Problems of interpretation in multivariate analysis of variance

Abstract

This dissertation is concerned with developing objective criteria to eliminate "unimportant" variables to aid in the interpretation of significant results in the multivariate analysis of variance. Chapter I discusses the problem in terms of the structures of the error and hypothesis matrices and gives a review of the pertinent literature. The MANOVA matrices are displayed in terms of inner product spaces. Basis vectors, linear transformations and successive orthogonalization are discussed in terms of these matrices and the invariance of statistical hypothesis in Chapter II. Chapter III discusses the effective dimensionality of the error and hypothesis spaces and proposes a variable elimination procedure based on properties developed in Chapter II. Six different variable elimination procedures are tested on artificial data sets with known variance-covariance structures in Chapter IV. The criteria judged "best" are used with "live" data examples in Chapter V. Chapter VI contains the summary and conclusions of the study along with recommendations for further research in this area.