Least squares solutions for non-orthogonal two-way classifications Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6108vf282

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  • One answer to the problem of missing observations in two-way classification experiments is to insert estimates of missing observations into deficient cells. Once missing observations have been estimated, the experimenter may proceed with his analysis using the familiar normal equations which apply to complete data. This paper discusses generally the problem of obtaining the desired estimates and provides explicit solutions in certain special cases, among them the case where there appears no more than a single deficient cell in any row and column, the case where deficient cells occur in a block at the intersections of certain rows and columns, and a comprehensive generalization to an arbitrary number of blocks having no rows or columns in common. Also presented is an iterative process providing approximate solutions to the normal equations of a two-way classification, which is especially useful in dealing with a large layout having a majority of cells empty.
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