Peter H. Schonemann, Tim Dorcey, and K. Kienapple
Subadditive concatenation in dissimilarity judgements
Perception & Psychophysics, 1985, 38, 1-17.
Empirical results are presented that point towards consistent violations of intradimensional ("segmental") additivity in dissimilarity judgments about rectangles. These results contradict all Minkowski power metrics, and support a recently introduced "metric for bounded response scales" (MBR) that predicts intra- and interdimensional subadditivity.
We found strong indications of systematic individual differences. We, therefore, analyzed the individual dissimilarity judgements for four groups separately, first at the within-subjects level, and later at the group average level. The stability with which our results replicated accross the independent groups served as a consistency and robustneess check.
Since numerous metrics other than the MBR might account for segmental subadditivity, we compared the fit of four versions of the MBR, the three major Minkowski metrics, and two alternative segmentally subadditive metrics. The city-block metric uniformly gave the worst fit. We obtained the best fit for an MBR that reduces the upper bound by about one-fifth of the response scale range. No significant improvement was obtained by permitting the upper bound to vary from subject to subject.
Although the orientation question (whether subjects employed a height/width or an area/shape system) could not be solved conclusively, it appeared that the largest group used height and width, wheras the second largest group uses shape predominantly.