If one correlates a total score of a multidimensional measure with a criterion, one builds two sources of uncertainty into one's test. One source of uncertainty is that, with a single score, one cannot know the nature of the different dimensions' contribution to that score. Conceivably, an overall correlation could reflect the same magnitude of relation between each dimension and the criterion, but that may well not be true. It is more likely that such a correlation reflects a kind of average of strong and weak relationships between different dimensions and the criterion (Smith, Fischer, & Fister, 2003; Smith & McCarthy, 1995). One cannot know the meaning of a single score representing a multidimensional measure (Borsboom et al., 2004; McGrath, 2005).
