Contributions to the planning and analysis of factorial designs

The thesis is structured in five articles. In the first article, two methods are compared to analyze the significance of the effects: the Lenth method and the one based on the estimation of the variance of the effects from interactions that can be considered negligible from scratch. For the most com...

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Detalles Bibliográficos
Autor: Xampeny Solaní, Rafael
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:CBUC, CESCA
Repositorio:TDR. Tesis Doctorales en Red
OAI Identifier:oai:www.tdx.cat:10803/620638
Acceso en línea:http://hdl.handle.net/10803/620638
https://dx.doi.org/10.5821/dissertation-2117-121006
Access Level:acceso abierto
Palabra clave:Àrees temàtiques de la UPC::Matemàtiques i estadística
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Descripción
Sumario:The thesis is structured in five articles. In the first article, two methods are compared to analyze the significance of the effects: the Lenth method and the one based on the estimation of the variance of the effects from interactions that can be considered negligible from scratch. For the most common factorial designs and in a set of scenarios that seek to reflect the situations that the experimenter can find in practice, simulation techniques are used to identify the errors that are committed with each method. Based on the analysis of the results obtained, we recommend in which situations it is more appropriate to use one method or the other. The second article analyzes the problem of estimating the results of experiments that could not be performed based on the expression of the interactions that can be considered negligible. The variance of the estimated values depends on what these values are and also on the interactions considered negligible. All possible encountered situations are analyzed and tables are presented with the values that can be estimated with minimum variance depending on the type of design and the contrasts available to perform the estimates. The third article deals with the same problem as the second but analyzing the impact of the estimate not on the variance of the estimated response values but on the variance of the effects and also on the correlations among them. The analysis of all the situations that can be given in the most common designs, allows us to make recommendations about what experiments should be skipped in the case that, due to time or budgetary constraints, all runs indicated by the factorial design cannot be executed.