Factorization of the residual operator and canonical decomposition of nonorthogonal factors in the analysis of variance

SUMMARY A factorization is given of the residual operator for nonorthogonal analysis of variance. It is interpreted geometrically in terms of the critical angles between the subspaces determined by the factors. The factorization determines a recursive procedure for analysis as described by Wilkinson (1970). Canonical components are defined and a method of computing them is given together with formulae for their variances, since these would be required for combining information, as for instance, in the recovery of interblock information.