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Análise fatorial exploratória e análise de componentes principais aplicadas a um questionário para avaliação da qualidade escolar
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Abstract(s)
Neste trabalho apresenta-se uma aplicação de técnicas de Estatística Multivariada. Comparam-se os resultados de duas técnicas, a Análise de Componentes Principais (ACP) e a Análise de Componentes Principais para Dados Categóricos (CATPCA), utilizando para tal dois conjuntos de dados de respostas a dois questionários. Pretende-se verificar se a violação de alguns pressupostos da ACP relativamente ao tipo de escala da variável e à forma dos dados (simétrica ou não simétrica) influencia a qualidade e o número das componentes extraídas e se difere significativamente da solução da CATPCA. Para esta análise comparativa são utilizados dados recolhidos através de dois questionários de autoavaliação interna de uma escola secundária do interior do distrito de Coimbra. Um dos questionários foi administrado a uma amostra de 161 alunos do 10º ao 12ºanos, e o outro foi aplicado a uma amostra de 97 encarregados de educação, sendo assim representados dois tamanhos amostrais.
Os itens de cada questionário estão agrupados em 6 ou 8 grupos respetivamente, no caso do questionário dos alunos e no questionário dos encarregados de educação. Usando a técnica de estatística multivariada Análise Fatorial Exploratória (AFE) exploram-se os fatores subjacentes à estrutura dos questionários e verifica-se se estes refletem os que tinham sido definidos previamente pela equipa da avaliação escolar.
Apresenta-se ainda uma caracterização teórica das 3 técnicas de estatística multivariada aplicadas neste trabalho e, finalmente, procura-se dar um contributo para a melhoria do instrumento utilizado na avaliação da qualidade escolar.
In this work, is presented an application of exploratory multivariate statistical techniques. It has been designed to compare the results of two techniques, the Principal Component Analysis (PCA) and Principal Component Analysis for Categorical variables. The two techniques are compared through two sets of data taken from an application of two questionnaires. The purpose of this comparison is to verify whether the violation of some assumptions of the PCA, related with the type of variables, the form of the data distribution (symmetric or nonsymmetrical), influences significantly the solution obtained, the quality and the quantity of the extracted components. To carry out the comparative analysis, the data used was collected through two auto-administered questionnaires of internal self-assessment of a secondary school in the district of Coimbra. One of the questionnaires was administered to a sample of 161 students from 10th to 12th grade, and the other survey was applied to a sample of 97 educational responsible. The items of the student’s questionnaire are theoretically grouped into 6 groups while the items of the parent’s questionnaire are grouped into 8 groups. This theoretical structure was explored using the multivariate technique Exploratory Factor Analysis (EFA), in order to determine how this structure is reflected in the data collected. It also presents a more developed theoretical characterization of three multivariate statistical techniques applied in this study and, finally, some suggestions are made to contribute to improving the tool used in the evaluation of the quality of school services.
In this work, is presented an application of exploratory multivariate statistical techniques. It has been designed to compare the results of two techniques, the Principal Component Analysis (PCA) and Principal Component Analysis for Categorical variables. The two techniques are compared through two sets of data taken from an application of two questionnaires. The purpose of this comparison is to verify whether the violation of some assumptions of the PCA, related with the type of variables, the form of the data distribution (symmetric or nonsymmetrical), influences significantly the solution obtained, the quality and the quantity of the extracted components. To carry out the comparative analysis, the data used was collected through two auto-administered questionnaires of internal self-assessment of a secondary school in the district of Coimbra. One of the questionnaires was administered to a sample of 161 students from 10th to 12th grade, and the other survey was applied to a sample of 97 educational responsible. The items of the student’s questionnaire are theoretically grouped into 6 groups while the items of the parent’s questionnaire are grouped into 8 groups. This theoretical structure was explored using the multivariate technique Exploratory Factor Analysis (EFA), in order to determine how this structure is reflected in the data collected. It also presents a more developed theoretical characterization of three multivariate statistical techniques applied in this study and, finally, some suggestions are made to contribute to improving the tool used in the evaluation of the quality of school services.
Description
Dissertação de Mestrado em Estatística, Matemática e Computação apresentada à Universidade Aberta
Keywords
Estatística Métodos estatísticos Questionários Principal Components Analysis for Categorical Data Principal component analysis Comparison Exploratory factor analysis Quality of school services
Pedagogical Context
Citation
Costa, Anabela da Silva Jorge da - Análise fatorial exploratória e análise de componentes principais aplicadas a um questionário para avaliação da qualidade escolar [Em linha]. Lisboa : [s.n.], 2012. [112] p.