The dominance axiom states that the dissimilarity
of a pair of stimuli differing on two dimensions
must exceed the dissimilarities of the
corresponding pairs of stimuli that differ on only
one of the dimensions. This axiom is presented as
a test of dissimilarity data to determine if the
dimensions of the perceptual space are perceived
independently, and as a diagnostic tool in assessing
the INDSCAL model’s assumption of independent
dimensions. The general recognition theory of
similarity, which contains both the three-mode and
INDSCAL multidimensional scaling models as special
cases, is used to motivate the test. It is shown
that general recognition theory predicts consistent
violations of the dominance axiom with dependent
dimensions, but not independent dimensions. A
consistent pattern of violations of dominance suggests
that the three-mode model is most appropriate.
When the test of dominance is satisfied, the
INDSCAL model is appropriate for the data. A
simulation study was conducted to examine the
pattern of violations of the dominance axiom
when varying degrees of perceptual dependence
exist. An examination of dissimilarity data from
a study of the size-weight illusion revealed the
expected pattern of violations of the dominance
axiom. Index terms: dominance axiom, general
recognition theory, INDSCAL, MDS, perceptual independence,
Perrin, Nancy A & Ashby, F. Gregory. (1991). A test for perceptual independence with dissimilarity data. Applied Psychological Measurement, 15, 79-93. doi:10.1177/014662169101500109
Perrin, Nancy A.; Ashby, F. Gregory.
A test for perceptual independence with dissimilarity data.
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