Abstract
It is suggested that bounded response scales may induce nonlinearities in psychophysical functions. This point is illustrated with an example of MDS, in which the intuitively plausible rationale of the city-block metric, which is based on ordinary addition of line segments, may conflict with the boundedness of the dissimilarity scale provided by the experimenter. On replacing ordinary addition with the addition rule for hyperbolic tangents, a metric intermediate between the city-block and the sup metrics is obtained that preserves the upper bound. In the one-dimensional case, it predicts overestimation for halving, underestimation for doubling, and an upward shift of the midpoint for middling.
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Schönemann, P.H. A metric for bounded response scales. Bull. Psychon. Soc. 19, 317–319 (1982). https://doi.org/10.3758/BF03330269
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DOI: https://doi.org/10.3758/BF03330269