e SNK.
Title in English
Multiple comparisons in the Gauss-Markov model with simple classification and balanced data
Abstract in English
Objecting to study the behavior of nine multiple comparison procedures (LSD, Bonferroni, SNK, Tukey, Scheffé, Duncan, Sidák, GT2 and Waller-Duncan), for all possible comparisons among means two by two, simulation techniques were applied by the SAS (Statistical Analysis System). In this study, were considered the general model of simples classification of the fixes effects of the variance analysis, expressed by the model: Yij = µi + εij, were: i = 1, 2, ..., k; j = 1, 2, ..., ni; εij, are independent with N ~ (0, σ2). Fiftheen configurations of three true means of treatments and three coefficients of variation fixed in 10%, 20% and 40% were used for samples of size 10, 5 and 3. For each size of sample, 30 experiments were simulated, resulting a total of 450 experiments. For each simulated experiment, all the possible contrasts among means were tested, two by two, with significance level α = 0.01 and α = 0.05, fixed for the procedures of Tukey, Sheffé, LSD, Bonferroni, Sidák and GT2, and Duncan procedures. For the Waller-Duncan method were fixed K 100 and K = 500, that approach of α = 0.05 α 0.01 respectively. Under the conditions that this work was developed, the results indicate that the procedures less sensitives in to show real differences-among treatment means, in order, were Scheffé, Sidák, GT2, Bonferroni, Tukey, and the most sensitives were the Duncan, Waller­Duncan, LSD and SNK procedures.
 
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Publishing Date
2022-02-08
 
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