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Stochastically Independent Components in the Analysis of Variance
Author(s) -
Drwięga T.
Publication year - 1982
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710240202
Subject(s) - lack of fit sum of squares , explained sum of squares , mathematics , residual sum of squares , rank (graph theory) , generalized least squares , total sum of squares , least squares function approximation , non linear least squares , parametric statistics , total least squares , linear model , variance (accounting) , ordinary least squares , statistics , combinatorics , regression analysis , accounting , estimator , business
In this paper an analysis of a sum of squares for linear hypothesis in a fixed linear model is presented. The analysis is based on a partition of sum of squares into independent components. These components are treated as sums of squares for hypotheses implied by an overall one. In the special case components of a sum of squares are distributed with one degree of freedom each and hypotheses concern single parametric functions. In the model not of full rank the form of a sum of squares is transformed before partitioning. The case of the model for cross classification is considered in details. Next the cases of the model of full rank and the one with restrictions on parameters are discussed. The model for balanced design with unweighted restrictions on parameters is considered in details. In this case sume of squares for orthogonal contrasts are obtained from analysis of the sum of squares for hypothesis concerning main or interaction effects.