Reason to avoid triangular designs in nonmetric scaling.

Triangular designs analyzed by contemporary nonmetric scaling procedures can yield estimated scales that are nonlinearly related to the "true" scale values. In nonmetric unidimensional scaling, observers rate the "difference," "similarity," or "dissimilarity" of stimulus pairs, and a subtractive model is used to estimate scale values that will reproduce the rank order of the judgments. For example, subjects could be asked to listen to two tones and judge the "dissimilarity" in loudness. If the subjects report that the "dissimilarity" of A to B exceeds the "dissimilarity" of C to D, then the absolute difference in scale values between A and B is assumed to exceed the difference in sensation between C and D.