Peter H. Schonemann and Alejandro Lazarte
Psychophysical maps for subadditive dissimilarity ratings
Perception and Psychophysics, 1987, 42, 342-354
Earlier findings on pairwise dissimilarity ratings of "flat" rectangles (Schonemann, Dorcey, & Kienapple, 1985) were replicated with a larger stimulus set, which included squares and "tall " rectangles. The data were again strongly subadditive and indicated systematic individual differences in judgements strategies.
A metric for bounded response scales (MBR) with slightly reduced upper bound gave the best fit among several negatively accelerated response functions that might account for the subadditivity.
Simple four-parameter psychophysical maps of the general form d = 9tanh [Sum akxk], k = 1,4 (where the xk are simple functions of physical height and width and the ak parameters are of the order .2) reproduced the 120 average ratings within each strategy group with squared etas in the high 90s.
These results suggest that subjects use simple composition rules for rating dissimilarities of rectangles. The judgements can be explained without appeal to any global internal spatial representation of the stimuli, solely in terms of the pairwise rating task.
(In an Appendix, the MBR is generalized to m > 2 dimensions).