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

Abstract

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 Immunode®ciency 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 con®guration 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 dierential cognition. Furthermore, it is argued that tests of statistical signi®cance 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 con®guration from which they have been derived.

Strategic consensus mapping: A new method for testing and visualizing strategic consensus within and between teams

“…Therefore, the use of the permutation test as a nonparametric method of hypothesis testing is more appropriate given our method. Moreover, Hodgkinson () warns against the conditional dependency problem of observations associated with significance tests of MDS‐related outputs and distances derived from proximities. However, because in our analyses the α and r statistics are derived from pairs of VMU solutions rather than from MDS, conditional dependency is not an issue.…”