| Abstract: | This dissertation is concerned with deveoloping a unified canonical analysis of singular data arising form the inclusion of linear combinations of variables already considered. The analysis is based on existing methods of analysis of non-singular data. Test statistics for testing the goodness of fit of hypothetical discriminant functions in the case of two or more groups and q + 1 factors are the same in the case of singular data as those of non-singular data with generalized inverses of singular matrices replacing the natural inverses. A method of calculating the canonical correlations and canonical variables is developed which is parallel to that of non-singular methods with only generalized inverses used instead of natural inverses when a singular matrix is encountered. A test statistic for testing equality of mean vectors in MANOVA is developed and shown appropriate. |
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