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Publication
Planos em blocos incompletos equilibrados e aplicações na educação
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Advisor(s)
Abstract(s)
Neste trabalho, começamos por abordar o Delineamento experimental, que pode ser
visto como parte do processo científico. Ainda trataremos da importância das técnicas
avançadas do Planeamento de Experiências, a utilização de Blocos com o intuito de
redução da variabilidade que é introduzida pelos tratamentos, explorando ainda algumas
das metodologias e respetivas componentes de computação.
No seguimento do desenvolvimento da dissertação destaca-se uma abordagem
essencialmente teórica dos BIBD, sendo posteriormente apresentadas definições e
abordadas questões de existência dos mesmos, evidenciando-se uma primeira abordagem
aos vários modelos BIBD.
Também focaremos dentro da Análise Estatística dos BIBD, a construção da tabela
Anova com a análise intrabloco e interbloco para os BIBD.
Iremos igualmente rever os métodos de construção dos BIBD, fazendo a apresentação de
alguns exemplos práticos da sua construção e algoritmos; bem como, a importância da
utilização do software R.
Para a análise dos dados do nosso questionário foi utilizado o software R, versão 2.12.2.
Por fim, iremos testar uma aplicação prática dos BIBD na Área da Educação. Neste
exemplo prático procurarei aferir o grau de preparação dos alunos em final de ciclo (9º ano
de escolaridade) na disciplina de Matemática, dentro das Metas Curriculares de Final de 3ª
Ciclo.
Constatamos que existiam diferenças ao nível de significância entre alguns dos domínios
testados, por exemplo, entre os domínios dos Números e Cálculo e a Geometria.
This work presents the results of the study and of the research of the Balanced Incomplete Block Designs (BIBD) and also Balanced Incomplete Block Designs with Repetition (BIBDR), being applied in a practical case, in the analysis to a questionnaire carried out in six Schools of the 3rd cycle of Portugal. We start by addressing the experimental design, which can be seen as part of the scientific process. We will also discuss the importance of Advanced Experimental Design techniques, the use of Blocks in order to reduce the variability that is introduced by the treatments, and explore some of the methodologies and their computational components. Following the development of the dissertation, an essentially theoretical approach to the BIBD is highlighted, and definitions and questions about the existence of the BIBD are presented, evidencing a first approach to the various BIBD models. We will also focus on Statistical Analysis of BIBD, the Anova on BIBD, construction of Anova table and intrablock and interblock analysis for BIBDs. We will also review the methods of construction of the BIBD, presenting some practical examples of its construction and algorithms; as well as the importance of using the R software. For the analysis of the data of our questionnaire, software R, version 2.12.2 was used. Finally, we will study a practical application of the BIBD in the Education Area. In this practical example, we will try to measure the level of preparation of the students at the end of the cycle (9th year of schooling) in the Mathematics discipline, within the Curricular Goals of the 3rd Cycle End. We found that there were significant differences between some of the domains tested, for example between Numbers and Calculus and Geometry domains at the significance level.
This work presents the results of the study and of the research of the Balanced Incomplete Block Designs (BIBD) and also Balanced Incomplete Block Designs with Repetition (BIBDR), being applied in a practical case, in the analysis to a questionnaire carried out in six Schools of the 3rd cycle of Portugal. We start by addressing the experimental design, which can be seen as part of the scientific process. We will also discuss the importance of Advanced Experimental Design techniques, the use of Blocks in order to reduce the variability that is introduced by the treatments, and explore some of the methodologies and their computational components. Following the development of the dissertation, an essentially theoretical approach to the BIBD is highlighted, and definitions and questions about the existence of the BIBD are presented, evidencing a first approach to the various BIBD models. We will also focus on Statistical Analysis of BIBD, the Anova on BIBD, construction of Anova table and intrablock and interblock analysis for BIBDs. We will also review the methods of construction of the BIBD, presenting some practical examples of its construction and algorithms; as well as the importance of using the R software. For the analysis of the data of our questionnaire, software R, version 2.12.2 was used. Finally, we will study a practical application of the BIBD in the Education Area. In this practical example, we will try to measure the level of preparation of the students at the end of the cycle (9th year of schooling) in the Mathematics discipline, within the Curricular Goals of the 3rd Cycle End. We found that there were significant differences between some of the domains tested, for example between Numbers and Calculus and Geometry domains at the significance level.
Description
Keywords
Estatística Análise estatística BIBD Delineamento experimental Experimental design Software R ANOVA
Citation
Martins, José Eduardo Lima e Veiga Ferraz - Planos em blocos incompletos equilibrados e aplicações na educação [Em linha]. [S.l.]: [s.n.], 2017. 172 p.