Using linear algebra this thesis developed linear regression analysis including analysis of variance, covariance analysis, special experimental designs, linear and fertility adjustments, analysis of experiments at different places and times. The determination of the orthogonal projection, yielding efficient unbiased estimates and playing a dominant role in statistical tests, was extensively considered, in particular by iterative time-saving procedures based on geometrical considerations and on power-series expansions. Subspaces were systematically introduced for levels, for main effects and for interactions. This allowed a general interpretation of orthogonality of classifications. This introduction of subspaces also permitted the simultaneous account of orthogonal polynomia in one or more variables with concurrent classifications. Designs such as balanced and partially balanced incomplete block designs, as lattices and as Latin squares could be characterized by fixed angles between spaces or between physically meaningful subspaces of these effect spaces. The missing-plot technique was developed in a more general and simple form. Finally, estimation and testing problems were discussed for several non-orthogonal classifications, of which one or more had random effects or interactions. This included recovery of inter-block information, and analysis of split- plot designs and series of experiments.<p/>
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