Multivariate Designs - Sum Scores versus MANOVA
Even experienced users of ANOVA and MANOVA techniques are often puzzled by the differences in results that sometimes occur when performing a MANOVA on, for example, three variables as compared to a univariate ANOVA on the sum of the three variables. The logic underlying the summing of variables is that each variable contains some "true" value of the variable in question, as well as some random measurement error. Therefore, by summing up variables, the measurement error will sum to approximately 0 across all measurements, and the sum score will become more and more reliable (increasingly equal to the sum of true scores). In fact, under these circumstances, ANOVA on sums is appropriate and represents a very sensitive (powerful) method.
However, if the dependent variable is truly multi-dimensional in nature, then summing is inappropriate. For example, suppose that my dependent measure consists of four indicators of success in society, and each indicator represents a completely independent way in which a person could "make it" in life (e.g., successful professional, successful entrepreneur, successful homemaker, etc.). Now, summing up the scores on those variables would be like adding apples to oranges, and the resulting sum score will not be a reliable indicator of a single underlying dimension. Thus, one should treat such data as multivariate indicators of success in a MANOVA.