Similarity of rectangles: An analysis of subjective dimensions

Two defining properties of psychological dimensions (intradimensional subtractivity and interdimensional additivity) are introduced and their consequences, formulated in terms of an ordinal dissimilarity scale, are derived. These consequences are investigated using dissimilarity judgments between rectangles to determine which of two alternative dimensional structures area (A) and shape (S), or width (W) and height (H), satisfies additivity and/or subtractivity. The results show that neither dimensional structure is acceptable, although A × S provides a better account for the data of most Ss than does W × H. Tests of relative straightness show that A is the least “curved” of the four attributes. Methodological and substantive implications of the study are discussed.