Ratio and subtractive processes in psychophysical judgment.

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Abstract
Discusses a basis for distinguishing between subtractive and ratio models of perceptual judgment. Illustrations demonstrate the inadequacy of direct scaling methods and the advantages of applying algebraic models and factorial designs. Scales obtained using difference and ratio instructions were linearly related only when both of the resulting data matrices were fit to the same model—either subtractive or ratio. Exp I found the same ratio-difference indeterminacy for another stimulus dimension—grayness. This indeterminacy was also replicated for both category ratings of differences and magnitude estimations of differences. The raw data appeared to more closely approximate the predictions of a ratio model when magnitude estimations were used and a subtractive model when category ratings were used. The appropriateness of the subtractive model was demonstrated by using a new task in which judges estimated the ratio of differences. Data conform to the qualitative predictions of the ratio-of-differences model and allow rejection of the ratio-of-ratios, difference-of-differences, and difference-of-ratios models. Scales derived from the ratio-of-differences model agreed with those derived from the fit of the subtractive model to data obtained from difference and ratio tasks, suggesting that experimental observers estimate intervals when instructed to judge either differences or simple ratios. Data also imply that magnitude estimations induce a nonlinear response transformation that can make subtractive processes appear multiplicative. (35 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)

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