SOME RESULTS RELATING TO THE CHOICE OF AN EXPERIMENTAL UNIT IN MULTlVARIATE RESEARCH

Several analytic expressions are presented and discussed interms of differences which are to be expected between results obtained from applying the same multivariate analysis to data based on different experimental units. The 2 units considered are the individual observation and the group as a unit, i.e., some function, typically the mean, of the individual observations with in a group. It is demonstrated that certain statistical properties of the class of design matrices where this choice of units arises lead to substantial differences in the results and interpretations of multivariate analyses. This development provides a partial mathematical account for such observed differences as are frequently encountered in practice.