Estruturas e esperanças de quadrados médios para modelos não aditivos em delineamentos experimentais

Abstract

This work was developed to discuss and present a methodology of construction of linear models and obtain medium squares of quadratic forms in general. These quadratic forms are directed here to the medium squares related with the analysis of variance of results obtained in analysis of experimental designs. The proposal oft he methodology presented by the authors started in the 1950s. It was presented more recently and was given a fundamental approach, standing out the importance of the methodology which does not depend upon any initial presuppositions on the model in issue for the warrant of analysis of variance. The present work seeks to discuss and relate the others presented up to now, above all, by presenting examples of application linked to the most utilized experimental designs. Here the definition of the population structure leads to the definition of the model and to the construction of components which may be transformed into the sources of linear models in analysis of variance. At last, the work presents an algorithm for construction of these analyses and obtaining of the respective médiumsquare expectations. Themethodologyis presented also in the form of matrices, the demonstration of orthogonality of components as well as the other procedures being presented through Kronecker's products among matrices.