Points or vectors? A comment on Irwin et al . ‘Risk perception and victim perception: the judgment of HIV cases’

Recently Irwin et al . (1996) employed the method of three‐way multidimensional scaling as part of an investigation into respondents' representations of perceptions of various scenarios relating to the Human Immunodeficiency Virus (HIV). While the reported analyses revealed a number of interesting insights into the collective cognitive structure of the respondents, as captured by the ‘group space’ stimulus configuration associated with the three‐way MDS analysis, it is argued that the authors' treatment of the accompanying source weights, in an attempt to shed light on the nature and sources of variation in individuals' perceptions, was inappropriate and may have led to some erroneous conclusions. This stems from the fact that the source weights associated with matrix unconditional analyses, of the form adopted by Irwin et al ., are vectors whose lengths vary approximately in proportion to the variance accounted for in the ‘private’ cognitions of a given source by the group space, rather than points in a multidimensional Euclidean space. As such, it is the relative directionality of these vectors, rather than the absolute magnitude of the raw source weights per se , that is useful for exploring differential cognition. Furthermore, it is argued that tests of statistical significance associated with secondary analyses of source weights are not valid, except for descriptive purposes, due to the fact that these weights are not independent of the group space configuration from which they have been derived. © 1998 John Wiley & Sons, Ltd.